UK Secondary (7-11)
Order of Operations with Fractions II
Lesson

In the chapter Maths in Order, we saw that some operations need to be completed before others.

The order goes:

Order of operations

Step 1: Do operations inside grouping symbols such as parentheses (...), brackets [...] and braces {...}.

With fractions, the numerator and denominator are in unwritten brackets, so we work with these first.

Step 2: Do multiplication (including powers) and division (including roots) going from left to right.

Step 3: Do addition and subtraction going from left to right.

These rules apply to all of mathematics, yes - even fractions! So order of operations with fractions is just following the normal order of operations, with fractions in the picture.

#### Worked Examples

##### QUESTION 1

Evaluate $5\times\left(\frac{3}{2}+\frac{2}{7}\right)$5×(32+27), writing your answer in its simplest form.

##### QUESTION 2

Evaluate $4\frac{5}{9}\times3\frac{4}{9}\div\frac{3}{5}$459×349÷​35, writing your answer in its simplest form.

##### QUESTION 3

Evaluate $\frac{3}{4}\times\left(\frac{10}{9}+\frac{4}{3}\right)$34×(109+43), writing your answer in its simplest form.