 Four operations with negative fractions

Lesson

We've already learnt how to add, subtract, multiply and divide fractions. Similarly, we've looked at each of these operations with negative numbers.

The process is just the same when we have questions with negatives fractions. We saw this in The More or Less of Plus and Minus when we learnt how to add and subtract negative fractions.

Remember!
• Subtracting a negative number is the same as adding a positive number, e.g. $5-\left(-3\right)$5(3) is equivalent to $5+3$5+3.
• Adding a negative number is the same as subracting a positive number, e.g. $2+\left(-7\right)$2+(7) is equivalent to $2-7$27.
• The product of two negative terms is a positive answer, e.g. $-6\times\left(-9\right)=54$6×(9)=54
• The product of a positive and a negative term is a negative answer, e.g. $-5\times10=-50$5×10=50
• The quotient of a negative a positive term (in either order) is a negative answer, e.g. $20\div\left(-4\right)=-5$20÷​(4)=5
• The quotient of two negative terms is a positive answer, e.g. $\left(-144\right)\div\left(-12\right)=12$(144)÷​(12)=12

Examples

Question 1

Calculate: $3+4-\frac{-4}{5}$3+445.

Think: Following the order of operations, we will solve the addition and subtraction, working from left to right.

Do:

 $3+4-\frac{-4}{5}$3+4−−45​ $=$= $7-\frac{-4}{5}$7−−45​ $=$= $7+\frac{4}{5}$7+45​ $=$= $7\frac{4}{5}$745​

Question 2

Evaluate $4\times\left(\frac{5}{9}-\frac{5}{6}\right)$4×(5956), writing your answer in its simplest form.

So we can write our final answer as $\frac{-10}{9}$109 or $-1\frac{1}{9}$119.

Question 3

Evaluate $1\frac{8}{9}\times\left(-3\frac{1}{5}\right)\div\frac{8}{11}$189×(315)÷​811

QUESTION 4

Calculate $3+4-\left(-\frac{4}{5}\right)$3+4(45).

Outcomes

9D.NA2.01

Simplify numerical expressions involving integers and rational numbers, with and without the use of technology