3.7

Finding equivalent
fractions and simplifying
fractions

3.8

Common denomination:
more adding and
subtracting

3.9

Multiplying and dividing
fractions by a whole
number 

3.10

Linking fractions, decimals
and percentages

Teaching point 1: When two fractions have different numerators and denominators to one another but share the same numerical value, they are
called ‘equivalent fractions’.

Teaching point 2: Equivalent fractions share the same proportional (multiplicative) relationship between the numerator and denominator.
Equivalent fractions can be generated by maintaining that relationship through the process of multiplication and division.

Teaching point 3: Fractions can be simplified by dividing both the numerator and denominator by a common factor.

Teaching point 1: In order to add related fractions, first convert one fraction so that both share the same denominator (a ‘common denominator’).

Teaching point 2: To subtract related fractions, first convert one fraction so that both share a common denominator.

Teaching point 3: The common denominator method can be extended to adding and subtracting non unit related fractions.

Teaching point 4: To add and subtract non-related fractions, the product of the two denominators provides a common denominator.

Teaching point 5: Converting to common denominators is one of several methods that can be used to compare fractions.

Teaching point 1: When a fraction is multiplied by a proper fraction, it makes it smaller. To multiply two fractions, multiply the numerators and
multiply the denominators.

Teaching point 2: When a fraction is divided by a whole number, it makes it smaller. To divide a fraction by a whole number, convert it to an
equivalent multiplication.

Teaching point 3: A more efficient method can be used to divide a fraction by a whole number when the whole number is a factor of the
numerato

Teaching point 1: Some fractions are easily converted to decimals.
Teaching point 2: These fraction–decimal equivalents can be found throughout the number system.
Teaching point 3: Fraction–decimal equivalence can sometimes be used to simplify calculations.
Teaching point 4: ‘Percent’ means number of parts per hundred. A percentage can be an operator on a quantity, indicating the proportion of a
quantity being considered.
Teaching point 5: Percentages have fraction and decimal equivalents.
Teaching point 6: If the value of a whole is known, a percentage of that number or amount can be calculated.