Multiply and divide rational numbers · lesson

The sign rules

💡 Same signs give a positive answer, different signs give a negative answer, and you can count negatives to decide.

Multiply or divide the sizes as usual. Then pick the sign.

Two numbers with the same sign give a positive answer. Two numbers with different signs give a negative answer.

With more than two numbers, count the negatives. An even count gives a positive answer. An odd count gives a negative answer.

🧠 Let's work it out

Find −2 × (−3) × (−4).

What do you think comes next?

💡 Multiply or divide the decimals as if they were positive, then put the sign on at the end.

Ignore the signs at first. Multiply or divide the decimals the usual way.

When you divide by a decimal, you can move both decimal points the same number of places. Then you divide by a whole number.

Last, use the sign rule.

🧠 Let's work it out

Find −4.2 ÷ 0.7.

What do you think comes next?

💡 Multiply tops and bottoms, or flip and multiply to divide, then simplify and apply the sign rule.

To multiply fractions, multiply the tops and multiply the bottoms. Simplify at the end.

To divide, flip the second fraction and multiply.

The sign rule is the same as for whole numbers.

🧠 Let's work it out

Find (−3/4) × (2/9).

What do you think comes next?

💡 A loss or a drop is negative, so repeated losses multiply and steady drops divide into a negative rate.

A loss that repeats is a negative number times how many times it happens.

A total drop shared over equal steps is a negative number divided by the number of steps.

🧠 Let's work it out

A toy loses $1.75 in value each day for 6 days. What is the total change in value?

A loss is negative, so multiply: −1.75 × 6.
1.75 × 6 = 10.5.
The signs differ, so the change is −10.5 dollars.
Another example: a diver who drops to −36 feet in 9 minutes changes by −36 ÷ 9 = −4 feet each minute.

What do you think comes next?