how to solve integer word problems grade 7

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Last modified on August 3rd, 2023

Integer Word Problems

We use integers in our everyday life for counting money and measuring the speed of sound and light, height and weight of objects, temperature and pressure of the atmosphere, and depth of a sea. Solving word problems related to the above measurements will help us relate better to the concept with applications.

A submarine was located 600 feet below sea level. Calculate its new position if it ascends 250 feet from its position.

Given, The initial position of the submarine is 600 feet It ascends 250 feet Thus, the new position of the submarine is (600 – 250) feet = 350 feet Thus, the new depth of the submarine is 550 feet

Today’s weather report suggested that the temperature of New York City increased from 10-degree celsius to 20-degree celsius. What is the rise in temperature?

Given, Initial temperature = -10 degree celsius Final temperature = 20 degrees celsius Increase in temperature = 20 – (-10) = 30 degrees celsius Thus, the rise in temperature of New York City is 30 degree Celsius.

Demitri owes her mother \$5.00. He earns \$12.00 doing chores. How much is left with him after he gives his mother what she owes?

Given, Amount to be given to his mother = \$5.00 He earns = \$12.00 Thus, he is left with = \$(12.00 – 5.00) = \$7.00 Thus, Demitri is left with \$7.00.

The local movie theater reported losses of \$475 each day for 3 days. What was the total loss incurred for the 3 days?

Given, Loss incurred by the movie theater per day = \$475 The loss incurred in 3 days = \$(3 × 475) = \$1,425 Thus the total loss incurred by the movie theater in 3 days is \$1,425

The Second World War began in the year 1939 and ended in 1945. How long did it last?

Given, The Second World War began in 1939 and ended in 1945 Thus, it lasted (1945 – 1939) = 6 years

Mt. Everest is 29,028 feet above sea level, and the Dead Sea is 1,312 feet below sea level. Find the difference between the 2 elevations.

Given The height of Mt. Everest is 29,028 feet above sea level The height of the Dead Sea is 1,312 feet below sea level Thus, the difference between the 2 elevations = (29,028 + 1,312) feet = 30,340 feet

Dakota withdrew a total of \$600 over 4 days. If he withdrew the same amount daily, find the amount he withdrew each day.

Given, Total amount Dakota withdrew = \$600 Number of days he withdrew = 4 days Amount withdrawn each day = \$(600 ÷ 4) = \$150 Thus, Dakota withdrew \$150 per day.

Andrew had \$12,000 in his account. He once withdrew \$2,000 and then deposited $6,000. What is the current balance in the account?

Given, Initial balance Andrew had = \$12,000 Amount withdrawn = \$2,000 Amount deposited = \$6,000 Thus, the current balance = \$(12,000 – 2,000 + 6,000) = \$16,000 Thus, the current balance Andrew has currently in his account is \$16,000

A kite rises 100 feet from the ground and then falls back 40 feet. What is the current height of the kite from the ground?

Given, The kite rises = 100 feet and then falls back = 40 feet Thus, the current height of the kite from the ground is (100 – 40) feet = 60 feet

If it is 3°C outside and the temperature drops 15° C in the next 6 hours, how cold will it be after 6 hours?

Initially, the outside temperature was 2°C Then, the temperature drops to = (2 – 15)°C  = -13°C Thus, the temperature after 6 hours will be -13°C

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Integer Word Problems Worksheets

An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses. Integers are closed under the operations of addition and multiplication . Integer word problems worksheets provide a variety of word problems associated with the use and properties of integers. 

Benefits of Integers Word Problems Worksheets

We use integers in our day-to-day life like measuring temperature, sea level, and speed limit. Translating verbal descriptions into expressions is an essential initial step in solving word problems. Deposits are normally represented by a positive sign and withdrawals are denoted by a negative sign. Negative numbers are used in weather forecasting to show the temperature of a region. Solving these integers word problems will help us relate the concept with practical applications.

Download Integers Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

☛ Check Grade wise Integers Word Problems Worksheets

• 6th Grade Integers Worksheets
• Integers Worksheets for Grade 7
• 8th Grade Integers Worksheets

Integer Word Problems

An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses. Integers are closed under the operations of addition and multiplication.

We use integers in our day-to-day life like measuring temperature, sea level, and speed limit. Translating verbal descriptions into expressions is an essential initial step in solving word problems. Deposits are normally represented by a positive sign and withdrawals are denoted by a negative sign. Negative numbers are used in weather forecasting to show the temperature of a region. Solving these integers word problems will help us relate the concept with practical applications.

