Skip to content
Brainsladder

Divide Rational Numbers and Understand Quotient Sign

Students understand that integers can always be divided (except by zero) and the result is a rational number. They apply sign rules to divide positive and negative integers, fractions, and decimals, and recognize that −(p/q) = (−p)/q = p/(−q).

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Divide Rational Numbers and Understand Quotient Sign

Grade 7 · The Number System · question 1 of 3

0 of 20

20 rungs. A star at the top.

−3/4 ÷ 1/2 =

How it is taught

0:00 of 3:11

Dividing two negatives gives a positive rational number.

To divide fractions, multiply by the reciprocal.

Read it: Multiplying and dividing signed numbers

−3 × (−4): the sizes multiply, 3 × 4 = 12, and the signs are the same, so the product is positive: 12.

  1. Multiply or divide the sizes, as if there were no signs.
  2. Look at the signs: the same gives a positive answer, different gives a negative one.
  3. Put that sign on the answer.

The pattern 2 × (−4) = −8, 1 × (−4) = −4, 0 × (−4) = 0 goes up by 4 each step, so (−1) × (−4) = 4.

Division undoes multiplication, so it follows the same sign rule: −12 ÷ (−4) = 3.

Factors can be grouped in any order, so pair the ones that are easy to multiply first.

Same signs: positive. Different signs: negative.

Two negatives make a negative: −3 × (−4) = −12.

The signs are the same, so the product is positive: 12.

81 ÷ (−9) = ___ — −9. The sizes: 81 ÷ 9 = 9; the signs are different, negative: −9.

−12 ÷ 4 and three equivalent forms

Today we'll divide rational numbers. The trick has two parts: figure out the sign, then divide the numbers.

Let's try negative twelve divided by four.

First the sign. A negative divided by a positive is...

...negative. Different signs give a negative answer.

Now divide the numbers without the signs: twelve divided by four is three.

Put it together: negative twelve divided by four equals negative three.

Here's something cool. Negative three can be written three different ways.

We can put the negative sign out front: the opposite of twelve fourths.

Or we can put it on the top: negative twelve over four.

Or even on the bottom: twelve over negative four.

All three forms equal negative three. The sign can live anywhere!

Dividing rational numbersStep 1: pick the signStep 2: divide the numbersFind the quotient−12÷4=?negative ÷ positive = negative12 ÷ 4 = 3−3Three ways to write −3The sign can move around!−124−12412−4==all three = −3−(p/q) = (−p)/q = p/(−q)ANSWER−3−12 ÷ 4Sign first, then divide.The negative can sit anywhere.
Grade 7 · Sign rules and equivalent fraction forms

Negative twelve divided by four is negative three. Divide the numbers, then place the sign wherever you like.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free