Adding and subtracting fractions
You add or subtract fractions when they have the same denominator. If they do not, you first give them a common denominator.
Why
You eat 1/4 of a pizza, your sister eats 1/3. How much of the pizza is gone?
You cannot just add those two pieces: a quarter and a third are pieces of different sizes.
Cut the pizza into twelve equal slices and everything fits: 1/4 is 3 slices, 1/3 is 4 slices. Together 7 of the 12 slices, so 7/12 of the pizza.
See it
Choose two fractions. Watch both strips being split into smaller, equal boxes until they share a denominator, then count the boxes together.
Description of the picture
Two strips, one with 1/4 coloured and one with 1/3. Below, both strips are split into twelve boxes: 3 and 4 coloured boxes, together 7/12.
Get it
When two fractions have the same denominator, the pieces are the same size. You add (or subtract) the numerators and keep the denominator: 2/7+
When the denominators are different, first find a denominator that suits both: a common multiple. The smallest one is the handiest. For 4 and 6 that is 12.
Rewrite each fraction with that denominator by multiplying the numerator and the denominator by the same number. Then work as with equal denominators and simplify the result.
A mixed number such as 21/3 is first written as a fraction: 21/3=
With equal denominators: a/n+
Worked example
Work out and simplify: 5/6−
The least common multiple of 6 and 4 is 12.
6,
12, 18and4, 8, 12 Write both fractions with denominator 12.
5/6=
10/12and1/4= 3/12 Subtract the numerators and keep the denominator.
10/12−
3/12= 7/12 7 and 12 have no common divisor except 1, so 7/12 is already as simple as it gets.
- Answer
5/6−
1/4= 7/12
Do it
Pick a level. You get a new exercise every time, checked straight away.
Pitfalls
Wrong: 1/2+
1/3= 2/5: numerators together and denominators together. The denominator tells you how big the pieces are. You do not add it. Besides, 2/5 is smaller than 1/2, even though you added something.
Right: 1/2+
1/3= 3/6+ 2/6= 5/6. Wrong: 3/4=
3/8 because I multiplied the denominator by 2. If you only change the denominator, you make the pieces smaller without taking more of them. The fraction gets smaller.
Right: Multiply both the numerator and the denominator by 2: 3/4=
6/8. Wrong: 21/2+
11/4= 32/6. With mixed numbers too, the fraction parts need the same denominator first.
Right: 21/2+
11/4= 22/4+ 11/4= 33/4.
In real life
- A recipe needs 1/2 litre of milk for the batter and 1/4 litre for the sauce: 3/4 litre in total.
- You cycle 2/3 of the way to school and walk the rest. So you walk 1/3 of the way.
- At music school, a half note lasts as long as two quarter notes: 1/4+
1/4= 1/2. - You have 3/4 of a cake left and give away 1/2 of the whole cake. That leaves 1/4.
History
The ancient Egyptians added fractions too. Because they used almost only unit fractions such as 1/2, 1/3 and 1/4, they wrote 2/5, for example, as 1/3+
At the table
Take a bar of chocolate. How many squares make 1/2 of the bar, and how many make 1/3? Does it work out together, and into how many squares would you like the bar to be split?
A question to talk about together, for parents and children. There is no wrong answer.