Estimate each sum: (a) 356 + 275 (to the nearest ten) (b) 538 + 276 (to the nearest ten) (c) 32,835 + 16,466 (to the nearest thousand) (d) 1,270 + 2,326 (to the nearest hundred)
The Correct Answer and Explanation is:
Let’s break down each estimation step-by-step:
(a) 356 + 275 (to the nearest ten)
- Round 356 to the nearest ten: 360
- Round 275 to the nearest ten: 280
- Now, add the rounded numbers:
360 + 280 = 640
So, the estimated sum is 640.
(b) 538 + 276 (to the nearest ten)
- Round 538 to the nearest ten: 540
- Round 276 to the nearest ten: 280
- Now, add the rounded numbers:
540 + 280 = 820
So, the estimated sum is 820.
(c) 32,835 + 16,466 (to the nearest thousand)
- Round 32,835 to the nearest thousand: 33,000
- Round 16,466 to the nearest thousand: 16,000
- Now, add the rounded numbers:
33,000 + 16,000 = 49,000
So, the estimated sum is 49,000.
(d) 1,270 + 2,326 (to the nearest hundred)
- Round 1,270 to the nearest hundred: 1,300
- Round 2,326 to the nearest hundred: 2,300
- Now, add the rounded numbers:
1,300 + 2,300 = 3,600
So, the estimated sum is 3,600.
Explanation:
In each of these estimations, we round the numbers to a specified place value—either to the nearest ten, hundred, or thousand. By rounding first, we simplify the calculation and get a quick estimate of the sum without performing exact addition.
- Rounding to the nearest ten makes sense when you want a simple approximation for relatively small numbers, ensuring the sum is accurate enough for general purposes (like a quick mental calculation or rough estimate).
- Rounding to the nearest hundred or thousand is often used when dealing with larger numbers or when an approximation for a broader sense of scale is needed. For example, rounding to the nearest thousand allows us to estimate sums of large numbers in the context of things like population counts or financial figures.
Using these methods allows for quicker calculations in many scenarios while still providing a reasonable level of accuracy.
