Macy jogs 27 miles a month.

Question

Part A
Explain how to use compensation to find how many miles Macy jogs in 6 months.

Answer 1

To use compensation to find out how many miles Macy jogs in 6 months, follow these steps:

1. Identify the multiplication problem: Macy jogs 27 miles a month, and you want to find out how many miles she jogs in 6 months. This can be represented as \(27 \times 6\).

2. Choose a number to compensate: To make the multiplication easier, we can round 27 to a nearby multiple of 10. A good choice is 30, because it's easier to multiply by 6.

3. Adjust for the compensation: When we round 27 up to 30, we need to consider how much we adjusted (which is +3). So, we will first calculate \(30 \times 6\).

4. Calculate the compensation: \[ 30 \times 6 = 180 \]

5. Account for the compensation: Since we added 3 miles to 27, we need to subtract the extra miles that we included in our initial calculation. We calculated the miles based on 30 instead of 27. Since we multiplied by 6, we must subtract the compensation from the total: \[ 180 - (3 \times 6) = 180 - 18 = 162 \]

6. Conclusion: Thus, using compensation, we find that Macy jogs a total of 162 miles in 6 months.

In summary, using compensation, you can simplify the multiplication by rounding the number and then adjusting the total after calculation to ensure the result remains accurate.

Answer 2

put it as a 4th grader

Answer 3

Sure! Here’s how to explain it to a 4th grader:

---

How to Find Out How Many Miles Macy Jogs in 6 Months Using Compensation

1. What We Know: Macy jogs 27 miles every month. We want to find out how many miles she jogs in 6 months.

2. Change the Number to Make it Easier: Instead of using 27, let’s round it up to 30 because it’s easier to multiply by 6.

3. Multiply the Easier Number: Now, we can multiply: \[ 30 \times 6 = 180 \] (So it looks like she jogs 180 miles.)

4. Fix the Change We Made: Since we rounded up from 27 to 30, we added 3 extra miles. We need to subtract that extra. First, we find out how much that is for 6 months: \[ 3 \times 6 = 18 \]

5. Subtract the Extra Miles from Our Total: Now, we take the 180 miles and subtract the extra 18 miles: \[ 180 - 18 = 162 \]

6. Final Answer: So, in 6 months, Macy jogs 162 miles!

---

That’s how you can use compensation to find out how many miles Macy jogs! It makes the math easier and helps us find the answer.