math problem and solution grade 6

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Grade 6 Math Worksheets

Related Pages Math Worksheets according to Topics Math Worksheets according to Grades Interactive Zone Grade 6 Math Lessons

These free interactive math worksheets are suitable for Sixth Grade and Grade 6. Use them to practice and improve your mathematical skills.

Multiplication Worksheets

Multiply 2-digit by 1-digit Multiply 3-digit by 1-digit Multiply 2-digit by 2-digit Multiply 3-digit by 2-digit Multiply 3-digit by 3-digit Multiply 4-digit by 3-digit

Division Worksheets

Divide 2-digit by 1-digit Divide 3-digit by 1-digit Divide 2-digit by 2-digit Divide 3-digit by 2-digit Divide 3-digit by 3-digit Divide 4-digit by 3-digit

Order of Operations Worksheets (PEMDAS, BEDMAS)

Order of Operations (+, –) Order of Operations (parenthesis, +, –) Order of Operations (×, ÷ ) Order of Operations (parenthesis, ×, ÷) Order of Operations (×, ÷, +, –) Order of Operations (parenthesis, ×, ÷, +, –) Order of Operations (parenthesis, ×, ÷, +, –) Order of Operations (parenthesis, exponent, ×, ÷ +, –) Order of Operations (mixed) Order of Operations (mixed) Order of Operations (mixed)

Decimal Worksheets

Multiply Decimals by 10, 100, 1000 Multiply Decimals by Powers of 10 Multiply Decimals by Whole Numbers Multiply Decimals by Decimals

Divide Decimals by 10, 100, 1000 Divide Decimals by Powers of 10 (eg. 74.2 ÷ 10 3 ) Divide Whole Numbers to give Decimal Quotients Divide Decimals by Whole Numbers (without rounding) Divide Decimals by Whole Numbers (with rounding) Divide Decimals by Decimals (with or without rounding)

Multiply Decimals by Tens (10s, 100s, 1000s) Multiply Decimals by Whole Number (1-digit) Multiply Decimals by Whole Number (Multi-digit) Multiply two Decimals (Tenths) Multiply Two Decimals (Hundredths) Multiply two Decimals (Thousandths) Divide Decimals by Ten (10s, 100s, 1000s) Division with Decimal Quotients (Tenths) Division with Decimal Quotients (Hundredths) Divide Decimals Decimal Word Problems (One-Step, Addition & Subtraction) Decimal Word Problems (Two-Step, Addition & Subtraction) Decimal Word Problems (Mixed Operations) Decimal Word Problems (Mixed Operations)

Integer Worksheets

Add Integers 2 operands Add Integers 3 operands or more Subtract Integers 2 operands Subtract Integers 3 or more operands Multiply Integers Divide Integers Add Integers 1 Digit Add Integers 2 Digits Subtract Integers 1 Digit Subtract Integers 2 Digits Multiply Integers 1 Digit Multiply Integers 2 Digits Divide Integers 1 Digit in Divisor Divide Integers 2 Digits in Divisor Integers Mixed Operations Specify your own conditions for Integer Operations Add, Subtract, Multiply, Divide, Mixed

Integers, Less & More (one less, one more) Compare Integers (use <, >, = ) Ordering Integers (increasing or decreasing order)

Adding Integers Subtracting Integers Multiplying Integers Dividing Integers Order of Operations with Integers

Exponent Worksheets

Squares with base 0-10 Squares with base 2-20 Cubes with base 0-10 Cubes with base 2-20 Evaluate Exponents Evaluate Exponents

Squares & Cubes (whole number, fraction & decimal bases) Squares & square roots Cubes & cube roots

Whole number exponents Negative whole number exponents Unit fraction exponents (positive or negative) Fractional exponents (positive or negative)

Time Worksheets

Time Conversion (weeks, days, hours, minutes, seconds) Adding and Subtracting Time Multiplying and Dividing Time Time Word Problems (Elapsed Time) Convert from 12-hr System to 24-hr System Convert from 24-hr System to 12-hr System Calculate Time Intervals in 12-hr System and 24-hr System

Fraction Worksheets

Divide Fractions by Whole Numbers Divide Whole Numbers by Fractions Divide Fractions by Fractions Divide Mixed Numbers

Add & Subtract Fractions (with common denominator & simplifying answers) Least Common Multiple or Least Common Denominator Add & Subtract Fractions (with unlike denominators & step-by-step guide) Add & Subtract Fractions (with unlike denominators) Add Fractions (mixed) Subtract Fractions (mixed)

Multiply Fractions by Whole Numbers Multiply Two Fractions Divide Whole Numbers by Fractions Divide Fractions by Whole Numbers Divide Fractions by Fractions Divide Two Fractions

Add Mixed Numbers Subtract Mixed Numbers Multiply Mixed Numbers Divide Mixed Numbers Add Mixed Numbers Subtract Mixed Numbers Multiply Mixed Numbers Divide Mixed Numbers

Fraction Word Problems Add & Subtract Fractions Fraction Word Problems Add & Subtract Mixed Numbers (One-Step) Fraction Word Problems Add & Subtract Mixed Numbers (Two-Step) Fraction Word Problems Add & Subtract Mixed Numbers (Two-Step)

Algebra Worksheets

Evaluate Expressions by Substitution Simplify Expressions by Combining Like Terms Simplify Expressions using Distributive Property Simplify Expressions using Distributive Property & Combine Like Terms

Solve One-Step Equations Solve Two-Step Equations Solve Equations by Combining Like Terms Solve Equations with the Variable on Both Sides Solve Equations by Distributive Property Solve Multi-Step Equations Solve Multi-Step Equations Solve Word Problems using Algebra

