Question

Estimating Quotients with Two-Digit Divisors

_____ 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.**