Math PicnicFree printable practice

Dividing and signs worksheets

−(x − 7) becomes −x + 7, and the second sign is the one that gets left behind. These free printable worksheets show a line of working with a sign or a divisor that reached only the first term, and ask which answer is correct.

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Dividing and signs
Dividing and signs worksheet — A minus, or a divisor, across two terms, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

An invisible multiplier is the hardest one to remember. A child who confidently expands 3(x − 7) will often write −(x − 7) as −x − 7, because there is no number in front to prompt the second multiplication — the minus is doing the work of a −1 that nobody wrote down.

Why this sheet works

Dividing through has the same shape and the same failure. In (6x + 24) ÷ 6 both terms have to be divided, and the tempting shortcut is to strike the 6 against the 6x and lose the x with it. Seeing that written out by somebody else is what makes it noticeable.

How this one works

One question from this sheet, worked through a step at a time.

Ana wrote (3x + 24) ÷ 3 − (x + 5) = 13. Which is correct?

(3x + 24) ÷ 3 − (x + 5)
(3x + 24) ÷ 3 − (x + 5)=x + 8 − x − 5
(3x + 24) ÷ 3 − (x + 5)=x + 8 − x − 5
(3x + 24) ÷ 3 − (x + 5)=3
(3x + 24) ÷ 3 − (x + 5)=3
they wrote:13
  1. Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.
  2. On your own, and writing the step nobody writes down: (3x + 24) ÷ 3 − (x + 5) becomes x + 8 − x − 5.
  3. Tidy that up and it is 3.
  4. Now compare. They wrote 13, and the minus reached the x in the second bracket but not the number — so the correct answer is 3.

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