FRACTIONS

In the fraction 3/4, 3 is the numerator and 4 is the denominator.
 
Proper Fraction

The numerator is less than the denominator, example 2/3, 4/5, 7/12, 13/20.
 
 Improper Fraction

The numerator is greater than the denominator, example 5/2, 7/3, 11/8, 19/10.
 
Mixed Number

It is made up of a whole number and a fraction, example 1 1/4, 2 3/5, 5 7/8, 7 11/12.
 
Equivalent Fraction

If we multiply or divide the numerator and denominator of a fraction by the same number, we get the equivalent fraction. 

Examples:

1 = 1 x 2 = 2 
2    2 x 2     4

6 = 6 x 3 = 18
8    8 x 3     24

16 = 16 ÷ 8 = 2
24    24 ÷ 8    3

Equivalent fractions are sets of fractions which are equal in value. When both the numerator and denominator of a fraction cannot be further divided by the same number, it is in its lowest terms or simplest form, 

example 2/3, 1/5, 3/8, 11/12.
 
 

Addition and Subtraction of Fractions

Points to remember:

  1. Express all fractions in the same denominator or find the L.C.M of the denominator.
  2. Add or subtract the whole numbers and fractions.
  3. Give the answers in the lowest terms.

Examples:

  1. Simplify 21/3 – 3 7/12 + 2 3/4
    2. 21/3 – 3 7/12 + 2 3/4
    = 2 4/12 – 3 7/12 + 2 9/12 Express fractions in the same denominator.
    = 1 6/10 Add / subtract the whole numbers and fractions.
    = 1 3/5 Reduce to lowest terms.
  2. Simplify 4 1/10 – 2 3/5.
4 1/10 – 2 3/5
= 4 1/10 – 2 6/10 Change 2 3/5 to 2 6/10.
= 3 11/10 – 2 6/10 Change 4 1/10 to 3 11/10.
= 1 5/10 Subtract the whole numbers and fractions.
= 1 1/2 Reduce to lowest terms.


 

Multiplication of Fractions

Points to remember:

  1. Change mixed numbers to improper fractions.
  2. Reduce to the lowest terms by cancelling where possible.
  3. Multiply the numerators together, then the denominators.
  4. Answers should be given in mixed numbers or fractions in the lowest terms.

Example: Simplify 2 1/6 x 2 2/5.

2 1/6 x 2 2/5
= 13/6 x 12/5 Change to improper fractions.
= 13/6 x 12/5 Reduce the numerator and the denominator to the lowest terms by dividing with the same number.
= 26/5 Multiply the numerators, then the denominators.
= 5 1/5 Express answer in mixed numbers.

 

Division of Fractions

Points to remember:

  1. Change mixed numbers to improper fractions.
  2. Invert the divisor.
  3. Reduce to the lowest terms by cancelling where possible.
  4. Multiply the numerators together, then the denominators.
  5. Answers should be given in mixed numbers or fractions in the lowest terms.

Example: Simplify 5 1/2 ÷ 3 1/7.

5 1/2 ÷ 3 1/7
= 11/2÷ 22/7 Change to improper fractions.
= 11/2 x 7/22 Change ÷ to x and invert the divisor.
= 11/2 x 7/22 Reduce the numerator and the denominator to the lowest terms by dividing with the same number.
= 7/4 Multiply the numerators, then the denominators.
= 1 3/4 Express answer in mixed numbers.


 

Application of the Four Rules in Fractions

Follow these steps:

  1. Simplify terms within the brackets first.
  2. Next, do the multiplication and division (work from left to right).
  3. Finally, do the addition and subtraction.

Example: Simplify 3/4 x (5/6 – 1/3) + 15/16.

3/4 x (5/6 – 1/3) + 15/16
= 3/4 x (5/6 – 2/6) + 15/16
= 3/4 x 1/2 + 15/16 Simplify terms within the brackets.
= 3/4 x 1/2 + 15/16 Do the multiplication.
= 3/8 + 15/16 Do the addition.
= 6/16 + 15/16
= 21/16
= 1 5/16 Change to mixed numbers.

 

Expressing One Quantity as a Fraction of Another Quantity

Both quantities must be expressed in the same unit.

Examples:

  1. Express 60 cm as a fraction of 2 m.

    Fraction = 60 cm
                      2 m
    = 60 cm                Express in the same unit.
       200 cm 

    = 3/10
     

  2. Express 25 min as a fraction of 1 h.

    Fraction = 25 min
                        1 h

    = 25 min                    Express in the same unit.
       60 min

    = 5/12

  3. Express 500 g as a fraction of 2 kg.

    Fraction = 500 g
                      2 kg

    = 500 g                       Express in the same unit.
       2000 g

    = 1/4

Problems on Fractions

Examples:

  1. When Mr Huang had travelled 45 km, he had gone 5/7 of his way. How many more kilometres did he have to travel to complete his journey? 
      fractn1.jpg (28466 bytes)

    5/7 of the journey = 45 km

    1/7 of the journey = 45/5 = 9 km

    1 – 5/7 = 2/7

    He had to travel 2/7 of the journey.

    2/7 of the journey = 2 x 9 = 18 km.
     
    Mr Huang had to travel 18 km more.
     
     

  2. Leela spent 3/8 of her money on a dictionary, 1/4 of it on a pen and 1/8 of it on a magazine. She had $16 left. How much did she have at first?

    fractn2.jpg (52049 bytes)

    3/8 + 1/4 +1/8 + 6/8 = 3/4

    Leela spent 3/4 of her money altogether.

    1 – 3/4 = 1/4

    She had 1/4 of her money left.

    1/4 of her money = $16

    4/4 of her money = 4 x $16 = $64

    Leela had $64 at first.
      
     

  3. Henry spent 2/5 of his money on a pair of shoes and 1/3 of the remaining money on a shirt. If he had $75 left, how much did he have to start with?
    fractn3.jpg (56149 bytes)
    1 – 2/5 = 3/5

    He had 3/5 of the money left after buying shoes.

1/3 x 3/5 = 1/5

1/3 of the remaining money = 1/5

1 – (2/5 + 1/5) = 2/5

He had 2/5 of his money left.

2/5 of the money = $75

1/5 of the money = $75/2

= $37.50

5/5 of the money = 5 x $37.50

= $187.50

Henry had $187.50 to start with.