Primary 3 Fractions
Use equal-sized wholes to see equivalent fractions, change fractions to simplest form, compare and order unlike fractions, and add or subtract related fractions within one whole.
Keywords
- Whole
- The complete object or amount being divided.
- Numerator
- The top number: how many equal parts are chosen.
- Denominator
- The bottom number: how many equal parts make one whole.
- Equivalent fractions
- Different fraction names for the same amount.
- Simplest form
- An equivalent fraction whose numerator and denominator have no common factor greater than 1.
- Unlike fractions
- Fractions with different denominators.
- Related fractions
- Fractions whose denominators are related by a whole-number multiple.
Equivalent fractions
Equivalent fractions name the same amount of the same whole. Multiply the numerator and denominator by the same number, or split every part equally, to make a new name for the same shaded length.
Choose an equivalent pair
Shade 1 of 2 equal parts on the first strip.
See worked example
Show that 2/3 and 4/6 are equivalent.
- Shade 2 of 3 equal parts on one strip.
- Split each third into 2 equal parts. There are now 6 parts in all and 4 shaded parts.
- The shaded length stayed the same: 2/3 = 4/6.
Answer: 2/3 = 4/6.
Try together
Complete 3/4 = ?/8.
Reveal the answer
6/8. Multiply both 3 and 4 by 2.
Change a fraction to simplest form
Divide the numerator and denominator by the same common factor. The fraction is in simplest form when they have no common factor greater than 1. The shaded amount stays the same.
Choose a fraction to simplify
Numerator: 8 ÷ 4 = 2
Denominator: 12 ÷ 4 = 3
Find a number that divides both 8 and 12.
See worked example
Write 8/12 in simplest form.
- Find a common factor of 8 and 12: both can be divided by 4.
- Divide the numerator and denominator by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3.
- 2 and 3 have no common factor greater than 1.
Answer: 8/12 = 2/3.
Try together
Write 6/9 in simplest form.
Reveal the answer
6/9 = 2/3. Divide both the numerator and denominator by 3.
Compare and order unlike fractions
Unlike fractions have different denominators. For given denominators up to 12, use equal-sized strips or equivalent fractions with a shared denominator, then compare the numerators and put the fractions in increasing or decreasing order.
Compare and order
In twelfths: 6/12, 8/12, 9/12.
1/2 < 2/3 < 3/4
Compare equal-sized twelfths, then write the original fractions in order.
Fraction comparison facts
For the same whole, the smaller denominator gives the greater fraction.
For the same whole, the larger numerator gives the greater fraction.
See worked example
Put 1/2, 2/3 and 3/4 in increasing order.
- Use twelfths: 1/2 = 6/12, 2/3 = 8/12 and 3/4 = 9/12.
- Compare 6, 8 and 9 equal-sized twelfths.
- Write the original fractions from smallest to largest.
Answer: 1/2 < 2/3 < 3/4.
Try together
Put 2/3, 3/4 and 5/6 in decreasing order.
Reveal the answer
5/6 > 3/4 > 2/3, because these are 10/12, 9/12 and 8/12.