Adding Integers 1. Rearrange the terms so that integers with the same sign are next to each other. 2. Add integers with like signs together. 3. Subtract the absolute values of integers with different signs. 4. The sign of the solution will be the sign of the larger integer.

Subtracting Integers 1. Rewrite the problem by changing the second term to its additive inverse. 2. Add the values.

Multiplying Integers 1. Multiply the absolute values of the integers. 2. If the two factors have the same sign, the product is positive. 3. If the two factors have different signs, the product is negative.

The price of one share of stock fell 4 dollars each day for 8 days. How much value did one share of the stock lose?

The stock price fell, so it is represented by -4. This happened for 8 days. -4 x 8 = -32 The stock’s value dropped by $32.

Practice Integer Word Problems

Practice Problem 1

Practice Problem 2

Practice Problem 3

Practice Problem 4

Integer – whole numbers and their opposites {…, -3, -2, -1, 0, 1, 2, 3, …}

Negative integer – any integer less than zero.

Positive integer – any integer greater than zero.

Absolute value – the positive distance that a number is from 0 on a number line.

Zero Pair – a yellow counter and a red counter that represents zero.

Opposites – two integers that are the same distance from 0 on a number line but in opposite directions, like -5 and 5.

Additive inverses – two integers that are opposites.

Pre-requisite Skills Multi-Step Word Problems II Order of Operations

Related Skills Evaluating Algebraic Expressions Evaluate Algebraic Expressions Add Linear Expressions Subtract Linear Expressions Solve Complex Equations

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How to Add and Subtract Integers: Word Problems

Mastering the art of tackling word problems involving the addition and subtraction of integers is a vital skill in the mathematical universe. Integers, which include positive, negative, and zero, are more nuanced than their natural number counterparts. To craft a highly detailed, comprehensive, and sophisticated guide, let's dive into the labyrinth of integers, unraveling the mystery of word problems step-by-step.

A Step-by-step Guide to Solve Integers Addition and Subtraction: Word Problems

Here is a step-by-step guide to solving word problems of integers addition and subtraction:

Step 1: Decipher the Problem

The journey begins with an intensive reading of the word problem. Identify the integers involved, noting their signs (\(+\) or \(-\)), and the operations stated or implied (addition or subtraction). Understand the context and constraints of the problem to guide your strategy.

Step 2: Pinpoint the Unknowns

Next, determine what the problem demands you to find. This could be an unknown quantity or a relationship between different quantities. Assign variables to these unknowns, typically ‘\(x\)’, ‘\(y\)’, or ‘\(z\)’.

Step 3: Translate into Mathematical Language

Now, morph the word problem into an equivalent mathematical expression or equation. Expressions such as “increased by” or “more than” often signify addition, while “decreased by” or “less than” hint towards subtraction. This translation serves as a bridge between the narrative of the problem and the mathematical steps to solve it.

Step 4: Construct the Equation(s)

Based on your translation, construct an equation or a system of equations that encapsulate the conditions outlined in the problem. Be vigilant of the signs of the integers; a positive integer added to a negative integer can be treated as subtraction and vice versa.

Step 5: Resolve the Equation(s)

Once your equation(s) are set, deploy your arithmetic and algebraic skills to solve them. Remember the basic rules of integer arithmetic, such as the fact that subtracting a negative integer is equivalent to adding a positive one.

Step 6: Validate Your Solution

Substitute your solution back into the original equation(s) to verify its correctness. If it stands the test, your solution is accurate. If it fails, reexamine your steps to identify potential missteps or miscalculations.

Step 7: Answer the Query

The final act is responding to the original question asked in the problem. Ensure your answer aligns with the question and is phrased appropriately, incorporating units if necessary.

by: Effortless Math Team about 12 months ago (category: Articles )

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Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

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• Word Problems on Integers

Understanding Integers

For solving integer word problems students need the right base of knowledge on integers. Proper practice is required for solving integer questions correctly. In this article, we will help students develop the base required for answering word problems on integers for Class 7.

Let’s start with the fact that an arithmetic operation is an elementary branch of mathematics. Arithmetic operations are subtraction, addition, division, and multiplication. These arithmetic operations are used for solving integer problems. There are also other types of numbers that can be solved with the help of arithmetic operations.

It should also be noted that integers are a special group that does not contain any decimal or fractional part. Integers include positive numbers, negative numbers, and zero . Also, arithmetic operations on integers are similar to whole numbers .