Coordinate Worksheets

Slope of a Line Slope and Intercept of a Line Midpoint Formula 1 Midpoint Formula 2 Distance Formula 1 Distance Formula 2 Activity to explore Slope and Intercept of a Line

Geometry Worksheets

Names of Polygons Give the number of sides Names of Polygons Give the names of polygons Types of Angles (Acute, Obtuse, Reflex) Angles in a Straight Line Angles at a Point Complementary Angles Supplementary Angles

Area and Perimeter of Rectangles Area and Perimeter of Rectangles Area and Perimeter of Rectangles Area and Perimeter of Parallelogram Area of Triangle Area of Parallelograms Area of Triangle and Parallelogram Area of Trapezoid Area of Shapes Area of Shaded Region (rectangles and triangles)

Circumference of Circle Area of Circle Area & Circumference of Circle Circle Problems: Radius, Diameter, Circumference, Area Circle Word Problems I Circle Word Problems II Area of shaded regions that include circles Area of figures that include circles

Surface Area Worksheets Surface Area of Cylinder Surface Area of Sphere Surface Area of Solids I Surface Area of Solids II Surface Area of Solids III Surface Area of Solids IV Surface Area of Solids V Surface Area of Cylinders & Pipes Surface Area of Cylinders & Spheres

Volume of Cylinders Volume of Sphere Volume of Prisms & Pyramids Volume of Square Pyramids Volume of Cones

Surface Area & Volume of Cubes Surface Area & Volume of Rectangular Prisms or Cuboids Surface Area & Volume of Cube Surface Area & Volume of Rectangular Prisms or Cuboids Volume & Surface Area of Cylinder Volume & Surface Area of Sphere

Ratio Worksheets

Ratio of Quantities Ratio Word Problems I Ratio Word Problems II Ratio Word Problems III Ratio Word Problems IV Ratio with Algebra

Percent Worksheets

Percents to Decimals and Fractions Percents to Fractions in Lowest Terms Percents to Fractions Fractions to Percents Fractions to Percents Decimals to Percents Percentages (What is X% of Y) Percentages (X is what % of Y) Percentages (X is Y% of what) Percent of a Number Finding Percent Finding the Base

Convert Decimals to Fractions Convert Decimals to Mixed Numbers Convert Repeating Decimals to Fractions

Convert Fractions to Decimals (denominator 10, 100, or 1000) Convert Mixed Numbers to Decimals (denominator 10, 100, or 1000)

Convert Fractions to Decimals (use equivalent fractions) Convert Fractions to Decimals (use long division) Convert Fractions to Repeating Decimals (recurring decimals)

Decimals to Percents Percents to Decimals Fractions to Percents Percents to Fractions

Percentage of a Number or Part (30% of 60 = ___ ) Find the Base or Total (20% of ___ = 18) Find the Percent or Rate (___% of 50 = 25)

Increase a Number by a Percentage Decrease a Number by a Percentage

Percentage Increase Worksheet Percentage Decrease Worksheet

Statistics Worksheets

Mode Median Mean Range Mean, Median & Mode Mean, Median & Mode Find the possible values for the Median Given the Mean, find the missing number(s) in a set Word problems that involve the Mean Word problems that involve the Mean

Probability Worksheets

Probability Problems Complementary Probability Probability Word Problems Probability & Geometry Mutually Exclusive Probability Independent Events Probability Dependent Events Probability

Divide (2-digit divisors), Divide (3-digit divisors), Order of Operations (PEMDAS)

Division with Decimal Quotients, Multiply Two Decimals, Divide Two Decimals, Decimals and Fractions, Decimal Word Problems

Add Integers, Subtract Integers, Multiply Integers, Divide Integers

Squares, Cubes, Evaluate Exponents

Convert Time, Add and Subtract Time, Multiply and Divide Time, 12-hr and 24-hr System, Elapsed Time, Time Word Problems

Add Fractions, Subtract Fractions, Multiply Fractions, Divide Fractions, Add Mixed Numbers, Subtract Mixed Numbers, Multiply Mixed Numbers, Divide Mixed Numbers, Fraction Word Problems

Add and Subtract Like Terms, Distributive Property, Solve One-Step Algebra Equations, Solve Two-Step Algebra Equations, Solve Equations involving Like Terms

Slope and Intercept of a Line, Distance between Two Points, Midpoint of Two Points

Types of Angles, Number of sides of Polygons, Names of Polygons, Perimeter and Area (Rectangles), Perimeter and Area (Triangles), Perimeter and Area (Parallelogram), Perimeter and Area (Trapezoids), Circumference and Area (Circles), Volume of Cubes, Volume of Rectangular Prisms, Volume of Spheres, Volume of Cylinders, Volume of Square Pyramids, Surface Area of Cubes, Surface Area of Rectangular Prisms, Surface Area of Spheres, Surface Area of Cylinders, Surface Area of Square Pyramids

Ratio, Proportion, Percent

Mean, Median, Mode, Range, Statistics Word Problems

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Expressions and Equations 6th Grade

Welcome to our Expressions and Equations 6th Grade Worksheets.

Here you will find a range of algebra worksheets to help you learn about basic algebra, including generating and calculating algebraic expressions and solving simple equations.

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Expressions and Equations Support

Generate the expression worksheets, calculate the expression worksheets.

• Simplify Expressions Worksheets
• Solve the Equations Worksheets
• Expressions and Equations Mixed Worksheets
• More recommended resources
• Expressions and Equations 6th Grade Online Quiz

Want to gain a basic understanding of algebra?

Looking for some simple algebra worksheets?

