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.