Problem Description:
The image provides a worksheet titled "Division With Partial Quotients." It explains the method of dividing numbers using partial quotients and includes examples and practice problems. The task is to solve one of the division problems using the partial quotients method.
Solution Approach:
The partial quotients method involves breaking down the division problem into smaller, easier steps by subtracting multiples of the divisor from the dividend repeatedly until the remainder is less than the divisor. Here’s how to solve a problem step-by-step:
#### Example Problem:
Let's solve the problem
78 ÷ 7 using the partial quotients method.
#### Step-by-Step Solution:
1.
Set Up the Problem:
\[
7 \longdiv{78}
\]
2.
Estimate Multiples of the Divisor (7):
- Start by estimating how many times 7 can go into 78. Common multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, etc.
- Choose an easy multiple to subtract, such as 70 (which is \(7 \times 10\)).
3.
Subtract the Multiple:
- Subtract 70 from 78:
\[
78 - 70 = 8
\]
- Write down the partial quotient (10) and the remainder (8).
4.
Repeat the Process:
- Now, divide the remaining part (8) by 7. The largest multiple of 7 that is less than or equal to 8 is 7 (which is \(7 \times 1\)).
- Subtract 7 from 8:
\[
8 - 7 = 1
\]
- Write down the next partial quotient (1) and the remainder (1).
5.
Sum the Partial Quotients:
- The partial quotients are 10 and 1. Add them together:
\[
10 + 1 = 11
\]
6.
Final Answer:
- The quotient is 11, and the remainder is 1.
- Therefore, \(78 \div 7 = 11\) with a remainder of 1.
#### Verification:
To verify, multiply the quotient by the divisor and add the remainder:
\[
11 \times 7 + 1 = 77 + 1 = 78
\]
This confirms the solution is correct.
Final Answer:
\[
\boxed{11 \text{ R } 1}
\]
Explanation:
The partial quotients method simplifies division by breaking it into smaller, manageable steps. By choosing easy multiples of the divisor and subtracting them from the dividend, we gradually reduce the problem until the remainder is less than the divisor. This method is particularly useful for larger numbers or when mental math is challenging.
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Parent Tip: Review the logic above to help your child master the concept of partial quotients division worksheet.
