Wholes and parts together
A wall is measured in paces. First 1 3/4 paces, then 2 1/2 more paces. A pace is one step. What is the total?
- Two strips of quarters, side by side.
- Shade 3/4, then 1/2 renamed as 2/4.
- That is 5/4: 1 whole and 1/4 left.
- Add the wholes: 3 + 1 1/4 = 4 1/4.
Two routes, one answer
The total is 4 1/4 paces.
One route is to flatten. Write each mixed number as one fraction. 1 3/4 is 7/4, because 1 × 4 + 3 = 7. 2 1/2 is 5/2, which is 10/4. Then 7 + 10 = 17. So the total is 17/4. And 17 ÷ 4 is 4 with 1 left, so 4 1/4.
The other route keeps the wholes and the parts separate. Add the wholes: 1 + 2 = 3. Add the parts. Rename 1/2 as 2/4. Then 3/4 + 2/4 is 5/4. That is more than a whole. So carry the extra whole. 5/4 is 1 1/4, and 3 + 1 1/4 = 4 1/4.
For 3 1/4 − 1 1/2, the parts give 1/4 − 1/2. But 1/2 is more than 1/4, so there is not enough. Borrow a whole from the 3. The 3 becomes 2. The borrowed whole is 4/4, so 1/4 becomes 5/4. Rename 1/2 as 2/4. Now 5/4 − 2/4 = 3/4. The wholes are 2 − 1 = 1. The answer is 1 3/4.
Watch out!
In 3 1/4 − 1 1/2, do not take 1/4 from 1/2. That gives 2 1/4. Borrow a whole to get 1 3/4.
Tap the answer you trust in the lab. Then read both routes.
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