Page 206 - Math Smart - 7

Reading and writing fractions
.
^
and
• A proper fraction has a numerator that is smaller than the denominator, for example |
.
• An improper fraction has a numerator that is greater than the denominator, for example |, y and ^
• A mixed number is a number that is made up of a whole number and a proper fraction.
The whole number is 1 *"1 ^ —The proper fraction is ^

Parts of a whole
of the shape is shaded

Equivalent fractions

Equivalent fractions are fractions that are equal in value even though their numerators
or denominators are not the same.

3 1
3
6 '
Simplest form
We simplify fractions by dividing the numerator and denominator by their highest common factor (HCF).

Converting between improper fractions and mixed numbers
A mixed number can be converted to an improper fraction, for example 3 ^ ^.

An improper fraction can be converted to a mixed number, for example 13 y

Comparing and ordering fractions
We compare and order fractions by first converting them to fractions with the same denominator.

Add or subtract fractions

if the fractions do not have the same denominator, express them as equivalent fractions with the same
denominators by finding the lowest common multiple (LCM) of their denominators. Then add or subtract
the numerators.
3 .i_24^_7__31 5I _ 2I -3^ - 2
5 40 " 40 40 ~ 40 ^3 ^2 ^6 6
7_ 24 _7_ 17
40 40 40 40
=^1
Fraction of a quantity
We divide the quantity by the denominator, then multiply by the numerator.
I of 24 sweets = 24 sweets -r 8 x 3 = 9 sweets

i i i i

Fractions