# Fractions

A fraction represents parts of a collection, the numerator being the number of parts we have and the denominator being the total number of parts in the collection

If we want to find one third of a number, we can do it by dividing with number 3.

For example, 1/3 of 15 and 15 ÷ 3 could both be modelled using 15 counters partitioned into 5 equal groups of 3. The mathematical relations suggested by the five equal groups of 3 counters are:

3x5=115

15/3 =5

1/3 of 15 = 5

Working with fractions based on the data collected is based on a sound knowledge of factors and multiples.

Using arrays and area grids strengthens the relationships between multiplication, division and fractions, by making the inverse relations more apparent. An array of 15 and a grid of 15.

3x5 = 15                                             5x3 = 15

15/3 = 5                                              15/5 = 3

1/3 of 15 = 5                                      1/5 of 15 = 3

Fractions also appear in whole number division with remainders.

For example, 13 of 13 (or 13 ÷ 3)  results in 4 with 1 as the remainder. The remainder 1 can be partitioned into three equal parts and the sharing process continued, leading to the mixed-number answer 413. Demonstration:

Q 1: 3/4 of 12 = • 8
• 9
• 10