Do you need a bank of useful algebra resources?

Look no further! The pages you need are below!

Here is our selection of basic algebra sheets to try.

We have split the worksheets up into 3 different sections:

• Generate the algebra - and write your own algebraic expressions;
• Calculate the algebra - work out the value of different expressions;
• Solve the algebra - find the value of the term in the equation.
• Mixed questions involving all 3 of the above.

By splitting the algebra up into sections, you only need to concentrate on one aspect at a time!

Each question sheet comes with its own separate answer sheet.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

What is an algebraic expression?

An expression is a mathematical statement where variables and operations are combined.

• 2a + 5 is an expression involving the variable a
• 5(y 2 - 6) is another expression

What is an algebraic equation?

An equation is where an algebraic expression is equal to something, which might be a number, or another algebraic expression.

• 2a + 5 = 7 is an equation
• 5(y 2 - 6) = 3y + 8 is another equation

How to Generate an Expression

When we are generating an expression, we are taking a rule and turning it into algebra.

• Subtract 6 from n could be written as n - 6.
• Multiply d by 4 could be written as d x 4 or 4d.
• Add 5 to p and then double the result is written as (p + 5) x 2 or 2(p + 5)

How to Calculate an Expression

When we are calculating the value of an expression, we work out the value of the expression when we give a value to the variable.

• p + 5 has a value of 11 when p = 6 because 6 + 5 = 11
• 4 - q has a value of 1 ½ when q = 2 ½ because 4 - 2 ½ = 1 ½
• 4(n - 2) has a value of 32 when n = 10 because 4 x (10 - 2) = 4 x 8 = 32
• 4(n - 2) has a value of -8 when n = 0 because 4 x (0 - 2) = 4 x (-2) = -8

How to Solve a Simple Equation

When we are solving an equation, we are finding out the value(s) of the variable in the equation.

• then p = 4 because 4 + 5 = 9
• Answer: p = 4
• then n = 56 ÷ 7 = 8
• Answer: n = 8
• means that f = 4 because 12 - 4 = 8
• Answer: f = 4
• then t = 5 because 0.6 x 5 = 3
• Answer: t = 5
• then r = 32 because ½ x 32 = 16
• Answer: r = 32

Expressions and Equations 6th Grade Worksheets

• Generate the Expressions Sheet 6:1
• PDF version
• Generate the Expressions Sheet 6:2
• Calculate the Expression Sheet 6:1
• Calculate the Expression Sheet 6:2

Calculate the Expressions Walkthrough Video

This short video walkthrough shows several problems from our Calculate the Expression Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Simplifying Expressions Worksheets

• Simplifying Expressions Sheet 6:1
• Simplifying Expressions Sheet 6:2

Simplifying Expressions Walkthrough Video

This short video walkthrough shows several problems from our Simplifying Expressions Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

Solve the Equation Worksheets

• Solving Equations Sheet 6:1
• Solving Equations Sheet 6:2

Expressions and Equations 6th Grade Mixed Worksheets

These questions involve solving equations, working out the value of expressions and also generating expressions.

They are a combination of questions from all the above categories.

• Expressions and Equations Mixed Questions Sheet 6:1
• Expressions and Equations Mixed Questions Sheet 6:2

Expressions and Equations Walkthrough Video

This short video walkthrough shows several problems from our Expressions and Equations Mixed Questions Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Inequalities Worksheets

• Inequalities on a Number Line
• Writing Inequalities from Word Problems
• 6th Grade Distributive Property Worksheets

The sheets on this page have been designed to factorize and expand a range of simple expressions using the distributive property..

• Basic Algebra Worksheets

We have a selection of basic algebra worksheets which are aimed at 6th and 7th graders and involve similar skills to the sheets here.

Input and Output Function Tables

Have a go at these input and output tables.

Test your skills at finding inputs, outputs and rules.

Our easier sheets have rules instead of algebraic functions.

Our harder sheets use algebraic functions.

• Input and Output Tables Worksheets (easier)
• Input and Output Function Tables with Algebraic Functions

Free Algebra Problem Solver

The Mathway Calculator is a great way to solve algebra problems that you can type into a calculator.

Try using this online calculator tool to solve one of your problems and watch it work!

There are a range of calculators to choose from to meet your needs.

The Mathway problem solver will answer your problem instantly and also give you a link to view each of the steps needed.

If you choose to 'View the steps' you will be directed to the Mathway website where you will be able to see in more detail each of the steps needed to solve the problem. Please note that Mathway may charge you a small fee for this!

Factorising Quadratic Equations

Are you stuck on a quadratic equation and don't know what to do?

Are you looking for some worksheets on factorising quadratic equations to print out?

Take a look at our support pages on quadratic equations where you will hopefully find what you are looking for.

• Factorising Quadratic Equations Support page
• Factoring Quadratic Equations worksheets
• Algebra Math Games

If you are looking for a fun printable algebra game to play then try out our algebra game page.

You will find a range of algebra games that make learning algebra fun and non-threatening.

The only equipment you need is a scientific calculator, some dice, and a few counters!

PEMDAS Worksheets

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

Using these worksheets will help your child to:

• know and understand how parentheses works;
• understand how exponents work in simple calculations.
• understand and use PEMDAS to solve a range of problems.
• PEMDAS Problems Worksheets 5th Grade
• 6th Grade Order of Operations

Interactive Equality Explorer

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

Probably the most useful part of the app is to use the 'Solve It' section once you are confident how it works.

You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

• Interactive Equality Explorer by PhET

Expressions and Equations 6th Grade Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

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For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick expressions and equations 6th grade quiz tests your knowledge and skill at generating and calculating expressions, as well as solving equations.

