Question

One pygmy shrew weighs 3 3/18 ounces, and another weighs 4 4/7 ounces. Estimate the total weight.

O about 8 1/2
O about 7 1/2
O about 9 ounces
O about 7 ounces

Answer 1

About 7 1/2 ounces

Explanation:

Add your whole numbers first, 3 + 4 = 7

Now the fractions:

3/18 = 1/6

Estimate 4/7 + 1/6, the answer is somewhere between 1/2 and 1 whole. Therefore the answer is about 7 1/2

Check:

3/18 × 7/7 = 21/126

4/7 × 18/18 = 72/126

21/126 + 72/126 = 93/126

The actual answer is 7 31/42, so the closest answer is 7 1/2

Answer 2

Answer: about 7 1/2 (choice B)

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Reason:

It might help to draw a number line for this.

3/18 is closer to 0 than it is to 1/2 = 9/18, so the mixed number 3 & 3/18 rounds to 3 when rounding to the nearest half.

4/7 is closer to 1/2 = 4/8 than it is to either 0 or 1, so 4 & 4/7 rounds to 4 & 1/2 when rounding to the nearest half.

Adding 3 to 4 & 1/2 gets 7 & 1/2 since we add the whole parts 3+4 = 7, and the fractional part stays as it is.

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Check:

(3 + 3/18) + (4 + 4/7) = 7.738 approximately

7 + 1/2 = 7.5 exactly

The two results aren't too far off. The estimate of 7 & 1/2 is an underestimate.