Week 07 · Unlike denominators
Thursday
The pond walk
// Add and subtract fractions with different denominators
⏱ about 15 min
Thursday: The pond walk
Chris the Coyote settles on a log and tips his feathered hat.
"One bright morning, Riley and Lucy the Ladybug walked to the pond," he says.
"First they walked 1/2 mile. Then they walked 2/5 mile more."
"Riley said, we walked 3/7 of a mile in all."
"Lucy wiggled her antennae. But 3/7 is less than 1/2, she said kindly."
"We walked more than half a mile before the second part even started!"
"So Riley checked again, with tenths this time."
Learn it: check with benchmark fractions
Benchmark fractions like 0, 1/2 and 1 help us estimate.
2/5 is a little less than 1/2. So 1/2 + 2/5 is a little less than 1.
The exact sum: 5/10 + 4/10 = 9/10. That is a little less than 1, so it makes sense.
3/7 is less than 1/2, so it cannot be right.
ESTIMATE WITH BENCHMARKS
- Read the question.
- Tap your answer.
Without finding the exact answer: is 2/5 + 1/2 more or less than 1?
Without finding the exact answer: is 3/4 + 2/3 more or less than 1?
Without finding the exact answer: is 5/8 + 3/8 more or less than 1?
Without finding the exact answer: is 1/3 + 1/8 more or less than 1/2?
IS IT REASONABLE?
- Read the question.
- Tap your answer.
Riley says 1/2 + 2/5 = 3/7. Is that reasonable?
A friend says 7/8 - 1/2 = 6/6. Is that reasonable?
Riley and Lucy walk 1/2 mile, then 2/5 mile. How far do they walk?
A jug holds 7/8 liter of water. Lucy pours out 1/2 liter. How much is left?
MORE TRAIL STORIES
- Read the question.
- Tap your answer.
Chris reads 1/3 of his book on Monday and 1/4 on Tuesday. What part has he read?
Chris has read 7/12 of his book. What fraction of the book is left to read?
Lucy walks 3/5 mile to the daisies, then 1/10 mile to the pond. How far?
The pond trail is 2 1/4 miles. Riley has walked 1 2/3 miles. How much is left?
Estimate with 1/2 and 1 first, then find the exact answer.
| Sentence | True or false? |
|---|---|
| 1/2 + 2/5 = 3/7 | ? |
| 1/2 + 2/5 = 9/10 | ? |
| 3/4 - 1/3 = 5/12 | ? |
| 1/3 + 1/4 = 2/7 | ? |
WHY THIS EXERCISE1/2 + 2/5 is 9/10, and 1/3 + 1/4 is 7/12. Adding tops and bottoms does not work.
Try it
Walk across a room in two parts, and stop partway.
Guess what fraction of the way you went in each part, like 1/2 and 1/3.
Add your two fractions. Is the sum close to 1 whole?
Use a benchmark to check if your guesses make sense.
Guess what fraction of the way you went in each part, like 1/2 and 1/3.
Add your two fractions. Is the sum close to 1 whole?
Use a benchmark to check if your guesses make sense.
Draw Riley and Lucy on a trail map that shows 1/2 mile and 2/5 mile.
What a walk! Tomorrow Freddy has a fraction game.