🔢 MathGrade 6Lesson 3
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Multiply and Divide Integers

Lesson preview: the Mini Lesson and Vocabulary are open to everyone. Guided practice, exercises, the parent checklist and the printable PDF worksheet come with full access (free 7-day trial or membership).

Learning Objectives

  • 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
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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 x and div)

  • 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 integer is zero: 0 div -7 = 0.
  • Dividing by zero is undefined — you can never split into zero equal groups.
Sign Rules for Multiply and DivideA two-by-two table of sign combinations for multiplication and division: same signs give a positive result, different signs give a negative result.Sign Rules for x and divSame signs give a positive result.Different signs give a negative.x or divPositiveNegativePositiveNegative(+) (+) = (+)4 x 3 = 1212 div 4 = 3(+) (-) = (-)5 x (-2) = -1015 div (-3) = -5(-) (+) = (-)-6 x 2 = -12-20 div 4 = -5(-) (-) = (+)-7 x (-3) = 21-24 div (-6) = 4Multiplying by zero gives zero. Dividing by zero is undefined.
Same signs go positive — different signs go negative.
Worked Examples for Sign RulesFour worked expressions showing how to decide the sign first, then multiply or divide the digits.Worked Examples-6 x 4 = -24different signs -> negative-12 div (-3) = 4same signs -> positive8 x (-5) = -40different signs -> negative-36 div (-9) = 4same signs -> positiveDecide the sign first. Then multiply or divide the digits.
Pick the sign, then handle the digits.
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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.

Vocabulary
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.
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← Lesson 2: Add and Subtract IntegersLesson 4: Factors, Multiples and Prime Factorization →