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Problem solving with arithmetic procedures involving fractions

I can use my knowledge of arithmetic procedures involving fractions to solve problems.

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Lesson 10 of 10

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Year 7

Problem solving with arithmetic procedures involving fractions

I can use my knowledge of arithmetic procedures involving fractions to solve problems.

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Lesson details

Key learning points

When calculating with fractions and decimals, a common form can be easier.
A calculator removes the need for a common form.
The commutative law can be applied to make calculations easier.

Keywords

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

Common misconception

Incorrectly inputting a mixed number into the scientific calculator.

A mixed number has it's own separate button. Incorrectly inputting in the mixed number will return brackets on the calculator screen.

Some pupils will not have the Casio fx991 Classwiz, but still have a scientific calculator. Allow pupils to peer support one another to find the relevant functions and/buttons required for the lesson e.g mixed number button, standard <->decimal.

Teacher tip

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This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
Work out the answer to $$\frac{1}{3}+\frac{2}{5}$$.

$$\frac{2}{8}$$

$$\frac{3}{8}$$

$$\frac{10}{15}$$

Correct answer: $$\frac{11}{15}$$

$$\frac{1}{4}$$

Q2.
Work out the answer to $$\frac{6}{7}\times\frac{2}{3}$$.

$$\frac{8}{10}$$

$$\frac{4}{5}$$

$$\frac{32}{21}$$

Correct answer: $$\frac{4}{7}$$

Q3.
Work out the answer to $$\frac{2}{9}\div\frac{3}{4}$$.

Correct answer: $$\frac{8}{27}$$

$$\frac{27}{8}$$

$$\frac{6}{36}$$

$$\frac{1}{6}$$

Q4.
Match the calculation on the left with the answer on the right.

Correct Answer:$$\frac {\sqrt{25}}{9}$$,$$\frac{5}{9}$$

Correct Answer:$$\sqrt{\frac{25}{9}}$$,$$\frac{5}{3}$$

Correct Answer:$$\frac {25}{\sqrt{9}}$$,$$\frac{25}{3}$$

Correct Answer:$$\frac{5^2}{3^2}$$,$$\frac{25}{9}$$

Q5.
Work out the answer to $$1 + \sqrt{\frac{4}{9}}\times \frac{1}{2}$$.

$$\frac{3}{4}$$

Correct answer: $$\frac{4}{3}$$

$$\frac{11}{12}$$

$$\frac{1}{2}$$

Q6.
Without using a calculator, work out $$2 - \frac{1}{2} + \sqrt{\frac{25}{16}}$$.

$$\frac{4}{11}$$

Correct answer: $$\frac{11}{4}$$

$$\frac{13}{2}$$

$$\frac{4}{13}$$

$$\frac{13}{4}$$

Assessment exit quiz

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6 Questions

Q1.
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$$^2$$.

$$\frac{30}{28}$$ m$$^2$$

$$\frac{14}{11}$$ m$$^2$$

$$\frac{11}{14}$$ m$$^2$$

Correct answer: $$\frac{21}{40}$$ m$$^2$$

$$\frac{15}{14}$$ m$$^2$$

Q2.
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.

1.45 cm

145 cm

Correct answer: 290 cm

29 cm

300 cm

Q3.
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?

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.

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

Q4.
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?

£45.80

£39.50

£23.80

Correct answer: £38.40

£40

Q5.
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?

Correct Answer: 400

Q6.
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?

Correct Answer: 45, £45, £45.00

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UnitMaths / Arithmetic procedures with fractions

Maths

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Problem solving with arithmetic procedures involving fractions

Problem solving with arithmetic procedures involving fractions

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Work out the answer to $$\frac{1}{3}+\frac{2}{5}$$.

Q2.Work out the answer to $$\frac{6}{7}\times\frac{2}{3}$$.

Q3.Work out the answer to $$\frac{2}{9}\div\frac{3}{4}$$.

Q4.Match the calculation on the left with the answer on the right.

Q5.Work out the answer to $$1 + \sqrt{\frac{4}{9}}\times \frac{1}{2}$$.

Q6.Without using a calculator, work out $$2 - \frac{1}{2} + \sqrt{\frac{25}{16}}$$.

Assessment exit quiz

6 Questions

Q1.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$$^2$$.

Q2.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.

Q3.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?

Q4.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?

Q5.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?

Q6.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?

Lesson appears in

UnitMaths / Arithmetic procedures with fractions

Maths

Q1.
Work out the answer to $$\frac{1}{3}+\frac{2}{5}$$.

Q2.
Work out the answer to $$\frac{6}{7}\times\frac{2}{3}$$.

Q3.
Work out the answer to $$\frac{2}{9}\div\frac{3}{4}$$.

Q4.
Match the calculation on the left with the answer on the right.

Q5.
Work out the answer to $$1 + \sqrt{\frac{4}{9}}\times \frac{1}{2}$$.

Q6.
Without using a calculator, work out $$2 - \frac{1}{2} + \sqrt{\frac{25}{16}}$$.

Q1.
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$$^2$$.

Q2.
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.

Q3.
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?

Q4.
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?

Q5.
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?

Q6.
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?