Fractions of numbers
🎯 In this topic you will
- Use fraction strips to find fractions of quantities and numbers
- Find fractions of numbers
- Solve simple fraction problems
🧠 Key Words
- denominator
- diagram
- dividing line
- non-unit fraction
- numerator
- unit fraction
Show Definitions
- denominator: The bottom number in a fraction that shows how many equal parts the whole is divided into.
- diagram: A drawing or model used to help show and understand a mathematical idea.
- dividing line: The horizontal or slanted line in a fraction that separates the numerator from the denominator.
- non-unit fraction: A fraction where the numerator is greater than 1, such as 3/5.
- numerator: The top number in a fraction that tells how many parts are being considered.
- unit fraction: A fraction with numerator 1, such as 1/4, showing one equal part of a whole.
📏 Finding a Fraction of a Number
Y ou can use a paper strip or a 2D shape such as a mat to help you find a fraction of a number. Finding a fraction works in the same way as division. When you split a whole into equal groups, each group represents a fraction of the whole.
❓ EXERCISES
$1.$ A fraction strip is $15$ cm long. Majak is marking thirds on the strip.
a. Where should he mark $\dfrac{1}{3}$? At ___ cm.
b. Where should he mark $\dfrac{2}{3}$? At ___ cm.
👀 Show answer
a. $\dfrac{1}{3}$ is at $5$ cm.
b. $\dfrac{2}{3}$ is at $10$ cm.
$2.$ A fraction strip has fifths marked at $5$ cm, $10$ cm, $15$ cm and $20$ cm. How long is the fraction strip?
👀 Show answer
$3.$
a. Draw a ring around $\dfrac{1}{10}$ of the marbles.
b. What fraction of the marbles are not ringed?
👀 Show answer
a. $\dfrac{1}{10}$ of $20$ is $2$ marbles.
b. $18$ marbles are not ringed, which is $\dfrac{18}{20} = \dfrac{9}{10}$.
$4.$ Here is $\dfrac{1}{3}$ of a set of cars. How many cars are in the whole set?
👀 Show answer
$5.$ Find these fractions of $20$.
👀 Show answer
$\dfrac{1}{3}$ of $20$ is $\dfrac{20}{3}$
$\dfrac{1}{4}$ of $20$ is $5$
$\dfrac{1}{5}$ of $20$ is $4$
$\dfrac{1}{10}$ of $20$ is $2$
$\dfrac{3}{4}$ of $20$ is $15$
$6.$ In the table below, what is the whole?
👀 Show answer
🧠 Think like a Mathematician
Task: Find a number that you can complete the whole table for.
The table uses these fractions:
👀 show answer
- A convenient whole number is $60$ (it is divisible by $2$, $3$, $4$, and $10$).
- $\dfrac{1}{2}$ of $60$ is $30$
- $\dfrac{1}{3}$ of $60$ is $20$
- $\dfrac{1}{4}$ of $60$ is $15$
- $\dfrac{1}{10}$ of $60$ is $6$
- $\dfrac{3}{4}$ of $60$ is $45$
So the completed row would be: $30,\;20,\;15,\;15,\;6,\;45$.
❓ EXERCISES
$7$. Find each fraction and complete the matching division calculation.
a. $\frac{1}{4}$ of $8$ = $\square$, $8 \div \square = \square$
b. $\frac{1}{5}$ of $5$ = $\square$, $5 \div \square = \square$
c. $\frac{1}{3}$ of $24$ = $\square$, $24 \div \square = \square$
d. $\frac{1}{10}$ of $90$ = $\square$, $90 \div \square = \square$
👀 Show answer
a. $\frac{1}{4}$ of $8$ = $2$, so $8 \div 4 = 2$.
b. $\frac{1}{5}$ of $5$ = $1$, so $5 \div 5 = 1$.
c. $\frac{1}{3}$ of $24$ = $8$, so $24 \div 3 = 8$.
d. $\frac{1}{10}$ of $90$ = $9$, so $90 \div 10 = 9$.
$8$.
a. Continue the pattern to $10$.
$\frac{1}{4}$ of $4$ = $1$, $4 \div 4 = 1$
$\frac{1}{4}$ of $8$ = $2$, $8 \div 4 = 2$
$\frac{1}{4}$ of $12$ =
$\frac{1}{4}$ of $16$ =
b. What do you notice?
👀 Show answer
a.
$\frac{1}{4}$ of $12$ = $3$, $12 \div 4 = 3$
$\frac{1}{4}$ of $16$ = $4$, $16 \div 4 = 4$
$\frac{1}{4}$ of $20$ = $5$, $20 \div 4 = 5$
$\frac{1}{4}$ of $24$ = $6$, $24 \div 4 = 6$
$\frac{1}{4}$ of $28$ = $7$, $28 \div 4 = 7$
$\frac{1}{4}$ of $32$ = $8$, $32 \div 4 = 8$
$\frac{1}{4}$ of $36$ = $9$, $36 \div 4 = 9$
$\frac{1}{4}$ of $40$ = $10$, $40 \div 4 = 10$
b. Finding $\frac{1}{4}$ of a number is the same as dividing by $4$. Each time the number goes up by $4$, the answer goes up by $1$.
$9$. At a party, the sandwiches have been cut into quarters. Four people share two sandwiches. How much do they get each?
👀 Show answer
Each sandwich is cut into $4$ quarters, so $2$ sandwiches make $8$ quarters. Shared between $4$ people: $8 \div 4 = 2$ quarters each, which is $\frac{1}{2}$ of a sandwich.
$10$. There are four apples in a pack. Roshni takes one apple. What fraction of the apples does she take?
👀 Show answer
She takes $1$ apple out of $4$, so the fraction is $\frac{1}{4}$.