Question

consider the sum of 3/5 + 3/4 . round each fraction and estimate the sum. add the two fractions using a common denominator and then round the result. which estimate is closer to the actual answer.

Answer 1

To estimate 3/5 and 3/4, each fraction is rounded to the nearest whole number, giving an estimated sum of 2. Exact addition, using a common denominator of 20, yields 27/20, which rounds to 1, giving a final round sum of 2. Therefore, both the estimate and the exact result are the same when rounded to the nearest whole number.

Step-by-step explanation:

To estimate the sum of 3/5 and 3/4, we need to round each fraction to the nearest whole number. Estimating 3/5 is approximately 1 (as it is closer to 1 than to 0), and estimating 3/4 is approximately 1 (as it is closer to 1 than to 0). Thus, the estimated sum is 1 + 1 = 2.

For the exact sum, we find a common denominator. Multiplying the denominators 5 and 4, we get 20. So, we convert each fraction: 3/5 becomes 12/20 (since 3×4=12) and 3/4 becomes 15/20 (since 3×5=15). Adding them gives us 12/20 + 15/20 = 27/20. The result of 27/20, when rounded to the nearest whole number, is also 1, as 27/20 is closer to 1 (1.35) than to 2. Therefore, the exact answer after rounding is also 2.

Comparing both methods, we see that the estimate is indeed closer to the actual answer because both give us the same result of 2 after rounding to the nearest whole number.

Answer 2

Let's round to the nearest whole number.

3/5 = 0.6 = 1
3/4 = 0.75 = 1

1 + 1 = 2

Now let's find the common denominator:

The least common denominator between 5 and 4 is 20, so change both fractions to denominators of 20:

12/20 + 15/20

Add the numerators and keep the denominator:

27/20

27/20 = 1.35 = 1.5

Therefore adding the two fractions using a common denominator and then rounding gives us a closer answer.