Problem solving with arithmetic procedures involving fractions | Maths

Starter quiz

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

$\frac{2}{8}$

$\frac{3}{8}$

$\frac{10}{15}$

$\frac{11}{15}$ ✓

$\frac{1}{4}$
Work out the answer to $\frac{6}{7}\times\frac{2}{3}$ .

$\frac{8}{10}$

$\frac{4}{5}$

$\frac{32}{21}$

$\frac{4}{7}$ ✓
Work out the answer to $\frac{2}{9}\div\frac{3}{4}$ .

$\frac{8}{27}$ ✓

$\frac{27}{8}$

$\frac{6}{36}$

$\frac{1}{6}$
Match the calculation on the left with the answer on the right.

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

⇔

$\frac{5}{9}$ ✓

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

⇔

$\frac{5}{3}$ ✓

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

⇔

$\frac{25}{3}$ ✓

$\frac{5^2}{3^2}$

⇔

$\frac{25}{9}$ ✓
Work out the answer to $1 + \sqrt{\frac{4}{9}}\times \frac{1}{2}$ .

$\frac{3}{4}$

$\frac{4}{3}$ ✓

2

$\frac{11}{12}$

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

$\frac{4}{11}$

$\frac{11}{4}$ ✓

$\frac{13}{2}$

$\frac{4}{13}$

$\frac{13}{4}$

Exit quiz

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 $^2$

$\frac{21}{40}$ m $^2$ ✓

$\frac{15}{14}$ 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.

1.45 cm

145 cm

290 cm ✓

29 cm

300 cm
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 $18\times 20 = \pounds360$ "

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

Jun says " $\frac{29}{5}\times\frac{29}{10}=16{{41}\over{50}},17\times20=\pounds340$ " ✓
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

£38.40 ✓

£40
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?

'400' ✓
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?

'45' ✓

Worksheet

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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.

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.

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.