consider the sum 3/5+3/4. round each fraction and estimate the sum. add the two fraction using a common denominator and then round the result. which estimate is closer to the actual answer.
1+1 = 2
12/20+15/20 = 27/20 -> 2
Hmm. Looks the same to me.
To solve this problem step-by-step, let's follow the instructions given:
Step 1: Round each fraction separately.
Round 3/5 to the nearest whole number: 3/5 ≈ 1/1.
Round 3/4 to the nearest whole number: 3/4 ≈ 1/1.
Step 2: Estimate the sum of the rounded fractions.
The sum of 1/1 + 1/1 = 2/1.
Step 3: Convert the fractions to have a common denominator.
The fractions 1/1 and 1/1 already have a common denominator of 1, so we don't need to do any conversions.
Step 4: Add the fractions.
1/1 + 1/1 = 2/1.
Step 5: Round the result of the added fractions.
The result 2/1 is already a whole number, so we don't need to round it.
Finally, to determine which estimate is closer to the actual answer, we need to find the actual sum of the original fractions.
The original sum is: 3/5 + 3/4 = (12/20) + (15/20) = 27/20.
Comparing the estimates:
- Rounded estimate: 2/1
- Actual sum: 27/20
To compare these, we need to convert the actual sum to a rounded form:
27/20 ≈ 1.35
Now we can see that the actual sum (1.35) is closer to the rounded estimate (2/1) than the estimated sum (2/1) itself.
Therefore, the rounded estimate (2/1) is closer to the actual answer, 27/20.
To round a fraction, you typically would round either up or down based on the decimal value. In this case, let's round to the nearest whole number.
First, let's round the fractions individually:
1. 3/5 is approximately equal to 0.6 (rounded to one decimal place)
2. 3/4 is approximately equal to 0.8 (rounded to one decimal place).
Now, let's estimate the sum by adding these rounded values:
0.6 + 0.8 = 1.4.
Next, let's find the sum of the fractions by adding them using a common denominator.
To do this, we need to convert the fractions so that they have the same denominator. The least common multiple of 5 and 4 is 20. So, we can rewrite the fractions as:
3/5 * 4/4 + 3/4 * 5/5 = 12/20 + 15/20 = 27/20.
Now, let's round the result:
27/20 is approximately equal to 1.4 (rounded to one decimal place).
Comparing the two estimates, we find that both the individual rounded fractions and the sum of the fractions rounded to the same value, 1.4.
Therefore, both estimates are equally close to the actual answer.