Finding a fraction of a number or quantity

Vocabulary, suggested resources and teaching ideas for a lesson on using a calculator and mental methods to find a fraction of numbers of quantities.

Vocabulary:

• fraction
• decimal fraction
• numerator
• denominator

Resources:

• calculators
• whiteboards

Teaching ideas for guided activities

Write some fractions on the board, e.g. $\frac{1}{2}$, $\frac{1}{4}$, $\frac{2}{5}$, $\frac{1}{10}$, $\frac{3}{8}$.

Q: Do you know how to write any of these fractions as decimals?

Remind the children that:

• $\frac{1}{2}=0.5$
• $\frac{1}{10}=0.1$
• 0.5 and 0.1 are called decimal fractions.

Q: How can you use a calculator to show that $\frac{1}{2}=0.5$ and that $\frac{1}{10}=0.1$?

Give out calculators. Establish that $\frac{1}{2}$ means 1 divided by 2 and use a calculator to demonstrate this. Repeat for $\frac{1}{10}$.

Q: How do you convert $\frac{3}{8}$ to a decimal fraction?

Ask children to work out the equivalent decimal fraction using a calculator. Collect their responses and then ask them to use their calculator to work out the decimal fraction equivalent of $\frac{7}{16}$.

Repeat for different fractions.

Q: What is half of 40? What did you divide by to get the answer?

Repeat this by asking: What is $\frac{1}{3}\text{of}90$?, What is $\frac{1}{4}\text{of}80$? and What is $\frac{1}{10}\text{of}700$?

Establish that when finding a unit fraction you divide by the denominator.

Q: If $\frac{1}{4}\text{of}80$ is 20, what is $\frac{3}{4}\text{of}80$?

Establish that you multiply 20 by the numerator, 3, to get 60.

Q: What is $\frac{3}{10}\text{of}250$?

Ask the children to find one tenth ($250÷10=25$) and then three tenths($25\times 3=75$).

Record this on the board as:

• (Find $\frac{1}{10}$) $250÷10=25$
• (Find $\frac{3}{10}$) $25\times 3=75$

Write 680 on the board. Ask the children to find $\frac{1}{10}$ mentally and then to use their calculator to work out $\frac{1}{10}$, $\frac{4}{10}$, $\frac{9}{10}$, $\frac{3}{10}\text{of}680$, recording their method and answers on whiteboards. Discuss the calculations the children did mentally and those they did using a calculator.

Q: How can you find $\frac{5}{6}\text{of}300$?

Establish that this can be done first by finding $\frac{1}{6}\text{of}300$, and then multiplying this answer by 5 to find $\frac{5}{6}$.

Record as:

• (Find $\frac{1}{6}$) $300÷6=50$
• (Find $\frac{5}{6}$) $50\times 5=250$.

Set other questions and get the children to use a mix of mental and calculator methods.

Q: How can you find $\frac{4}{7}\text{of}490\mathrm{kg}$?

Take children’s responses and show how this can be written as one calculation: $\left(490÷7\right)\times 4=280$

Highlight the need to include the units in the answer.

Ask the children to now work out $\frac{2}{7}\text{of}490\mathrm{kg}$.

Write down:

• $\frac{1}{7}\text{of}490\mathrm{kg}=70\mathrm{kg}$
• $\frac{2}{7}\text{of}490\mathrm{kg}=140\mathrm{kg}$
• $\frac{4}{7}\text{of}490\mathrm{kg}=280\mathrm{kg}$

Q: What do the answers add up to?

Remind the children that they have found $1+2+4$ sevenths altogether; this is seven sevenths, and the total is 490 kg.

Remember:

• You find a fraction of a number or quantity by first dividing the quantity by the denominator and then multiplying by the numerator.
• Always include units in your answer.