Estimating Quotients with Two-Digit Divisors

Question

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the quotient of 456 ÷ 23.
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Round the divisor to the greatest place value, the tens.
23 → 20
Think: What can I multiply by 20 to get close to 456?
20 × 10 =
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20x
Double
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= 400
1?
456

Answer 1

To estimate the quotient of \( 456 \div 23 \), we can round the divisor to the nearest ten.

1. Round the divisor:

   • \( 23 \) rounds to \( 20 \).

2. Estimate the multiplication to get close to \( 456 \):

   • Think about what we can multiply by \( 20 \) to get close to \( 456 \).
   • Start with \( 20 \times 10 = 200 \).
   • Then try \( 20 \times 20 = 400 \).
   • We see that \( 20 \times 22 = 440 \), which is also close.

3. Calculate the quotient:

   • We found \( 20 \times 20 = 400 \) and \( 20 \times 22 = 440 \).
   • Since \( 440 < 456 < 480 \), we can estimate that the quotient is a little more than \( 20 \).

4. Result:

   • Therefore, our estimate for \( 456 \div 23 \) is about \( 20 \) (refined to possibly around \( 20-22 \) upon closer inspection).

In conclusion, the estimated quotient for \( 456 \div 23 \) is roughly 20.