Signed Division: Find the Missing Factor

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

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Watch the lesson | Try the second 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 -28 divided by 4. 7 -7 -24

Question 2 Calculate -32 divided by -8. 4 -4 24

Question 3 A model position changes by -30 units over 5 equal steps. What is the signed change per step? 6 units -25 units -6 units

Question 4 Calculate 0 divided by -9. -9 0 Undefined

Question 5 Why is 12 divided by 0 undefined? No number multiplied by 0 gives 12 The answer is 0 because 12 x 0 = 0 The answer is 12 because division keeps the first number

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