Fractions of shapes
In this topic you will
- Explain how fractions can represent division.
- Recognise and use quarters and three-quarters.
- Divide shapes into equal parts.
Key Words
- equal parts
- fraction
- quarter
- three-quarters
Show Definitions
- equal parts: Sections of a whole that are exactly the same size and shape.
- fraction: A number that represents part of a whole, often written using two numbers with one above the other.
- quarter: One of four equal parts of a whole, written as $\frac{1}{4}$.
- three-quarters: Three out of four equal parts of a whole, written as $\frac{3}{4}$.
Fractions in real life
Fractions are useful in cooking, making and building objects or houses and even sharing a pizza fairly.
Equal parts and unequal parts
Looking at fractions as being equal parts of a whole will help you to understand the difference between equal parts and unequal parts.
EXERCISES
$1$. Here are $4$ squares.
Use a ruler to draw straight lines to show $2$ squares divided into halves and $2$ squares that are divided into $2$ parts but not halves.
Label the squares $\frac{1}{2}$ or not $\frac{1}{2}$.
👀 Show answer
A square is $\frac{1}{2}$ only if it is split into $2$equal parts.
For the $\frac{1}{2}$ squares: draw a straight line exactly through the middle (for example, a vertical line down the centre or a diagonal corner-to-corner line). Label each of these squares $\frac{1}{2}$.
For the not $\frac{1}{2}$ squares: draw a straight line that makes $2$unequal parts (one part bigger than the other). Label each of these squares not $\frac{1}{2}$.
$2$. Four boys share a pizza equally.
How much pizza does each boy have?
Draw what $1$ boy has.
👀 Show answer
Sharing equally between $4$ boys means the pizza is split into $4$ equal parts.
Each boy gets $\frac{1}{4}$ of the pizza. (Draw one quarter slice.)
$3$. Four girls share a pie equally.
How much pie does each girl have?
Draw what $2$ girls have.
👀 Show answer
Sharing equally between $4$ girls means the pie is split into $4$ equal parts.
Each girl gets $\frac{1}{4}$ of the pie.
So $2$ girls have $\frac{2}{4}$, which is the same as $\frac{1}{2}$. (Draw half of the pie.)
$4$. Four children share a large cookie equally.
$1$ child eats their piece now.
How many quarters are left? ________
👀 Show answer
There are $4$ quarters in total. If $1$ quarter is eaten, then $3$ quarters are left.
$5$. $4$ boys share this bar of chocolate equally.
How many squares does each boy have?
👀 Show answer
Count the squares in the bar: there are $28$ squares.
Shared equally between $4$ boys: $28 \div 4 = 7$. Each boy has $7$ squares.
$6$.
a. Draw lines to show quarters of these shapes.
Colour one quarter of each shape.
How much of the shape is not coloured? ________
b. Draw lines to show quarters of these shapes.
Colour three-quarters of each shape.
How many quarters are not coloured? ________
👀 Show answer
a. If one quarter is coloured, then the part not coloured is $\frac{3}{4}$.
b. If three-quarters are coloured, then the number of quarters not coloured is $1$ quarter.
Think like a Mathematician
Let’s investigate
Work on your own.
This is three-quarters of a shape.
What could the whole shape be?
Use blocks or cubes to make your shapes.
Draw your shapes.
Tip: Remember $4$ quarters make a whole.
👀 show answer
Three-quarters means you have $\frac{3}{4}$ of the whole, so the whole must be made from $4$ equal quarters.
So you need to add $1$ more quarter (one more same-sized piece) to make the complete shape.
Example whole shapes (many answers are possible):
- Make a $2 \times 2$ square of $4$ cubes by adding one cube in the missing corner.
- Make a straight line of $4$ cubes by adding one cube to the end.
- Make a different $4$-cube shape (any arrangement of $4$ cubes), as long as the $3$ cubes shown could be part of it.