Question

Solve 4123 ÷ 78 two different ways using partial quotients. Which way do you prefer?

Answer 1

To solve 4123 ÷ 78 using partial quotients, one can use estimations with multiples of 78. Two methods are described, both resulting in the same quotient of 52 with a remainder of 67. The choice of method may depend on personal preference for estimation and calculation.

Step-by-step explanation:

To solve 4123 ÷ 78 using the partial quotients method, you can start by estimating how many times 78 can fit into the beginning of 4123. One way to approach this is:

1. Start with 78 × 50 because 50 is an easy number to work with and you know that 78 × 100 would be too much.
2. That gives us 3900 (78 × 50). Now subtract 3900 from 4123, which leaves us with 223.
3. Now consider how many times 78 goes into 223. It fits about 2 times (156), giving a remainder of 67.
4. Add the 50 and the 2 for a partial quotient of 52 with a remainder of 67.

Another way to solve this via partial quotients could be to start with smaller, more precise estimates:

1. Start with 78 × 40, because you know that 78 × 50 is too much. That gives us 3120.
2. Subtract 3120 from 4123, leaving 1003.
3. Estimate again with 78 × 10 to subtract 780, leaving 223.
4. Estimate once more with 78 × 2 to subtract another 156, leaving a remainder of 67.
5. Add the 40, 10, and 2 to get a partial quotient of 52 with a remainder of 67.

Both methods result in the same quotient of 52 and remainder of 67, but the second approach might feel more controlled and precise due to the more conservative estimates.