 Multiply or divide negative numbers with decimals

Lesson

In Order is Important, we looked at how to solve decimals problems with various combinations of operations. Now we are going to use and extend that knowledge by looking at questions that involve negative decimals.

Remember there are rules for when you add, subtract, multiply or divide with negative numbers.

When you're multiplying or dividing:

• If one of your terms is negative and the other is positive (such as $6.5\times\left(-2.1\right)$6.5×(2.1)), your answer will be negative.
• If both terms are negative (such as $\left(-12.2\right)\div\left(-2\right)$(12.2)÷​(2)), your answer will be positive.

Examples

Question 1

Evaluate: $-5.4\times\left(-3.6\right)$5.4×(3.6)

Think: The product of two negative numbers will be positive.

Do: $-5.4\times\left(-3.6\right)=19.44$5.4×(3.6)=19.44

Question 2

Evaluate$\left(-6.3\right)\div0.15$(6.3)÷​0.15

Think: The quotient of a negative number and a positive number will be negative.

Do: $\left(-6.3\right)\div0.15=-42$(6.3)÷​0.15=42

Question 3

Evaluate $7.4\times\left(-4.1\right)$7.4×(4.1).

Question 4

Evaluate: $\left(-33.6\right)\div\left(-8\right)$(33.6)÷​(8).

Question 5

Jenny takes out a loan of $\$2200$$2200. She pays back \42.60$$42.60 each month and doesn't have to pay interest.

If she has made $5$5 repayments so far, how much does Jenny still owe?