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6th grade (Illustrative Mathematics)

Unit 1: area and surface area, unit 2: introducing ratios, unit 3: unit rates and percentages, unit 4: dividing fractions, unit 5: arithmetic in base ten, unit 6: expressions and equations, unit 7: rational numbers, unit 8: data sets and distribution.

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Common Core - State Standards Initiative

Students are entering a new section of math that consists of algebra, geometry, decimals, and more complicated division problems. When there is not a parent or teacher around, students have access to on-demand videos for their sixth-grade mathematical lessons. Our video tutorials are taught by math teachers who go through the problem solving process.

• The key to learning math is repetition, and our math teachers go through multiple examples. 
• Math teachers show students step-by-step directions on how to solve these more complex problems.
• Students learn money, ratios, decimals, graphing, and other concepts from the 6th grade curriculum.

Algebra Questions and Problems for Grade 6

Grade 6 algebra questions and problems with detailed solutions are presented. Questions on expanding and simplifying expressions, solving linear equations, factoring expressions,....are included.

Questions and Problems

• List all like terms included in each of the expressions given below. A) 6 x + 5 + 12 x - 6 B) 2 x 2 - 4 + 9 x 2 + 9 C) x / 5 + x / 7 + 7 D) 0.2 x + 1.2 x + x / 2 + 5 E) 5 x - 8 + 7 x - 2 x 2 - 4 + 9 x 2 + 4 x 3 F) 5 a + 8 - 7 a b G) 5 a b+ 8 + 6 b a - a + 3 b Solution
• Evaluate each of the expressions for the given value(s) of the variable(s). A) 6 x + 5   for   x = 2 B) 12 x 2 + 5 x - 2   for   x = 1 C) 2( x + 7) + x   for   x = 0 D) 2 a + 3b - 7   for   a = 2 and b = 4 Solution
• Expand (if needed) and simplify each of the expressions below. A) 3 x + 5 x B) 2( x + 7) + x C) 2(x + 3) + 3(x + 5) + 3 D) 2 (a + 1) + 5b + 3(a + b) + 3 Solution
• Factor each of the expressions below. A) 3 x + 3 B) 8 x + 4 C) a x + 3 a D) (x +1) y + 4 (x + 1) E) x + 2 + b x + 2 b Solution
• Solve each of the equations below and check your answer. A) x + 5 = 8 B) 2 x = 4 C) x / 3 = 2 D) 0.2 x = 1 D) 3 x + 6 = 12 E) 3 (x + 2) + 2 = 8 Solution
• There are n boxes in a large bag and m toys in each box. What is the total number of toys in the bag? Solution
• Rewrite the expressions a × a × a - b × b using exponents. Solution
• The length of a rectangle is given by x + 2 and its width is equal to 3. Give a simplified expression of the area of this rectangle. Solution
• Two thirds of students in a class study math and the remaining eight students do not study math. What is the total number of students in this class? Solution
• A car travels 60 kilometers in one hour. At the same rate, what distance will be covered by this car in x hour? Solution
• Evaluate the expressions. A) 2 3 + 3 2 B) 0.1 3 C) 6 × (2 / 3) Solution
• A bag contains three red marbles; five blue marbles and seven green marbles. What is the ratio of blue marbles to the total number of marbles? Solution
• Solve the proportion : a / 3 = 5 / 18 Solution
• Which of the following ordered pairs is a solution to the equation 2 x + 3 y = 8? A) (0 , 0) B) (4 , 0) C) (1 , 2) Solution
• List all factors of the following numbers. A) 4 B) 12 C) 50 Solution
• Find the greatest common factor to each pair of the given numbers. A) 6 and 3 B) 18 and 24 C) 50 and 60 Solution
• Write the number " Six hundred seventy-two million two hundred fifty-nine" using the digits 0, 1, 2, ...9. Solution
• Which of the following expressions are equivalent? A) 2(x + 3) - 2 B) 2x + 4 C) 3(x + 3) - x - 5 Solution
• Find the lowest common multiple to each pair of the given numbers. A) 2 and 3 B) 7 and 14 C) 25 and 15 Solution
• Add and / or subtract and simplify A) 1 / 3 + 2 / 3 B) 2/5 - 1 / 7 Solution
• What is 2 / 3 of 21? Solution
• What is 40% of 1 / 4? Solution
• What is 20% of 50%? Solution
• How many seconds are there in one hour? Solution
• How many minutes are there in the month of January? Solution
• What is the location of each of the points: (-2 , 0) , (0 , 3) and (-2 , - 3) in a coordinate plane? Solution
• Order   7 / 5 , 12 / 10 , 21 / 20 and 111%   from the smallest to the largest. Solution

More References and links

Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers

• 6th Grade Math
• Solving word problems

Grade 6 Math Word Problems: Tips, Tricks, and Answers

Do you want to stimulate your 6 th grader’s creative thinking skills? Then, enjoy this brilliant math article. In this comprehensive guide, we will provide you with a treasure trove of fun solving strategies, tips, tricks, and answers to tackle those tricky grade 6 math word problems that have been confusing your students for some time now.

In this page, you will discover why math word problems are important for 6th-graders and simple methods of breaking down complex word problems into manageable steps.

Nevertheless, we will introduce you to Mathskills4kids.com , an outstanding website with thousands of common types of grade 6 math word problems and a step-by-step approach to solving them. Interestingly, we will illustrate how to use diagrams and models to solve math word problems efficiently.

Learn to love Grade 6 Math word problems with these worksheets and answers

Hello and welcome to Grade 6 Math word problems worksheets and answers , where your 6 th Grade students will learn to love and solve math problems and activities at all times.

