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In these lessons, we will learn how to multiply and divide integers using rules.
The following diagram shows the rule to multiply and divide integers. Scroll down the page for more examples and solutions on multiplying and dividing integers.
What will be the sign for the product when we multiply 2 integers together, for example ( - 2) × (+3)?
When multiplying signed integers, the following rules for signs apply:
(+) × (+) = (+)
(+) × (−) = (−)
(−) × (+) = (−)
(−) × (−) = (+)
Example:
(+2) ×
(+3) = +6
(+2) × (–3) = –6
(–2) × (+3) = –6
(–2) × (–3) = +6
Recall that any number multiplied by 0 will result in 0.
Example :
4 × 0 = 0
0 × (–103) = 0
Example:
Calculate the following:
a) (–7) × (–2) =
b) 5 × (–3) × (–3) =
c) (–4) × (–3) × (–2) =
Solution:
a) (–7) × (–2) = 14
b) 5 × (–3) × (–3)
= (–15) × (–3)
=
45
c) (–4) × (–3) × (–2)
= 12 × (–2)
= –24
Dividing Integers
When we dividing integers, the similar rules for signs apply:
(+) ÷ (+) = (+)
(+) ÷ (−) = (−)
(−) ÷ (+) = (−)
(−) ÷ (−) = (+)
Example:
(+6) ÷ (+2) = +3
(+6) ÷ (–2) = –3
(–6) ÷ (+2) = –3
(–6) ÷ (–2) = +3
Example:
Calculate the following:
a) (–8) ÷ (–2) =
b) (12) ÷ (–4) =
Solution:
a) (–8) ÷ (–2) = 4
b) (12) ÷ (–4) = –3
Multiply and Divide Integers
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Examples of multiplying and dividing negative numbers
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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
Multiplying integers word problems: This lesson will show you how to solve five word problems related to the multiplication of integers.
Interesting multiplying integers word problems
Problem #1
From sea level, a submarine descends 40 feet per minute. Where is the submarine in relation to sea level 5 minutes after it starts descending?
Solution
In 1 minute, the submarine is 40 feet below sea level. This situation can be represented with -40 feet. Notice that we use a negative sign since the submarine is descending.
After 5 minutes, the submarine is at -40 × 5 = -200 feet
Problem #2
The price of one share of a stock fell 4 dollars each day for 8 days. How much value did one share of the stock lose after 8 days?
Solution
Each day, one share of the stock goes down by 4 dollars. We can represent this situation with the integer -4 dollars.
After 8 days, one share of a stock has gone down by -4 × 8 = -32
One share of a stock is now worth 32 dollars less.
Problem #3
A test has 20 questions. The test awards 3 points if the answer is correct and takes away 1 point if the answer is incorrect. A student answered 5 questions incorrectly. How many points did the student lose?
Solution
For each incorrect answer, the student gets -1 point.
After answering 5 questions incorrectly the student get -1 × 5 = -5.
The students lost 5 points after answering five questions incorrectly.
Problem #4
A credit card company charges a late fee of 25 dollars each time a customer fails to pay on time. A customer missed the payment 4 times last year. At the customer's request and out of courtesy, the credit card company decides to cancel all late fees for that year. Write a numerical expression to show how much money was return.
Solution
The amount of late fee the bank charged last year was -25 × 4
In order to return the money, the bank can do this math: -25 × -4
Notice how the number 4 became negative. This is necessary so the amount of money the customer gets back is a positive number.
Did you have a hard time understanding the word problems above? If so, do not worry. Check also the word problem below and go over the ones above one more time.
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