ACARA v9 CONTENT DESCRIPTION “solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies”
Builds on comparing fractions and finding equivalent fractions with common denominators. Year 5 uses those ideas to add and subtract fractions, both when they already share a denominator and when their denominators are related. Adding and subtracting the parts, rewriting fractions to a common denominator first when needed, and choosing among different strategies turns fractions into quantities that can be combined and compared in real problems.
Adding fractions with the same denominator
When two fractions have the same denominator, they are made of parts of the same size, so they can be added simply by adding the numerators and keeping the denominator. Three eighths plus two eighths is five eighths, because three parts and two parts make five parts of the same eighth-sized piece. A bar divided into equal parts makes this clear: shading three parts and then two more shades five parts in all. The denominator never changes when adding fractions with a common denominator, because the size of each part stays the same.
Adding fractions with the same denominator
Add the numerators; the denominator stays the same.
Add 3/8 and 2/8.
Subtracting fractions with the same denominator
Subtracting fractions with the same denominator works the same way: subtract the numerators and keep the denominator. Five sixths minus two sixths is three sixths, because taking two of the sixth-sized parts away from five leaves three. On a bar shaded to five sixths, removing two shaded parts leaves three sixths. As with adding, the denominator stays the same throughout, since the parts being taken away are the same size as the parts that remain. Same-denominator addition and subtraction are the foundation for the harder cases.
Subtracting fractions with the same denominator
Subtract the numerators; the denominator stays the same.
Subtract 2/6 from 5/6.
Adding fractions with related denominators
When denominators are different but related, meaning one is a multiple of the other, the fractions must first be rewritten to a common denominator. To add one half and one quarter, notice that four is a multiple of two, so one half is rewritten as two quarters. Now both fractions have denominator four, and two quarters plus one quarter is three quarters. Finding a common denominator using equivalent fractions turns an addition of unlike fractions into the simple same-denominator case. The amounts are unchanged; they are only renamed so the parts match.
Adding fractions with related denominators
Rewrite to a common denominator, then add.
Add 1/2 and 1/4; their denominators are related.
Subtracting fractions with related denominators
Subtraction with related denominators follows the same first step. To work out five sixths minus one third, rewrite one third as two sixths, since six is a multiple of three. Now both fractions share the denominator six, and five sixths minus two sixths is three sixths. Choosing the common denominator is the key decision, and the related denominators make it easy because the larger one is already a multiple of the smaller. Once the fractions match, the subtraction is just a matter of taking one numerator from the other.
Subtracting fractions with related denominators
Rewrite to a common denominator, then subtract.
Subtract 1/3 from 5/6; their denominators are related.
Different strategies for the same problem
The same problem can often be solved in more than one way, and choosing a good strategy makes the work easier. A bar model or a number line shows the addition or subtraction as a picture, which helps when the fractions are unfamiliar. Rewriting to a common denominator and working with the numerators is quicker once the idea is secure. Some answers can be simplified, like three sixths becoming one half. Being able to switch between a picture, a common denominator and a known equivalent means a child can pick whichever strategy fits the numbers best.
Different strategies for the same problem
Match the denominators, then add or subtract.
Add or subtract the fractions.
Adding and subtracting with confidence
Adding and subtracting fractions comes down to making the parts match. If the denominators are the same, add or subtract the numerators and keep the denominator; if they are related, rewrite one fraction to the common denominator first, then add or subtract. A bar model or number line gives a picture when it helps, and answers can be simplified at the end. With these strategies a child can solve problems that combine or compare fractions, ready for the multiplying and dividing of fractions in later years.
Quick self-check
1. To add 3/8 + 2/8, you...
2. 5/6 - 2/6 equals...
3. To add 1/2 + 1/4, a good first step is to...
4. Rewriting 1/3 with denominator 6 gives...
5. When adding fractions with the same denominator, the denominator...