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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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New
New
Year 7

Problem solving with arithmetic procedures involving fractions

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

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. When calculating with fractions and decimals, a common form can be easier.
  2. A calculator removes the need for a common form.
  3. 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

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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

$$\frac{5}{9}$$

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

$$\frac{5}{3}$$

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

$$\frac{25}{3}$$

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

$$\frac{25}{9}$$

Q5.
Work out the answer to $$1 + \sqrt{\frac{4}{9}}\times \frac{1}{2}$$.
$$\frac{3}{4}$$
Correct answer: $$\frac{4}{3}$$
2
$$\frac{11}{12}$$
$$\frac{1}{2}$$
Q6.
Without using a calculator, work out $$2 - \frac{1}{2} + \sqrt{\frac{25}{16}}$$.
$$\frac{4}{11}$$
Correct answer: $$\frac{11}{4}$$
$$\frac{13}{2}$$
$$\frac{4}{13}$$
$$\frac{13}{4}$$

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?
An image in a quiz
Correct Answer: 45, £45, £45.00