Adding and subtracting fractions is typically introduced in 4th Grade and is limited to fractions with like denominators. In 5th Grade students then move on and use equivalent fractions to help add and subtract fractions that have different denominators.
Start with pizza
It is a good idea to get “hands-on” with math whenever possible and especially with fractions. If you enjoy a pizza then you can discuss adding and subtracting fractions as you share and eat it. And if you can manage a chocolate bar, try the ones that are split into equal-size bars and keep the fractions conversation going – just be sure to brush your teeth well afterwards.
Adding or subtracting fractions – same denominator
Start adding and subtracting fractions with the same denominator before trying to work with fractions with different denominators. The numeric technique will be better understood once the concept can be properly visualized.
Add or subtract the numerators, keeping the denominator the same..
Reduce the answer to its lowest term
It is good practice to finish by reducing the answer to its simplest form (lowest term) if it is not in that form already.
Be sure your child understands that an answer that is not in its simplest form is not necessarily wrong. There is more help here on converting a fraction to its simplest form.
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Adding or subtracting fractions – different denominator
Be sure your child understands equivalent fractions before tackling adding or subtracting fractions.
A common denominator must be found when adding or subtracting fractions that have different denominators. This is the most important (and probably the hardest) step in adding or subtracting fractions. A common denominator can always be found by multiplying the denominators.
Once the two fractions have the same denominator, the numerators can be added or subtracted with the denominator remaining the same as shown in the first example above.
Adding or subtracting mixed numbers
There are two methods of adding or subtracting mixed numbers. Either add the whole numbers and then add the fraction parts, or convert each mixed number to an improper fraction before calculating. remind your child to reduce any answers to their lowest term and to change any improper fractions to mixed numbers.
Tips and Reminders
When adding/ subtracting mixed numbers:
- Add the whole number parts.
- Change the fractions as required to their equivalent values so all fractions have the same denominator.
- Add/ subtract the numerators. Leave the denominator as is.
The example below shows the adding of two mixed numbers.
Note: An alternative to the above method involves changing the mixed numbers to improper fractions (7/3 and 15/4), converting these to equivalent values (28/12 and 45/12), adding these, and finally changing the improper fraction to a mixed number.
Worksheets – adding, subtracting fractions
Use the worksheets below to practice adding and subtracting fractions
- Adding Fractions Graphically
- Adding Fractions (same denominator) e.g. 4/7 + 2/7
- Adding Mixed Numbers (same denominator) e.g. 4 2/9 + 6 5/9
- Adding Fractions (different denominator) e.g. 2/3 + 1/4
- Adding Mixed Numbers (different denominator) e.g. 5 1/8 + 6 2/5
- Subtracting Fractions (same denominator) e.g. 4/7 – 2/7
- Subtracting Mixed Numbers (same denominator) e.g. 4 5/9 – 6 2/9
- Subtracting Fractions (different denominator) e.g. 2/3 – 1/4
- Subtracting Mixed Numbers (different denominator) e.g. 6 1/8 – 6
Try the fraction worksheet generator. It provides limitless questions on adding and subtracting fractions.