Multiply and Divide Integers
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What you will learn
- 1Apply the same-sign and different-sign rules to multiply two integers
- 2Apply the same-sign and different-sign rules to divide two integers
- 3Recognize that multiplying any integer by zero gives zero and dividing by zero is undefined
- 4Predict the sign of a product or quotient before computing the digits
Mini Lesson
Multiplying and dividing integers feels like multiplying and dividing whole numbers, but with one extra job: choose the sign. Once you know the sign, you only need your basic times tables and division facts to finish. The exact same sign rule covers both operations, so you only have to memorize it once.
The Sign Rule (Same for × and ÷)
- Same signs give a positive result. Both positive or both negative both produce a positive answer.
- Different signs give a negative result. One positive and one negative produce a negative answer.
- Decide the sign FIRST. Then multiply or divide the digits the normal way.
- The rule is the same for multiplication and division — there is only one rule to learn.
Multiplying Integers
- Positive x positive = positive: 6 x 4 = 24.
- Negative x negative = positive: -6 x -4 = 24.
- Positive x negative = negative: 6 x -4 = -24.
- Negative x positive = negative: -6 x 4 = -24.
- Any integer multiplied by zero is zero: -8 x 0 = 0 and 0 x 12 = 0.
Dividing Integers
- Positive div positive = positive: 24 div 4 = 6.
- Negative div negative = positive: -24 div -4 = 6.
- Negative div positive = negative: -24 div 4 = -6.
- Positive div negative = negative: 24 div -4 = -6.
- Zero divided by any non-zero divisor is zero: 0 div -7 = 0.
- Dividing by zero is undefined — you can never split a dividend into zero equal groups.
Words to know
product
The result of multiplying two or more numbers together.
quotient
The result of dividing one number by another.
factor
Each of the numbers being multiplied to make a product.
divisor
The number you divide by — the number on the bottom or to the right of the division sign.
dividend
The number being divided — the number on top or to the left of the division sign.
sign rule
Same signs give a positive result; different signs give a negative result. Used for both multiplication and division.
Tip: count the negative factors. An EVEN number of negatives gives a positive answer. An ODD number of negatives gives a negative answer. -2 x -3 x -4 has three negatives, so the product is negative.
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