Order of operations with fractions II
In the chapter Maths in Order, we saw that some operations need to be completed before others.
The order goes:
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.