Fractions

Ontario 09 Academic (MPM1D)

Order of operations with fractions

Lesson

In the chapter Math 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.

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

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

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

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