Question

Question

Use both rounding and compatible numbers to estimate 26×31
.
Which is closer to the actual solution? The actual solution is 806.

(1 point)
Responses

Using compatible numbers is closer.

Using compatible numbers is closer.

Rounding is closer.

Rounding is closer.

The estimates are the same.

The estimates are the same.

Both estimates are greater than the actual product.

Both estimates are greater than the actual product.
Remaining Attempts : 3
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Answer 1

To estimate the product of 26 × 31 using both rounding and compatible numbers, let's do the calculations:

Rounding:

• Round 26 to 30 (nearest ten).
• Round 31 to 30 (nearest ten).
• So the estimate using rounding is:
  \(30 × 30 = 900\).

Compatible Numbers:

• Compatible numbers are numbers that are easier to compute mentally. In this case, we can round 26 down to 25 and round 31 up to 30.
• So the estimate using compatible numbers is:
  \(25 × 30 = 750\).

Comparison:

• The estimate using rounding is 900.
• The estimate using compatible numbers is 750.
• The actual product is 806.

Now, looking at how close each estimate is to the actual product:

• \(900 - 806 = 94\) (for rounding)
• \(806 - 750 = 56\) (for compatible numbers)

Since 56 is less than 94, the estimate using compatible numbers is closer to the actual solution.

Conclusion:

Using compatible numbers is closer.