It also makes it a little confusing to solve word problems on integers for class 6 and word problems on integers for class 7 pdf because there are both positive and negative numbers. This is also why integers are different from whole numbers.

Integers can also be plotted on a number line. A number line might also be used by students when learning how to solve integers questions. These types of questions are more common when it comes to integers word problems Class 7. If you have never seen a number line, then an image of a number line is attached below.

Rules of Integers 

There are several rules that students need for learning how to solve integer word problems. Some of those rules are mentioned below.

The sum of any two positive integers will result in an integer.

The sum of any two negative integers is an integer.

The product of two positive integers will give an integer.

The product of two negative integers will be given an integer.

The sum of any integer and its inverse will be equal to zero.

The product of an integer and its reciprocal will be equal to 1.

Now, let’s look at addition, multiplication, subtraction, and division of signed integer numbers. This will help students to work on story problems with integers answer key.

The Addition of Signed Integer Numbers

As mentioned above, if we add two integers with the same sign, then we have to add the absolute value along with the sign that was provided with the number. For example, (+4) + (+7) = +11 and (-6) + (-4) = -10.

Also, if we add two integers with different signs, then we have to subtract the absolute values and write down the difference. This should be done with the sign of the number that has the largest absolute value. For example, (-4) + (+2) = -2 and (+6) + (-4) = +2.

Subtraction of Signed Integer Numbers

If a student wants to solve integer example problems, then he or she needs to know that while subtracting two integers, we have to change the sign of the second number. The second number should be subtracted and the rules of addition should also be followed. For example, (-7) - (+4) = (-7) + (-4) = -11 and (+8) - (+3) = (+8) + (-3) = +5.

Multiplication and Division of Signed Integer Numbers

When it comes to working on integer word problems with solutions of multiplying and dividing two integer numbers, then the rules are quite straightforward. If both the integers have the same sign, then the final results are positive. If the integers have different signs, then the final result is negative. For example, (+2) x (+3) = +6, (+3) x (-4) = -12, (+6) / (+2) = +3, and (-16) / (+4) = -4.

Properties of Integers

Students should also be familiar with the properties of integers if they want to work on integer word problems grade 6 with solutions. Some of those properties of integers are:

Closure property

Associative property

Commutative property

Distributive property

Additive inverse property

Multiplicative inverse property

Identity property

We also need to look at these properties in detail for solving integer problems in 6th grade. Let’s move on to that discussion.

Closure Property:

According to the closure property of integers, if two integers are added or multiplied together, the final result will be an integer only. This means that if a and b are integers, then:

a + b = integer

a x b = integer

For example, 2 + 5 = 7, which is an integer, and 2 x 5 = 10, which is also an integer.

Commutative Property:

According to this property, if a and b are two integers, then a + b = b + a and a x b = b x a. For example, 3 + 8 = 8 x 3 = 24 and 3 + 8 = 8 + 3 = 11. It should be noted that this property is not followed in the case of subtraction and division.

According to the associative property, if a, b, and c are integers, then:

a + (b + c) = (a + b) + c

a x (b x c) = (a x b) x c

For example, 2 + (3 + 4) = (2 + 3) + 4 = 9 and 2 x (3 x 4) = (2 x 3) x 4 = 24.

This property is only valid when it comes to addition and multiplication.

Distributive Property:

The distributive property states that if a, b, and c are integers, then a x (b + c) = a x b + a x c. For example, if we have to prove that 3 x (5 +1) = 3 x 5 + 3 x 1, then we should be start by finding:

LHS = 3 x (5 + 1) = 3 x 6 = 18

RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18

Since, LHS = RHS

This proves our example.

Additive Inverse Property:

This additive inverse property states that if a is an integer, then a + (-a) = 0. This means that-a is the additive inverse of integer a.

Multiplicative Inverse Property:

The multiplicative inverse property states that if a is an integer, then a x (1 / a) = 1. This  means that 1 / a is the multiplicative inverse of integer a.

Identity Property of Integers:

The identity property of integers states that a + 0 = a and a x 1 = a. For example, 4 + 0 = 4 and 4 x 1 = 4.

Types of Integers

Earlier, we mentioned that there are three types of integers. In this section, we will look at these types of integers in more depth. The list of those types of integers is mentioned below.

Zero can be characterized as neither a positive nor a negative integer. It can be best defined as a neutral number. This also refers to the fact that zero has no sign (+ or -).