We understand that word problems can often frustrate students, as they require a solid understanding of mathematical concepts and the ability to interpret and apply them to real-life situations. That's why we have compiled a collection of proven strategies and techniques to empower your students to approach word problems confidently and accurately.

From understanding problem-solving strategies to breaking down complex questions into manageable steps, this guide will equip you with the knowledge and resources to make math word problems a breeze. So, let's dive in and unlock the secrets to conquering grade 6 math word problems together!

BROWSE THE WEBSITE

Download free worksheets, grade 6 math topics.

• Whole numbers

Multiplication

• Exponents and square roots
• Number theory
• Add & subtract decimals
• Multiply & divide decimals
• Fractions & mixed numbers
• Add & subtract fractions
• Multiply fractions
• Divide fractions
• Operations with integers
• Mixed operations
• Rational numbers
• Problems solving
• Ratio & proportions
• Percentages
• Measuring units
• Consumer math
• Telling time
• Coordinate graph
• Algebraic expressions
• One step equations
• Solve & graph inequalities
• Two-step equations
• 2D Geometry
• Symmetry & transformation
• Geometry measurement
• Data and Graphs
• Probability

Start practice on Sixth Grade here

Why are math word problems important for 6th-graders.

Math word problems are about more than just doing calculations. They are also about applying your math knowledge to real-world situations. Math word problems are important for 6 th graders because they help them to:

• Learn how to use different math concepts and skills in various contexts
• Develop their logical thinking and reasoning abilities
• Enhance their communication and literacy skills
• Prepare them for standardized tests and future math courses

Math word problems also make math more exciting and relevant. They show us how math can solve everyday problems and challenges. They also expose us to different topics and scenarios we may not encounter in our regular math lessons.

Strategies for solving Grade 6 math word problems

Solving Grade 6 math word problems can be intimidating, especially involving multiple steps or operations. But don't worry. Some general strategies will help your students confidently approach any word problem. Here are some of them:

• Please encourage them to read the problem carefully and identify the given information, the unknowns, and the question.
• They should rewrite the problem in their own words or summarize it in a sentence.
• Let them choose a suitable method or strategy to solve the problem. Some standard methods are guessing and checking, making a table or chart, drawing a picture or diagram, using a formula or equation, working backward, or using logical reasoning.
• They must show their work and explain each step clearly. Use appropriate units, labels, symbols, and terms.
• Lastly, tell them to check their answer by plugging it back into the problem or using a different method. Ensure their answer makes sense and answers the question.

Breaking down complex word problems into manageable steps

Some word problems may seem too complex or confusing at first glance. They may have too much information, too many steps, or too many operations. In such cases, breaking down the problem into smaller and simpler parts is helpful. Here are some tips on how to do that:

Words like "difference," "subtract," "take away," or "minus" indicate s ubtraction .

Words like "product," "multiply," "times," or "of" indicate multiplication .

Words like "quotient," "divide," "per," or "out of" indicate division .

Words like "ratio," "fraction," "percent," or "part" indicate fractions or decimals .

Words like "equal," "same as," or "is" indicate equations .

Words like "more than,” “less than," "greater than," or "smaller than" indicate inequalities .

Words like "average," "mean," or "median" indicate statistics .

Words like "area," "perimeter," "volume," or "surface area" indicate geometry , etc.

• Use parentheses, brackets, or other symbols to group the parts of the problem that belong together . For example, if the problem says:

You can rewrite it as:

• (John has 12 apples) + (Mary has 8 apples) = (total number of apples) / (4 people) = (number of apples per person)

This way, you can see the structure of the problem more clearly and focus on one part at a time.

• Solve each part of the problem separately and write down the intermediate results . For example, using the previous problem:
• (John has 12 apples) + (Mary has 8 apples) = (total number of apples)
• 12 + 8 = 20
• (total number of apples) / (4 people) = (number of apples per person)

This way, you can keep track of your work and avoid making mistakes.

• Combine the intermediate results to get the final answer. For example, using the previous problem :

This way, you can answer the question and check your answer.

Common types of grade 6 math word problems

There are many types of word problems that you may encounter in grade 6 math . Some of the most common ones found on Mathskills4kids.com are:

• Ratio and proportion problems : These problems involve finding the relationship between two quantities with the same unit or measure. For example, if 12 pencils cost $3, how much do 20 pencils cost?
• Percent problems : These problems involve finding the part, whole, or percent of a quantity. For example, if 30% of a class is boys, and there are 24 students, how many boys are there?
• Fraction problems : These problems involve adding, subtracting, multiplying, or dividing fractions. For example, how much pizza do you have left if you have 2/3 of a pizza and eat 1/4?
• Decimal problems : These problems involve adding, subtracting, multiplying, or dividing decimals. For example, if you buy a shirt for $12.50 and a pair of jeans for $24.75, how much change do you get from $50?
• Measurement problems : These problems involve converting between different units of measurement or finding the perimeter, area, or volume of shapes. For example, if a rectangle has a length of 15 cm and a width of 10 cm, what is its area in square meters?
• Algebra problems : These problems involve finding the value of an unknown variable or expression. For example, if x + 5 = 13, what is the value of x?

A step-by-step approach to solving different types of word problems

No matter what type of word problem your 6 th graders are faced with, they can use the following steps to solve it:

• They should read the problem carefully and identify the given information and the question.
• They must choose a variable to represent the unknown quantity and write an equation or expression that relates the given information and the question.
• They can now solve the equation or expression and find the variable's value.
• They can check their answer by plugging it back into the equation or expression to see if it makes sense.
• They can now write their answer in complete sentences and include the appropriate units.

