Let's look at how to add any fractions together.
Here we're asked to find the sum of 1/2, 1/8, and 1/4. The shape is divided into halves, fourths, and eighs. So we can shade 1/2, 1/4, and 1/8.
Now let's see what fraction has been shaded.
We can express 1/2 and 1/4 in terms of eighs.
To get from halves to eighs, we multiply the numerator and denominator by 4. 1/2 is 48.
To get from 4ths to eighs, we multiply the numerator and denominator by 2. So 1/4 is 28.
Then we have 4/8 + 1/8 + 28 which equals 7/8.
Let's look at a different problem.
2 fths + 1/3.
It can be hard to add fractions with different denominators because the pieces are different sizes. This grid helps us see how to make them the same size.
two- fifths of the grid is shown by the two pink rows. That's six parts. So two- fifths is 6 15.
1/3 is equal to 5 parts. So 1/3 is 5 15.
The grid shows us the general strategy.
To add fractions with different denominators, we can find a common denominator by multiplying the two denominators together. We multiply two- fifths by 3 on the top and bottom. And we multiply 1/3 by 5 on the top and bottom. This gives us 6 15 + 5 15 which equals 11 15. Let's apply this to another sum. 3/4s + 1/5.
We can get a common denominator for four and 5 by multiplying them together. That gives us 20. To rewrite 3/4s, we multiply the numerator and denominator by 5. 3 * 5 is 15. So, we get 15 20ths.
For 1/5, we multiply the numerator and denominator by 4. 1 * 4 is 4. So we get 4 20ths.
What's 27th + 2 fths? We can get a common denominator by multiplying 7 and 5 which gives us 35. We multiply the top and bottom of 27th by 5 to get 10 35ths.
We multiply two- fifths by 7 on the top and bottom to get 14 35ths. 10 + 14= 24.
So the sum is 24 35ths.
The key to adding fractions is to rewrite fractions so they have a common denominator. We can always find a common denominator by multiplying the denominators of the fractions we're adding.