Positive Integers:

As the name indicates, positive integers are those numbers that are positive in their nature. These numbers are represented by a positive or plus (+) sign. The positive integers lie on the right side of the zero on the number line. This also means that all positive integers are greater than zero. For example, 122, 54, and 9087268292.

Negative Integers:

Negative integers, on the other hand, are numbers that are represented by a minus (-) or negative sign. These numbers are present on the left side of the zero on a number line. For example, -182, -8292, and -2927225.

Fun Facts About Integers

The word integer comes from the Latin word “ integer ” which literally means whole. 

You might find it interesting to note that integers are not just simple numbers on paper. Instead, these numbers have real-life applications! Both positive and negative integers are used to symbolize two contradicting situations in the real world. For example, if the temperature is above zero, then positive integers are used for denoting the temperature. But if the temperature is less than zero, then negative integers are used for denoting the temperature.

Integers can also help an individual in comparing and measuring two things like how small or big or few or more things are. These integers help in quantifying things. For example, in games like cricket and soccer, integers are used for keeping a track of scores. Movies and songs can also be rated by using integers!

FAQs on Word Problems on Integers

1. What are integers and what is their importance? 

An integer is usually defined as a number that can be written without any type of fractional component. These numbers tend to consist of zero, positive natural numbers or whole numbers, and their additive inverses. For example, 2, -56, 98, -302, etc. A set of integers is always denoted by the letter “Z”. 

The concept of integers is quite an important one to learn in mathematics. This is mainly because integers tend to help us compute the efficiency in both negative as well as positive numbers in a wide range of fields. They also help us to facilitate a number of calculations that are imperative to our daily lives. For example, we use integers to describe the temperature above or below the freezing point, to debit or credit money, etc. 

2. What are the rules for adding and subtracting integers?

There are some rules to be noted while adding two or more integers. They are as follows: 

The sum of an integer and its additive inverse is always zero. 

When you add two positive integers, the result will always be a positive number which will be greater than the two integers. 

When you add two negative integers, the result will always be a negative number which will be smaller than the two integers you added.

By finding the difference between the absolute value of a positive integer and a negative one, you can add both of them. And the sign of the greater number out of the two will be attached to the end product. 

When you add an integer with zero, you will get the same number as the answer. 

There are some rules to be noted while subtracting two or more integers. They are as follows: 

When you subtract any integer from zero, the answer will be either the additive inverse or the opposite of the integer. And when you subtract zero from any integer, then the result will always be the integer itself. 

If you want to subtract two integers that have the same sign, you ought to perform a subtraction operation on the absolute values of those numbers. 

If you want to subtract two integers that have different signs, you ought to add the absolute values. 

3. State the principles that the addition and subtraction of integers on a number line is based on. 

The principles upon which the addition of integers on a number line is based are as follows: 

Moving towards the right or the positive side of the number line will lead to the addition of a positive integer. 

Moving towards the left or the negative side of the number line will lead to the addition of a negative integer. 

Any of the integers can be taken as the base point (the point from where you start to move on the number line). 

The principles upon which the subtraction of integers on a number line is based are as follows: 

Every subtraction fact can also be written as an addition fact. 

Moving towards the left or the negative side of the number line will lead to the subtraction of a positive integer. 

Moving towards the right or the positive side of the number line will lead to the subtraction of a negative integer. 

4. Is multiplying rational numbers just like multiplying integers? If so, how?

To a certain extent, multiplying rational numbers is just like multiplying integers because the rules that are applicable to the latter, are also the same for the former. Rational numbers are just numbers that can be written in the fraction form of two given integers. So, if both the divisor and the dividend have the same signs, then the quotient will be positive. And if the divisor and the dividend have different signs, then the quotient will be negative. 

5. Can integers be decimals?

No. Just like whole numbers, integers can neither be fractions, nor can they be decimals. All integers can be expressed as a decimal, however, most of the numbers that are decimals cannot be expressed as integers. If there are any digits after the decimal point, and all of them are zeroes, only then can the number be identified as an integer. 

Integer Word Problems

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Add and Subtract Integers: Word Problems

Add and subtract integers in the context of real-world situations with this math practice worksheet! This seventh-grade worksheet asks students to find the sum or difference in nine one-step word problems. Beginning with word problems that include one- and two-digit numbers and progressing to word problems with three-digit numbers, this worksheet will engage and challenge learners as they apply their understanding of operations with integers to interesting and relatable scenarios. At the end of the worksheet, students are presented with a two-step bonus problem to further hone and challenge their number sense!

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