Using diagrams and models to solve math word problems

Sometimes, it can be helpful to use diagrams and models to visualize the problem and make it easier to solve. Some examples of diagrams and models for solving math word problems are:

• Tape diagrams : These are horizontal or vertical bars showing the relationship between two quantities. For example, you can use a tape diagram to show how much money each person gets when $60 is shared equally among 4 people.
• Number lines : These horizontal lines show numbers and their relative positions. For example, you can use a number line to show how to add or subtract fractions with different denominators.
• Tables : These are grids that show data in rows and columns. For example, you can use a table to show how to find equivalent ratios or fractions.
• Charts : These are graphical representations of data using bars, circles, lines, or other shapes. For example, you can use a chart to show how to find the percent of a quantity or compare different quantities.
• Drawings : These are sketches or illustrations that show shapes or objects. For example, you can use a drawing to show how to find a shape's perimeter, area, or volume.

Providing answers and explanations to sample Mathskills4kids’ Grade 6 math word problems

Here are some sample Grade 6 math word problems with answers and explanations available at Mathskills4kids.com :

Answer : 6 cups of flour

Explanation : This is a ratio problem. We can use a tape diagram to show the relationship between flour and sugar.

Flour →|<---2 cups--->|<---2 cups--->|<---2 cups---> = 6

Sugar→|<---3 cups--->|<---3 cups--->|<---3 cups---> = 9

We can see that for every 3 cups of sugar, we need 2 cups of flour. So, for 9 cups of sugar, we need 6 cups of flour.

Answer : $15

Explanation : This is a percent problem. We can use a formula to find the sale price of the shirt.

Sale price = Original price - Discount

Discount = Percent off x Original price

We know the percent off is 40%, and the original price is $25. So, we can plug these values into the formula and solve for the sale price.

Discount = 40% x $25

Discount = 0.4 x $25

Discount = $10

Sale price = $25 - $10

Sale price = $15

Tips for improving problem-solving skills in Grade 6 math

Here are some tips that can help students improve their problem-solving skills in grade 6 math :

• Please encourage them to practice regularly and try different types of word problems.
• They should review the concepts and skills they have learned and apply them to new situations.
• They can use different strategies and methods to solve word problems and compare their results.
• Let them ask for help from the teacher, parents, or peers if they get stuck or confused.
• They should learn from their mistakes and try to avoid them in the future.

Bonus: additional resources to reinforce Grade 6 math problem skills

If you want to enhance your student's Grade 6 math word problem skills , or if you need some extra help, here are some additional and useful web links that you can check out:

• Math Playground : This website has a lot of fun and interactive games that let 6 th graders practice different types of math word problems, such as fractions, decimals, ratios, proportions, and more. They can also watch videos explaining how to solve some problems. https://www.mathplayground.com/wordproblems.html .
• Khan Academy : This website has many videos and exercises covering various topics in Grade 6 math, including word problems. Students can learn at their own pace and track their progress. https://www.khanacademy.org/math/cc-sixth-grade-math .
• IXL : This website has many practice questions aligned with the Common Core standards for Grade 6 math. Students can choose from different categories of word problems, such as expressions and equations, geometry, statistics, and more. They can also get instant feedback and explanations for their answers. https://www.ixl.com/math/grade-6 .
• Math Goodies : This website has a lot of worksheets and lessons that teach 6 th graders how to solve different types of word problems, such as percent, ratio, proportion, and more. They can also find tips and tricks for solving word problems faster and easier. https://www.mathgoodies.com/math-mammoth/worksheets/pdf/grade_6_word_problems.pdf .

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Math word problems can be challenging for many 6th-graders, but they are also important for developing their mathematical thinking and reasoning skills.

Using the strategies and steps we discussed in this article, your student's ability to solve different types of word problems in Grade 6 math can be improved.

You can also use the diagrams and models we have shown you to help your students visualize the problem and find the solution. Encourage them to practice as much as possible, and they must not be afraid to ask for help if needed.

You can also use the web links that we have provided to reinforce your student’s learning and have fun with math. We hope this article has helped your 6th-grade students feel more confident and prepared for tackling Grade 6 math word problems.

Happy problem-solving!

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6th grade math word problems curriculum.

Grade 6 math word problems with solutions and explanations is a complete training program made of games, worksheets, lessons for 6th graders on addition and subtraction word problems, fractions and mixed numbers word problems, number theory word problems, multiplication and division word problems, mixed operation word problems, solving and estimation word problems, etc.

So, we invite you to quickly grab the best of 6th Grade math word problems which consist of all the concepts in grade 6 math. Of equal interest to generate your kid’s eagerness and love for solving these math problems, we have designed very captivating math word problem resources for grade 6 .

In this light, your young math learners will significantly enhance their understanding of how to confidently apply math skills to all 6th Grade math word problems curricula. In addition, we have devised plenty of fun strategies useful for quick and effective solving all real-life math problems.

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How 6th Grade math word problems enhance kids' math skills?

Most often than not, we begin to wonder how 6th-grade math word problems enhance kids’ math skills ! But after engaging in full practice of solving these grade 6 math word problems, you’ll be surprised at your kid’s new enriching math skills.

First and foremost, as we have selected problems from all areas of our daily lives relating to addition, subtraction, multiplication, division, fractions, measurements, etc., your kids will gain more expansive reasoning to determine how best to approach any real-life math problem quickly.

Moreover, as we have designed simple solving steps and tips for solving these problems, your kids will become accustomed to the solving process, thus gaining math fluency and skills.

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NCERT Solutions for Class 6 Maths

Ncert solutions for class 6 maths cbse 2023-24 edition- free pdf download.

