Finding third, quarter and half | Year 4 Mathematics PDF Download

What is a fraction?

• A fraction indicates how many parts of a whole you possess. Fractions are represented with one number above another, such as:
  
• There are two parts to a fraction:
  • The top number, known as the numerator, indicates how many parts you have (1 in this instance, making it a unit fraction).
  • The bottom number, referred to as the denominator, indicates into how many equal parts something has been divided (4 in this instance).

What is a quarter?

A quarter or 1/4 means '1 part of something that has been divided into 4 equal parts'.
If you add four quarters together you get one whole.

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Finding a quarter of an amount

• When calculating a quarter of an amount, you divide it by 4.
• For larger numbers, instead of drawing an array, you can use your knowledge of the 4 times table.
• Another method is to first find half and then half again, as a quarter is half of a half.

Examples

Example 1: What is quarter of 32?
How many 4s are in 32?
32 ÷ 4 = 8
We can double check the answer with the halving method.
1/2 of 32 is 16
1/2 of 16 is 8
You get the same answer: 8.

Example 2: Billy has 1/4 of 48 sweets. Hassan has 1/2 of 24. Who has the most sweets?
First, work out the amount of sweets both boys have.
Billy has 1/4 of 48.
48 ÷ 4 = 12
Hassan has 1/2 of 24.
24 ÷ 2 = 12
So both boys have the same number of sweets.

What is a third?

• A third is a fraction. A fraction indicates how many parts of a whole you have. Fractions are written by placing one number above another.
• Here is a third written as a fraction:
  
• As you can see, a fraction has two parts.
• The top number, called the numerator, shows how many parts you have. It represents the parts you have and is 1 in this example.
• The bottom number is called the denominator. It shows into how many equal parts the whole is divided. For a third, this number is 3.
• A third, or 1/3, means '1 part of something divided into three equal parts'.
• If you add three thirds together, you get a whole:
  

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Examples

Example 1: What is a third of 66?
Sol: You could also use Base 10 to help you.
Here is 66 in Base 10:
You can see that there are 6 tens and 6 ones. You can divide this into three groups, with 2 tens and 2 ones in each group:
A third of 66 is 22.

Example 2: What is a third of 36?
Sol: Working out a third of a whole is the same as dividing by 3.
Your three times table knowledge can come in handy:
36 ÷ 3 = 12
A third of 36 is 12.

What is a fraction?

• A fraction indicates how many parts of a whole you have. Fractions are represented with one number above another, such as:
  
• There are two parts to a fraction:
  • The top number, known as the numerator, indicates how many parts you have (1 in this case).
  • The bottom number, known as the denominator, indicates into how many equal parts something is divided (2 in this case).
    

What is a half?

• A half, denoted as 1/2, represents one part of a whole that has been divided into two equal parts. 
• If you add two halves together you get one whole.
  

Finding half of an amount

• Method: To find half of a number, you divide it by 2.
• Using Multiplication: Instead of drawing arrays for larger numbers, you can utilize your knowledge of the 2 times-table.

Examples

Example 1: What is half of 22
How many 2s are in 22?
22 ÷ 2 = 11

Example 2: What is half of 62?
You can use Base 10 to help you again.

Now share the sticks and cubes into two equal groups:
Half of 64 is 32.