Fractions of numbers
In this topic you will
- Find half of an even number up to $20$.
- Find a quarter of $4$, $8$, $12$, $16$, and $20$.
- Explore how to add fractions.
Key Words
- denominator
- numerator
- visualise
Show Definitions
- denominator: The bottom number in a fraction that shows how many equal parts the whole is divided into.
- numerator: The top number in a fraction that shows how many parts are being counted.
- visualise: To form a mental picture of a mathematical idea, such as imagining how a shape or fraction looks.
Finding a fraction of a number is the same as dividing the whole by the denominator.
EXERCISES
Exercise $1.10$
$1$. Find the missing numbers.
a. $\frac{1}{2}$ of $10$$=$ ________
b. $14 \div 2$$=$ ________
c. $\frac{1}{2}$ of $8$$=$ ________
d. $\frac{1}{2}$ of $4$$=$ ________
e. $20 \div 2$$=$ ________
f. $\frac{1}{2}$ of $20$$=$ ________
👀 Show answer
a.$\frac{1}{2}$ of $10$$=$$5$
b.$14 \div 2 = 7$
c.$\frac{1}{2}$ of $8$$=$$4$
d.$\frac{1}{2}$ of $4$$=$$2$
e.$20 \div 2 = 10$
f.$\frac{1}{2}$ of $20$$=$$10$
$2$. Complete the halves table.
👀 Show answer
| $\text{Number}$ | $2$ | $4$ | $6$ | $8$ | $10$ | $12$ | $14$ | $16$ | $18$ | $20$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $\text{Half}$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
$3$. $12$ children made two equal teams.
How many children are in each team?
👀 Show answer
$12$ shared into $2$ equal teams is $12 \div 2 = 6$, so there are $6$ children in each team.
EXERCISES
$4$. Half of a number is $7$. What is the number?
👀 Show answer
If half is $7$, the whole is $7 \times 2 = 14$, so the number is $14$.
$5$. Find the missing numbers.
a. $\frac{1}{4}$ of $12$$=$ ________
b. $4 \div 4$$=$ ________
c. $\frac{1}{4}$ of $8$$=$ ________
d. $8 \div 4$$=$ ________
👀 Show answer
a.$\frac{1}{4}$ of $12$$=$$3$
b.$4 \div 4 = 1$
c.$\frac{1}{4}$ of $8$$=$$2$
d.$8 \div 4 = 2$
$6$. Marcus and his $3$ brothers shared a bag of $8$ apples equally.
a. How many apples did they each get?
b. What fraction of the whole did they each get?
👀 Show answer
a. There are $4$ people in total, so $8 \div 4 = 2$. Each person gets $2$ apples.
b. Each person gets $\frac{1}{4}$ of the apples.
$7$. A quarter of a number is $3$. What is the number?
👀 Show answer
If $\frac{1}{4}$ is $3$, then the whole is $3 \times 4 = 12$, so the number is $12$.
$8$. Complete the quarters table.
👀 Show answer
| $\text{Number}$ | $4$ | $8$ | $12$ | $16$ | $20$ |
|---|---|---|---|---|---|
| $\text{Quarter}$ | $1$ | $2$ | $3$ | $4$ | $5$ |
$9$. Tick the correct sentences.
$\frac{1}{2}$ of the children are girls.
$\frac{1}{4}$ of the children are boys.
Three quarters of the children are girls.
👀 Show answer
There are $4$ children in the picture: $3$ girls and $1$ boy.
So $\frac{3}{4}$ of the children are girls and $\frac{1}{4}$ of the children are boys.
Tick:$\frac{1}{4}$ of the children are boys. ✓ Three quarters of the children are girls. ✓
$10$. Find the missing fractions. Use the fractions of the square pictures to help you.
$\frac{1}{4} + \frac{1}{4} =$ ________
$\frac{1}{2} + \frac{1}{4} +$ ________ $= 1$
$\frac{1}{4} + \frac{1}{4} + \frac{1}{4} +$ ________ $= 1$
$\frac{2}{2} = \frac{1}{2} +$ ________
$\frac{4}{4} = \frac{1}{4} +$ ________ $+$ ________ $+$ ________
👀 Show answer
$\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$
$\frac{1}{2} + \frac{1}{4} + \frac{1}{4} = 1$
$\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = 1$
$\frac{2}{2} = \frac{1}{2} + \frac{1}{2}$
$\frac{4}{4} = \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4}$
Think like a Mathematician
Investigation: What do you think?
Statements:
- A quarter of the Colombia flag is red.
- No it isn’t. The red is not one of four equal pieces.
- I can visualise the $4$ quarters.
Method:
- Look carefully at the flag and decide whether the red part is exactly one quarter of the whole flag.
- Imagine splitting the flag into $4$ equal parts.
- Compare the size of the red section with one of those equal parts.
- Write down what you think and give a short reason.
Follow-up Questions:
👀 show answer
1.No. A quarter means $1$ out of $4$equal parts. On the Colombia flag, the red stripe is one of the horizontal stripes, but it is not one of four equal parts of the whole flag.
2. The red part is smaller than a quarter of the flag.
3. “A quarter” means the whole is divided into $4$ equal parts, and you take $1$ of those parts: $\frac{1}{4}$.
EXERCISES
$11$. Show that $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent using numbers.
👀 Show answer
$\frac{1}{2}$ means “divide by $2$”.
Take a number like $12$:
$\frac{1}{2}$ of $12$$= 12 \div 2 = 6$.
$\frac{2}{4}$ of $12$$= (12 \div 4)\times 2 = 3 \times 2 = 6$.
Both give $6$, so $\frac{1}{2} = \frac{2}{4}$.
$12$. Label each of the marks on the number line.
You could give more than one label to some marks.
👀 Show answer
The line from $0$ to $1$ is split into $4$ equal parts, so the marks are:
- First mark after $0$: $\frac{1}{4}$
- Second mark: $\frac{2}{4}$ and also $\frac{1}{2}$
- Third mark: $\frac{3}{4}$