NCERT Solutions for Class 6 Maths provides detailed explanations for all the questions provided in the NCERT textbooks prescribed by the Central Board of Secondary Education. BYJU’S provides chapter-wise NCERT Class 6 Maths Solutions to help students clear their doubts by offering an in-depth understanding of the concepts. These materials including NCERT Solutions are available in PDF format so that students can download them and learn offline as well.

Students can practice the different types of questions given in the book, which are expected to be asked in the final exams, with the help of these NCERT Solutions for Class 6 . This has been designed by our experts in a well-structured format, to provide the best methods of solving the problems and to ensure the proper knowledge of concepts. Students are advised to practice CBSE Class 6 Maths textbook problems for the exams. This will also build a strong foundation of all these concepts for higher-level classes.

Class 6 Maths NCERT Solutions

CBSE Maths Solutions for Class 6 are given in the table below. Download chapter-wise CBSE 6th Class Maths textbook solutions and get the answers to all the questions.

The following chapters have been removed from the NCERT Class 6 Maths textbook 2023-24.

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Maths NCERT Solutions for Class 6 Maths Chapterwise

Students can access the CBSE class 6 maths solutions of all the chapters from the link below.

Chapter 1 Number System

The chapter, Knowing Our Numbers of Class 6 Maths, helps the students learn different concepts including large numbers up to one crore, Indian and universal arrangement of numeration, estimation of large numbers and roman numerals. Students will also be taught to read, write and compare large numbers. A total of 3 exercises are there in the chapter.

Also access the following resources for  Class 6 Chapter 1 Number System  at BYJU’S:

• NCERT Exemplar Solutions for Class 6 Maths Chapter 1 Number System
• Number System
• Numeral System: Indian And International
• RD Sharma Solutions for Class 6 Maths Chapter 1: Knowing Our Numbers

Chapter 2 Whole Numbers

The chapter begins with an introduction to the concept of Whole Numbers. Going forward, the chapter entails topics such as predecessor and successor of a natural number, addition, subtraction and representation of natural numbers on the number line. There are 3 exercises present in the chapter.

Also access the following resources for  Class 6 Chapter 2 Whole Numbers  at BYJU’S:

• Whole Numbers Class 6 notes – Chapter 2
• Whole Numbers
• RD Sharma Solutions for Class 6 Maths Chapter 3: Whole Numbers

Chapter 3 Playing with Numbers

In this chapter, students will learn to obtain the number of factors and multiples of a given number. Perfect number, prime, composite and co-prime numbers, along with common factors and common multiples, are some of the concepts discussed in the chapter. Finding LCM and HCF using prime factorisation method is also taught in the chapter. Seven exercises are present in the chapter to help the students in practicing problems based on the chapter.

Also access the following resources for  Class 6 Chapter 3 Playing with Numbers  at BYJU’S:

• Playing with numbers Class 6 notes – Chapter 3
• RD Sharma Solutions for Class 6 Maths Chapter 2: Playing with Numbers

Chapter 4 Basic Geometrical Ideas

There are a total of 6 exercises in the chapter, Basic Geometrical Ideas. Students will learn about a line segment, the distance between two points, type of lines, concepts based on angles, triangles, polygons, quadrilaterals, regular polygons, circles.

Also access the following resources for  Class 6 Chapter 4 Basic Geometrical Ideas  at BYJU’S:

• Basic Geometrical Ideas Class 6 Notes: Chapter 4
• RD Sharma Solutions for Class 6 Maths Chapter 10: Basic Geometrical Concepts

Chapter 5 Understanding Elementary Shapes

Understanding Elementary Shapes helps the students in understanding all types of shapes that are framed using curves or lines. Students learn to effectively observe the corners, edges, planes, open curves and closed curves in the surroundings. A total of 9 exercises are present in the chapter that help the students to understand the shapes better.

Also access the following resources for  Class 6 Chapter 5 Understanding Elementary Shapes  at BYJU’S:

• Understanding Elementary Shapes Class 6 Notes: Chapter 5
• RD Sharma Solutions for Class 6 Maths Chapter 16: Understanding Three-Dimensional Shapes

Chapter 6 Integers

Chapter 6 of Class 6 Integers deals with the presentation of the idea of negative numbers. Students learn the representation of Integers on a number line, ordering of Integers, the addition of Integers, subtraction of Integers, addition of Integers on a number line and subtraction of Integers with the help of a number line in this chapter. There are a total of 3 exercises present in the chapter.

Also access the following resources for  Class 6 Chapter 6 Integers  at BYJU’S:

• NCERT Exemplar Solutions for Class 6 Maths Chapter 3 Integers
• Integers Class 6 Notes: Chapter 6
• RD Sharma Solutions for Class 6 Maths Chapter 5: Negative Numbers and Integers

Chapter 7 Fractions

The chapter 7 of Class 6, Fractions, talks about number line, proper fractions, improper and mixed fractions, equivalent fractions, the simplest form of a fraction, like fractions, comparing fractions, comparing like fractions, comparing unlike fractions, addition and subtraction of fractions, etc. A total of 6 exercises are present in the chapter.

Also access the following resources for  Class 6 Chapter 7 Fractions  at BYJU’S:

• Fractions Class 6 Maths Notes – Chapter 7
• RD Sharma Solutions for Class 6 Maths Chapter 6: Fractions
• NCERT Exemplar Solutions for Class 6 Maths Chapter 4 Fractions and Decimals

Chapter 8 Decimals

The chapter, Decimals, discusses the idea of Decimals through word problems and later progresses to complex concepts related to Decimals. Tenths, hundredths, comparing and using Decimals, money, length, weight, the addition of numbers with Decimals and subtraction of Decimals are some of the topics covered in this chapter. The chapter contains 6 exercises with problems related to the concepts discussed in the chapter.

