Estimating Quotients with Two-Digit Divisors

Question

_____ the quotient of 456 ÷ 23.

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 =_____

20x _____ = 400
____ 1
)456

Answer 1

To estimate the quotient of 456 ÷ 23 by rounding the divisor and performing the multiplication, we can follow these steps:

1. Round the divisor.

   • The divisor 23 is rounded to 20 (the greatest place value).

2. Find a close multiple of the rounded divisor (20).

   • We want to see how many times 20 goes into 456.
   • Think about what multiple of 20 gets close to 456.
   • We can try \( 20 \times 20 = 400 \).

3. Set up the estimate.

   • You can calculate the next few multiples of 20 for reference:
     • \( 20 \times 21 = 420 \)
     • \( 20 \times 22 = 440 \)
     • \( 20 \times 23 = 460 \) (which is too high)
   • Based on this, 20 × 22 = 440 is the closest to 456 without exceeding it.

4. Estimate the final quotient.

   • The multiplier we determined is 22.
   • Therefore, the estimated quotient will be around 22.

So, filling in the blanks we get:

• Think: What can I multiply by 20 to get close to 456?
  • 20 × 22 = 440
• 20 x 22 = 440
• Quotient = 22.

Final Answer: The estimated quotient of 456 ÷ 23 is approximately 22.