Before you start
Use equal parts, simple diagrams and ten worked exercises to understand primary fractions. A free workbook for practice at home.
Divide into equal parts
A fraction describes equal parts of a whole. In 3/4, the denominator 4 tells you how many equal parts make the whole, and the numerator 3 tells you how many are selected. Unequal pieces cannot simply be counted as a fraction.
| Notation | How to read it |
|---|---|
| 1/2 | One half |
| 1/4 | One quarter |
| 3/4 | Three quarters |
Your turn
Draw a rectangle, split it into four equal parts and shade one part. What fraction is shaded?
Compare using the same whole
Two fractions can represent the same amount: 1/2 = 2/4. Use two same-sized rectangles to check. With the same denominator, compare numerators. With the same numerator, dividing the same whole into more pieces makes each piece smaller.
Before calculating
Draw two identical rectangles. Shade 1/2 of the first and 2/4 of the second. Compare the shaded areas.
Check the answers
The shaded areas are equal. The number of pieces changes, but the amount does not.
Ten short exercises
| No. | Question |
|---|---|
| 1 | One of two equal parts is selected. Write the fraction. |
| 2 | Three of eight equal parts are selected. Write the fraction. |
| 3 | What is the denominator in 5/6? |
| 4 | What is the numerator in 5/6? |
| 5 | 1/2 = ?/4 |
| 6 | 2/6 = ?/3 |
| 7 | Compare 3/8 and 5/8. |
| 8 | Compare 1/3 and 1/6 using the same whole. |
| 9 | How many objects are half of 10? |
| 10 | How many objects are one quarter of 12? |
My answers
Write the answers in order, then explain one answer with a drawing.
Check your answers
| No. | Answer and explanation |
|---|---|
| 1 | 1/2 |
| 2 | 3/8 |
| 3 | 6: the number of equal parts. |
| 4 | 5: the number of selected parts. |
| 5 | 1/2 = 2/4 |
| 6 | 2/6 = 1/3 |
| 7 | 3/8 < 5/8 |
| 8 | 1/3 > 1/6 |
| 9 | 5 objects, because 10 ÷ 2 = 5. |
| 10 | 3 objects, because 12 ÷ 4 = 3. |
To help a child, ask them to show the parts rather than recite a rule. If they make a mistake, return to the same drawing and check that the parts are equal. Then try one example with different numbers.
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