Add and subtract fractions with unlike denominators (grade 5) · lesson

When one bottom fits into the other

💡 If one bottom number goes into the other, rewrite just that fraction to match.

Thirds and ninths: 3 goes into 9. So change thirds into ninths.

1/3 = 3/9. Now both are ninths, and you can add or subtract the tops.

🧠 Let's work it out

Find 1/3 + 1/9.

What do you think comes next?

💡 If neither bottom fits the other, multiply the two bottoms to get a bottom both can use.

Fifths and thirds don't fit into each other. 5 × 3 = 15, so use fifteenths.

Rewrite each fraction in fifteenths. Then add or subtract the tops.

If the answer is more than 1, you can write it as a mixed number.

🧠 Let's work it out

Find 2/5 + 1/3.

What do you think comes next?

💡 With mixed numbers, use one bottom for both, then add or subtract the wholes and the parts.

To add, add the wholes. Then add the fractions with a shared bottom.

To subtract, it is often easiest to change both mixed numbers to fractions first.

🧠 Let's work it out

Find 3 1/2 − 1 2/3.

What do you think comes next?

💡 Compare each fraction to 0, 1/2, or 1 to tell about how big the answer is.

Is each fraction close to 0, close to 1/2, or close to 1? Use that to guess the answer.

5/6 and 4/7 are both more than 1/2. Two numbers more than 1/2 add to more than 1.

Subtracting works the same way. In 9/10 − 1/5, 9/10 is close to 1 and 1/5 is close to 0. Taking a small amount from almost 1 leaves more than 1/2.

Don't add the tops and the bottoms. The pieces must be the same size first.

🧠 Let's work it out

Is 5/6 + 4/7 more or less than 1?

What do you think comes next?