Multiply Positive and Negative Rational Numbers

Students extend multiplication to all rational numbers, understanding why the product of two negative numbers is positive. They multiply integers, fractions, and mixed numbers with any combination of signs and interpret products in context.

Try three of them

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

Grade 7 · The Number System · question 1 of 3

0 of 20

20 rungs. A star at the top.

(−5) × (−6) =

How it is taught

0:00 of 2:51

The product of two negatives is positive.

A negative times a positive is negative.

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.

Multiply or divide the sizes, as if there were no signs.
Look at the signs: the same gives a positive answer, different gives a negative one.
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.

−6 × 8 = ___ — −48. The sizes: 6 × 8 = 48; the signs are different, negative: −48.

(−3) × (−4)

What is negative three times negative four? Let's hunt for a pattern that shows us why.

Start with three groups of negative four. That's negative twelve.

Two groups of negative four is negative eight.

One group of negative four is just negative four.

Zero groups of anything is zero.

Look closely — each answer is going up by four!

If the pattern keeps going, negative one times negative four must be positive four.

Negative two times negative four is positive eight.

And negative three times negative four is positive twelve.

The pattern reveals a rule: a negative times a negative is always positive.

Grade 7 · Why two negatives make a positive

So negative three times negative four equals twelve. Two negatives make a positive — nice work!

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

Standards

CCSS.7.NS.A.2

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers

CCSS.7.NS.A.2a

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations

Grade 7

Quoted from the Common Core State Standards.

Where this sits

Comes after

Leads to

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 7

This is one rung of 40 in Grade 7 mathematics, in the order they build on each other.

Practise this skill free

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

Start free