Signed Division: Explain the Check

Use multiplication to explain signed quotients, model equal changes and decide when division is defined.

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Watch the lesson | Revisit the first signed-division practice

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For a divided by b, find q so that b x q = a. The divisor b must not be zero. With two nonzero integers, matching signs give a positive quotient and different signs give a negative one. Zero divided by a nonzero number is zero.

Worked example

-18 divided by -6 is 3 because (-6) x 3 = -18. Compare 0 divided by 6 = 0 with 6 divided by 0, which is undefined: 0 times any number cannot make 6.

A worked division model: three negative-six changes reach negative eighteen. Negative eighteen divided by negative six equals three because negative six times three equals negative eighteen. — Worked example: check a quotient by multiplying it by the divisor.

Would you believe it?

Dividing by -1 takes a number to its opposite, just as multiplying by -1 does. Zero stays zero because the divisor -1 is not zero.

OpenStax: division as inverse multiplication

Question 1 Calculate 42 divided by -6. 7 -36 -7

Question 2 Calculate -45 divided by -5. -9 9 40

Question 3 A model position changes by -24 units in equal steps of -3 units. How many steps were made? 8 steps -8 steps 21 steps

Question 4 Which pair is correct? Both quotients are 0 Both quotients are 7 0 divided by 7 = 0; 7 divided by 0 is undefined

Question 5 Why does 0 divided by 0 not have a defined quotient? Only 0 times 0 is 0, so the answer must be 0 Every number times 0 is 0, so no unique quotient is selected Only 1 times 0 is 0, so the answer must be 1

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