A mixed number is an improper fraction written as its integer part plus the fractional part where the fractional part is a proper fraction.

Problem solving with arithmetic procedures involving fractions

Maths

Checking understanding of addition and subtraction with fractions

Securing understanding of addition and subtraction with fractions

Checking understanding of multiplication with fractions

Securing understanding of multiplication with fractions

Deepening understanding of multiplication with fractions

Checking and securing dividing a fraction by a whole number

Dividing a whole number by a fraction

Dividing a fraction by a fraction

Priority of operations with positive and negative integers, decimals and fractions

In this unit, pupils generalised and developed their fluency of multiplying with fractions. In the future unit, this understanding is extended to ratio and connections between ratios and fractions are explored.

In the prior unit, pupils explored the structure of fractions and their relationship with decimals and integers. In this unit, pupils deepen their understanding of the arithmetic procedures involving fractions and integers.

This unit revisits and secures fraction operations and extends pupil understanding to division of whole numbers by fractions and division of fractions by fractions.

Arithmetic procedures with fractions

A small, rectangular plot of dirt has length $$\frac{3}{4}$$ metres by $$\frac{7}{10}$$ metres. Work out the area of the plot of dirt in m$$^2$$.

Andeep wants to put an edging around a small, rectangular plot of dirt. It has length $$\frac{3}{4}$$ m by $$\frac{7}{10}$$ m. Work out the total length of the edging, giving your answer in cm.

Andeep says "Rounding, the area is $$6\times 3= 18$$ so $$18\times 20 = £360$$"

Sofia says "$$5.8\times2.9$$ so rounding gives $$6\times3=18$$. Andeep is right.

Jun says "$$\frac{29}{5}\times\frac{29}{10}=16{{41}\over{50}},17\times20=£340$$"

A plot of land measures $$5 {{4} \over {5}}$$ m by $$2 {{9} \over {10}}$$ m. It will cost £20 per m$$^2$$ to grass this plot of land. Who has correctly worked out the cost?

A square picture frame is made from wood with length $$\frac {4}{5}$$ m. Laura wants to put a metal trim around the picture. The trim cost £1.20 per 10 cm. How much will it cost to trim the frame?

A piece of farmland has an area of $${{3} \over {5}}\times1 {{2} \over {3}}$$ km$$^2$$. One sheep needs $$2500$$ m$$^2$$ of land for grazing. How many sheep can live on the farmland?

Aisha is restoring some old picture frames.  She wants to cover the frame in gold leaf. Gold leaf costs £1 per cm$$^2$$. How much will it cost Aisha to gold leaf the picture frame?

Work out the answer to $$\frac{1}{3}+\frac{2}{5}$$. 

Work out the answer to $$\frac{6}{7}\times\frac{2}{3}$$.

Work out the answer to $$\frac{2}{9}\div\frac{3}{4}$$.

Match the calculation on the left with the answer on the right.

Work out the answer to $$1 + \sqrt{\frac{4}{9}}\times \frac{1}{2}$$.

Without using a calculator, work out $$2 - \frac{1}{2} + \sqrt{\frac{25}{16}}$$. 

Problem solving with arithmetic procedures involving fractions

Lesson outcome