Mixed numbers

Some lines on the number line were shorter than 1 unit and some were longer. Look at the fractions:

• When a fraction is less than 1, its numerator is smaller than its denominator (like 3/5). These are often called proper fractions.
• When a fraction is more than 1, its numerator is larger than its denominator (like 7/5 or 3/2). These are often called improper fractions.

We can see how many whole units such a fraction holds. 3/2 = 1/2 + 1/2 + 1/2 = 1 + 1/2, because two halves make one whole. 5/2 = 2 + 1/2. And 1/3 + 1/3 + 1/3 = 3/3 = 1, so 4/3 is one more third: 4/3 = 1 + 1/3, which is more than 1.

8/3 = 2 + 2/3. We call this 'two and two thirds' and write it 2 2/3 (a 2, then a space, then 2/3). This is a mixed number, also called a mixed fraction: it has a whole part (2) and a fractional part that is less than 1 (2/3). A quick way is to divide: for 8/6, 6 goes into 8 once with 2 left over, so 8/6 = 1 2/6: one whole and 2 sixths more.

Jaya shows how to go back from a mixed number to a fraction. 3 3/4 means 1 + 1 + 1 + 3/4. Each 1 is four quarters, so the three wholes are 4 + 4 + 4 = 12 quarters, and with 3 more quarters that makes 15 quarters: 3 3/4 = 15/4. The short way: multiply the whole part by the denominator and add the numerator. For 2 3/4: 2 × 4 + 3 = 11, so 2 3/4 = 11/4.