Also access the following resources for  Class 6 Chapter 8 Decimals  at BYJU’S:

• Decimals Class 6 Maths Notes – Chapter 8
• RD Sharma Solutions for Class 6 Maths Chapter 7: Decimals

Chapter 9 Data Handling

Chapter 9 of Class 6 Maths, Data Handling, introduces the students to the topic of data, types of data and the different representations of data. Introduction to data, recording data, organization of data, introduction to the idea of pictograph, interpretation of a pictograph, how to draw a pictograph, introduction to a bar graph, interpretation of a bar graph presentation and drawing a bar graph are the basic topics discussed in this chapter to help the students understand the concept of Data Handling. The chapter has 4 exercises to help the students understand the topic better.

Also access the following resources for  Class 6 Chapter 9 Data Handling  at BYJU’S:

• NCERT Exemplar Solutions for Class 6 Maths Chapter 5 Data Handling
• Data Handling Class 6 Maths Notes – Chapter 9
• RD Sharma Solutions for Class 6 Maths Chapter 23: Data Handling – III (Bar Graphs)

Chapter 10 Mensuration

In the tenth chapter of Class 6, Mensuration, students learn about the measurement of shapes and figures by their area and volume. Introduction to the measurement of the perimeter, perimeter of a rectangle, perimeter of regular shapes, introduction to the measurement of area, the area of a rectangle and the area of a square are the fundamental topics covered here. There are a total of 3 exercises in this chapter.

Also access the following resources for  Class 6 Chapter 10 Mensuration  at BYJU’S:

• Mensuration Class 6 Maths Notes – Chapter 10
• RD Sharma Solutions for Class 6 Maths Chapter 20: Mensuration
• NCERT Exemplar Solutions for Class 6 Maths Chapter 6 Mensuration

Chapter 11 Algebra

With a total of 5 exercises, Chapter 11, Algebra, takes the students to a brand new concept of Maths which includes solving problems using various alphabets. Introduction to Algebra, matchstick patterns, the idea of a variable, examples of variables, and use of variables in common rules, expressions with variables, using expressions practically, equation and solutions of an equation are the basic concepts discussed in the chapter.

Also access the following resources for  Class 6 Chapter 11 Algebra  at BYJU’S:

• Algebra Class 6 Maths Notes – Chapter 11
• RD Sharma Solutions for Class 6 Maths Chapter 8: Introduction to Algebra
• NCERT Exemplar Solutions for Class 6 Maths Chapter 7 Algebra

Chapter 12 Ratio and Proportion

Chapter 12, Ratio and Proportion, helps the students learn about certain circumstances that can be compared by division. The comparison by division is the ratio. Moreover, students will also come to know that if two ratios are equivalent, they are said to be proportional. The chapter starts with an explanation of the idea of ratio. Along with the concept of ratio, the chapter also deals with the idea of proportion, examples related to it and finally concludes with examples based on the unitary method. This chapter has 3 exercises to help the students understand the topics covered in the chapter in a better way.

Also access the following resources for  Class 6 Chapter 12 Ratio and Proportion  at BYJU’S:

• NCERT Exemplar Solutions for Class 6 Maths Chapter 8 Ratio and Proportion
• Ratio And Proportion Class 6 Maths Notes – Chapter 12
• RD Sharma Solutions for Class 6 Maths Chapter 9: Ratio, Proportion and Unitary Method
• Ratios And Proportion

Chapter 13 Symmetry

Chapter 13, Symmetry, has a total of 3 exercises that help the students learn how to determine symmetrical items and operations based on Symmetry. Making Symmetric Figures- Ink-blot Devils, Figures with Two Lines of Symmetry, Figures with Multiple (more than two) Lines of Symmetry, Reflection and Symmetry are the principal topics described in this chapter.

Also access the following resources for  Class 6 Chapter 13 Symmetry  at BYJU’S:

• Symmetry Class 6 Maths Notes – Chapter 13
• RD Sharma Solutions for Class 6 Maths Chapter 17: Symmetry
• NCERT Exemplar Solutions for Class 6 Maths Chapter 9 Symmetry and Practical Geometry

Chapter 14 Practical Geometry

Practical Geometry, the last chapter of CBSE Class 6 Maths, deals with making the shapes that the students are familiar with along with the tools used in creating the shapes. The topics discussed in the chapter include the circle, construction of a circle when its radius is known, a line segment, construction of a line segment of a given length, constructing a copy of a given line segment, perpendiculars, perpendicular to a line through a point on it, perpendicular to a line through a point not on it, the perpendicular bisector of a line segment, angles, constructing an angle of a given measure, constructing a copy of an angle of unknown measure, bisector of an angle, angles of special measures. There are 6 exercises present in the chapter.

Also access the following resources for  Class 6 Chapter 14 Practical Geometry  at BYJU’S:

• Practical Geometry Class 6 Maths Notes – Chapter 14

For students of 6th Standard, other online learning materials, such as notes, books, question papers, worksheets, etc . have been made available at BYJU’S. These materials are designed with respect to the CBSE syllabus (2023-2024) and NCERT curriculum. Students are also suggested to practise sample papers and previous year question papers to get an idea of the types of questions asked in the final exam.

Stay tuned to BYJU’S to get the updated materials for 6th class and prepare for your final exams. Students can also find NCERT solutions for Class 6 Science  consisting of all chapters.

Frequently Asked Questions on NCERT Solutions for Class 6 Maths

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