Back to: Mathematics Primary 5
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A fraction is a number that can name a part of a whole or part of a set. A fraction is made up of two parts: a numerator and a denominator. It is used to represent how many parts we have out of the total number of parts. In a fraction, the numerator tells the number of equal parts. The denominator tells the number of equal parts in all.
The line in a fraction that separates the numerator and denominator can be rewritten using the division symbol.
So, to convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.
Example 1: Mario baked 8 treats on a tray. He fed two treats to his puppy. What fraction of the treats were eaten?
Number eaten 2
Number in the group 8
So, 2/8 of the treats were eaten.
MIXED FRACTION
A mixed number has a whole number part and a fraction part. An improper has a
numerator that is greater than or equal to its denominator.
| Mixed Fractions
11/2 23/4 35/6 |
Improper Fractions
3/2 11/4 23/6 |
23/4 is read as two and three-fourth OR two whole number and three-fourth.
35/6 is read as three and five-sixth OR three whole number and five-sixth.
How to convert mixed fractions to improper fractions
How to convert improper fractions to mixed fractions
- i) 23 23 ÷ 6 = 3 R 5
6
So, write as 35/6.
- ii) 37 37 ÷ 5 = 7 R 2
5
So, write as 7 2/5.
Converting From Fraction to Decimal
Method 1
If the fraction has 10, 100 or 1000 as the denominator, we can reverse the process we used to convert decimals to fractions.
You should already know that:
To convert 
to a decimal, we need to write 37 so that the last digit appears in the hundredths column, i.e. 0.37.
From this we can see that:
Method 2
If the fraction isn’t like the one above, we may be able to change it to an equivalent fraction which does
have 10, 100 or 1000 as the denominator. The fractions can then be converted in the same way as before.
⁴/₅ as a decimal is 4 ÷ 5 = 0.8
⁷⁵/₁₀₀ as a decimal is 75 ÷100 = 0.75
³/₆ as a decimal is 3 ÷ 6 = 0.5
Look at the examples below:
Converting Decimals to Fractions
In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps:
Step I: Obtain the decimal.
Step II: Remove the decimal points from the given decimal and take as numerator.
Step III: At the same time write in the denominator, as many zero or zeros to the right of 1(one) (For example 10, 100 or 1000 etc.) as there are number of digit or digits in the decimal part. And then simplify it.
We can express a decimal number as a fraction by keeping the given number as the numerator without a decimal point and writing 1 in the denominator followed by as many zeroes on the right as the number of decimal places in the given decimal number has.
For example:
(i) 124.6 = 124610124610
(ii) 12.46 = 12461001246100
(iii) 1.246 = 1246100012461000
In 0.7 we will change the decimal to fraction.
First we will write the decimal without the decimal point as the numerator.
Now in the denominator, write 1 followed by one zeros as there are 1 digit in the decimal part of the decimal number.
= 7/10
Therefore, we observe that 0.7 (decimal) is converted to 7/10 (fraction).
- Convert each of the following into fractions.
(i) 3.91
Solution:
3.91
Write the given decimal number without the decimal point as numerator.
In the denominator, write 1 followed by two zeros as there are 2 digits in the decimal part of the decimal number.
= 391/100
(ii) 2.017
Solution:
2.017
= 2.017/1
= 2.017 × 1000/1 × 1000 → In the denominator, write 1 followed by three zeros as there are 3 digits in the decimal part of the decimal number.
= 2017/1000
- Convert 0.0035 into fraction in the simplest form.
Solution:
0.0035
Write the given decimal number without the decimal point as numerator.
In the denominator, write 1 followed by four zeros to the right of 1 (one) as there are 4 decimal places in the given decimal number.
Now we will reduce the fraction 35/10000 and obtained to its lowest term or the simplest form.
= 7/2000
- Express the following decimals as fractions in lowest form:
(i) 0.05
Solution:
0.05
= 5/100 → Write the given decimal number without the decimal point as numerator.
In the denominator, write 1 followed by two zeros to the right of 1 (one) as there are 2 decimal places in the given decimal number.
= 5/100 ÷ 5/5 → Reduce the fraction obtained to its lowest term.
= 1/20
(ii) 3.75
Solution:
3.75
= 375/100 → Write the given decimal number without the decimal point as numerator.
In the denominator, write 1 followed by two zeros to the right of 1 (one) as there are 2 decimal places in the given decimal number.
= 375/100 ÷ 25/25 → Reduce the fraction obtained to its simplest form.
= 15/4
(iii) 0.004
Solution:
0.004
= 4/1000 → Write the given decimal number without the decimal point as numerator.
In the denominator, write 1 followed by three zeros to the right of 1 (one) as there are 3 decimal places in the given decimal number.
= 4/1000 ÷ 4/4 → Reduce the fraction obtained to its lowest term.
= 1/250
(iv) 5.066
Solution:
5.066
= 5066/1000 → Write the given decimal number without the decimal point as numerator.
In the denominator, write 1 followed by three zeros to the right of 1 (one) as there are 3 decimal places in the given decimal number.
= 5066/1000 ÷ 2/2 → Reduce the fraction obtained to its simplest form.
= 2533/500
CHANGING FRACTIONS TO PERCENTAGE
Exanmple:
Change the following fractions to percentage:
- 1
Solution
- 1 = change the mixed fraction to improper fraction.
=
Now multiply by 100.
=
=
= 125%
Multiply by 100.
=
=
= 80%
CHANGING DECIMALS TO PERCENTAGE
To change decimals to percentage, we also multiply by 100 or move the decimal point two times forward.
Example:
Change the following decimals to percentage:
- 653
- 758
- 023
- 4
Solution
- 653
Multiply by 100 by moving the decimal point two times forward.
= 1.653 100
= 165.3%
- 758
Multiply by 100 by moving the decimal point two times forward.
= 0.758 100
= 75.8%
- 023
Multiply by 100 by moving the decimal point two times forward.
= 0.023 100
= 2.3%
- 4
Multiply by 100 by moving the decimal point two times forward.
= 0.4 100
= 40%
Quiz
Change the following to improper fractions.
1) 11/5 2) 32/5 3) 53/4
4) 41/7 5) 7 5/9 6) 93/7
Change the following to mixed fractions.
7) 4/3 8) 15/4 9) 32/3
10) 40/6 11) 55/7 12) 82/9
Reduce the following to lowest terms.
13) 4/8 14) 12/30 15) 32/40
16) 25/60 17) 35/70 18) 48/90
Compare the fractions. Write >, <, or for each .
19) 7/8 4/8 20) 3/7 3/4 21) 3/9 2/4
22) 4/8 1/4 23) 2/6 1/3 24) 3/9 2/9
Order the fractions from least to greatest.
25) 1/4, 3/4, 2/4 26) 1/2, 1/3, 1/4 27) 2/6, 1/12, 3/4
28) 5/10, 4/5, 2/5 29) 3/4, 3/5, 2/4 30) 2/4, 2/7, 2/6
31) Sally’s dog ate 2 out of 6 dog treats. What fraction of the dog treats was left? Write the fraction in simplest form.
32) Raul drank 1/4 of 12 cans of orange juice. Basil drank the same amount of orange juice as Raul. Find an equivalent fraction to show the amount Basil drank.
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