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Answer :
Let's solve the problem step-by-step using an area model to understand why Leanne's calculation is incorrect.
First, we need to find out what [tex]\( 8 \times 4.3 \)[/tex] actually equals.
### Step-by-Step Calculation
1. Break Down the Numbers:
- Break down 4.3 into whole number and fractional parts.
- [tex]\( 4.3 = 4 + 0.3 \)[/tex]
2. Use the Distributive Property:
- We can then use the distributive property to calculate the product [tex]\( 8 \times (4 + 0.3) \)[/tex].
- [tex]\( 8 \times (4 + 0.3) = (8 \times 4) + (8 \times 0.3) \)[/tex]
3. Calculate Each Part:
- Calculate [tex]\( 8 \times 4 \)[/tex]:
- [tex]\( 8 \times 4 = 32 \)[/tex]
- Calculate [tex]\( 8 \times 0.3 \)[/tex]:
- [tex]\( 8 \times 0.3 = 2.4 \)[/tex]
4. Add the Results Together:
- Add the two results from the above calculations:
- [tex]\( 32 + 2.4 = 34.4 \)[/tex]
So, [tex]\( 8 \times 4.3 = 34.4 \)[/tex].
### Checking Leanne's Answer:
Leanne's answer was 32.24. However, we have calculated that the correct answer is 34.4. Therefore, Leanne's answer is incorrect.
### Area Model Explanation:
We can also visualize this calculation using an area model.
- Imagine a rectangle split into two smaller rectangles:
- One rectangle represents [tex]\( 8 \times 4 \)[/tex] and the other represents [tex]\( 8 \times 0.3 \)[/tex].
- The total area of the larger rectangle is the sum of the areas of the smaller rectangles.
Area Model Parts:
1. Rectangle 1:
- One side is 8 (representing the number 8).
- The other side is 4 (from breaking down 4.3).
- Area = [tex]\( 8 \times 4 = 32 \)[/tex].
2. Rectangle 2:
- One side is 8.
- The other side is 0.3.
- Area = [tex]\( 8 \times 0.3 = 2.4 \)[/tex].
Total Area:
- The total area of the two rectangles together is:
- [tex]\( 32 + 2.4 = 34.4 \)[/tex].
Thus, this area model confirms that [tex]\( 8 \times 4.3 \)[/tex] equals 34.4.
Leanne's answer of 32.24 is not correct. The correct result is 34.4.
First, we need to find out what [tex]\( 8 \times 4.3 \)[/tex] actually equals.
### Step-by-Step Calculation
1. Break Down the Numbers:
- Break down 4.3 into whole number and fractional parts.
- [tex]\( 4.3 = 4 + 0.3 \)[/tex]
2. Use the Distributive Property:
- We can then use the distributive property to calculate the product [tex]\( 8 \times (4 + 0.3) \)[/tex].
- [tex]\( 8 \times (4 + 0.3) = (8 \times 4) + (8 \times 0.3) \)[/tex]
3. Calculate Each Part:
- Calculate [tex]\( 8 \times 4 \)[/tex]:
- [tex]\( 8 \times 4 = 32 \)[/tex]
- Calculate [tex]\( 8 \times 0.3 \)[/tex]:
- [tex]\( 8 \times 0.3 = 2.4 \)[/tex]
4. Add the Results Together:
- Add the two results from the above calculations:
- [tex]\( 32 + 2.4 = 34.4 \)[/tex]
So, [tex]\( 8 \times 4.3 = 34.4 \)[/tex].
### Checking Leanne's Answer:
Leanne's answer was 32.24. However, we have calculated that the correct answer is 34.4. Therefore, Leanne's answer is incorrect.
### Area Model Explanation:
We can also visualize this calculation using an area model.
- Imagine a rectangle split into two smaller rectangles:
- One rectangle represents [tex]\( 8 \times 4 \)[/tex] and the other represents [tex]\( 8 \times 0.3 \)[/tex].
- The total area of the larger rectangle is the sum of the areas of the smaller rectangles.
Area Model Parts:
1. Rectangle 1:
- One side is 8 (representing the number 8).
- The other side is 4 (from breaking down 4.3).
- Area = [tex]\( 8 \times 4 = 32 \)[/tex].
2. Rectangle 2:
- One side is 8.
- The other side is 0.3.
- Area = [tex]\( 8 \times 0.3 = 2.4 \)[/tex].
Total Area:
- The total area of the two rectangles together is:
- [tex]\( 32 + 2.4 = 34.4 \)[/tex].
Thus, this area model confirms that [tex]\( 8 \times 4.3 \)[/tex] equals 34.4.
Leanne's answer of 32.24 is not correct. The correct result is 34.4.
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