Grade 7 Mathematics Revision Notes

Grade 7 Mathematics Revision Notes

Grade 7 Mathematics Revision Notes

FRACTIONS

PROPER AND IMPROPER FRACTIONS
A fraction is a portion of a whole that has been divided into equal parts.

A common fraction is written as ½ or ¼ or ¾.

The number at the top represents a whole number called the numerator and the number at the bottom represents a whole number called the denominator.

In proper fractions, the numerator of the fraction is smaller than the denominator.
In improper fractions, the numerator of the fraction is bigger than the denominator.

MIXED NUMBERS
Sometimes we write an improper fraction as a mixed number, for example:

We would write 8/5 as 1 3/5
The mixed number has a whole number part and a fraction part.

CONVERTING FRACTIONS
To convert an improper fraction to a mixed number, simply divide the number by the denominator:

Example:

12/5 = 12 ÷ 5 = 2 r 2

We write this as 2 2/5

To convert a mixed number to an improper fraction, multiply the whole number by the denominator. Add the numerator to this. Write this answer as the numerator and keep the denominator the same.

Examples:
8 ½ = Multiply 8 by 2, and then add 1
This will give you a total of 17
The improper fraction will therefore be 17/2

Exercise 12

  1. Convert the improper fractions to mixed numbers:
    41/9 316/3 199/10 412/15 1000/125
  2. Convert the mixed numbers to improper fractions:
    132/3; 178/11; 43/7; 64/15; 97/12

Equivalent fractions

efraction dvaugda

SIMPLIFYING FRACTIONS
To simplify a fraction, you must reduce the fraction to its smallest form.
To do this, you need to divide both the numerator and the denominator by the same highest common factor.

Example:12/30 = ∗
The highest number that can fit into both 12 and 30 is 6.
6 is therefore the highest common factor (HCF)
Divide the numerator and denominator by the highest common factor.

e.g. 12/30÷ 6/6 = 2/5
SO: 12/30= 2/5

NB: A common fraction must always be written in the simplest form!

Exercise 13

  1. Equivalent fractions
    1. 30/35 = ∗/7
    2. 11/44 = 1/∗
    3. 63/90 = 7/∗
    4. 9/11 = 99/∗
  2. Simplifying fractions
    1890 ; 325/45 ; 946/112 ; 524/60