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Trail Day: Add and Subtract Mixed Numbers

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Trail Day: Add and Subtract Mixed Numbers

Find hiking distances with mixed numbers that share a denominator.

Add the miles

Add the mixed numbers. If the fraction part is 1 or more, trade it for a whole.

1.
Lena hikes 1 3/8 miles to the creek. Then she hikes 2 4/8 miles to the lookout. How far does she hike in all?

1 3/8 + 2 4/8 = miles

2.
Mateo walks 2 2/3 miles in the morning and 1 2/3 miles after lunch. Add the wholes and the fractions to find his total.

Wholes: 2 + 1 =
Fractions: 2/3 + 2/3 =
Total: miles

3.
Priya hikes 3 5/6 miles on Saturday and 1 3/6 miles on Sunday. How many miles does she hike in all?
Question 3 options
4.
The two parts of the Maple Trail are 1 3/5 miles and 2 1/5 miles long. Write each mixed number as a fraction, then add.

1 3/5 = /5
2 1/5 = /5
Sum = /5
As a mixed number, the Maple Trail is miles long.

Miles left to go

Subtract the mixed numbers. If the top fraction is too small, trade 1 whole for fraction parts first.

5.
The Pine Trail is 4 5/6 miles long. Ruby has hiked 2 1/6 miles. How many miles does she have left?

4 5/6 − 2 1/6 = miles

6.
The Lake Loop is 5 1/4 miles long. Sam has walked 2 3/4 miles. You cannot take 3/4 from 1/4, so trade 1 whole for 4/4 first.

5 1/4 = 4 /4
5 1/4 − 2 3/4 = miles left

7.
The Summit Trail is 6 miles long. Ezra stops to rest after 3 2/5 miles.

6 = 5 /5
6 − 3 2/5 = miles left to the top

8.
Nia finds that 4 3/10 − 1 6/10 = 2 7/10. Which addition equation checks her answer?
Question 8 options

Trail challenges

Use what you know about mixed numbers to solve each trail problem.

9.
Match each problem to its answer. One answer is not used.
10.
Each problem tells how far a hiker walks. Sort the problems by their answers.
11.
The Ridge Trail is 7 miles long. Ava hikes 2 3/4 miles before lunch and 1 2/4 miles after lunch.

Ava has hiked miles so far.
She has miles left to finish the trail.

12.
Diego says 3 1/4 − 1 3/4 = 2 2/4. He took 3 − 1 = 2 and 3/4 − 1/4 = 2/4. Explain Diego's mistake and find the correct answer.