Brian skied for 0.75 hours at an average speed of 9.25 miles per hour. His sister Tori calculated the distance Brian skied. Tori's work is shown below.
[tex]\begin{array}{r}
9.25 \\
\times 0.75 \\
\hline 4625 \\
+\quad 6475 \\
\hline 11.090 \text { miles }\\
\end{array}[/tex]
What errors did Tori make when solving the problem? Check all that apply.
A. She multiplied 5 and 925 incorrectly.
B. She did not correctly align the place values of the partial products.
C. She did not place the decimal point correctly.
D. She added the partial products incorrectly.
Answer (1)
Tori did not correctly align the place values of the partial products.
Tori did not place the decimal point correctly.
Tori added the partial products incorrectly.
The correct answer is 6.9375 miles, while Tori's calculation was incorrect.
She did not correctly align the place values of the partial products, She did not place the decimal point correctly, She added the partial products incorrectly.
Explanation
Problem Analysis Let's analyze Tori's calculation to identify the errors she made. The problem is to multiply 9.25 by 0.75.
Correct Multiplication First, let's perform the correct multiplication:
9.25
\times 0.75
\hline
Multiplying 9.25 by 5 (from 0.75) gives 46.25. Tori wrote 4625, which is 100 times larger. However, we will account for the decimal places later.
Multiplying 9.25 by 70 (from 0.75) gives 647.5. Tori wrote 6475, which is 10 times larger. Again, we will account for the decimal places later.
Analyzing Partial Products and Alignment Now, let's look at the partial products and their alignment. The first partial product is 9.25 multiplied by 0.05, which is 4.625. The second partial product is 9.25 multiplied by 0.7, which is 6.475. Tori aligned the place values incorrectly. The 6 in 6475 should be in the hundreds place, but it looks like she aligned it as if it was in the thousands place.
Adding Partial Products and Decimal Placement Adding the partial products:
4.625 + 6.475 = 11.100 = 11.1
Tori added 4625 and 6475 to get 11090. Then, she placed the decimal point to get 11.090. The correct sum of the partial products should account for the decimal places in 9.25 and 0.75. Since 9.25 has two decimal places and 0.75 has two decimal places, the product should have four decimal places. The correct product is 6.9375.
Identifying the Errors Now, let's identify the errors Tori made:
She did not multiply 5 and 9.25 incorrectly. 925 * 5 = 4625, so the multiplication itself is correct, but she didn't account for the decimal places during the multiplication.
She did not correctly align the place values of the partial products. This is true because she treated 0.7 as 70 instead of 0.7 when multiplying.
She did not place the decimal point correctly. This is true because the correct product is 6.9375, but she got 11.090.
She added the partial products incorrectly. This is also true because 4.625 + 6.475 = 11.1, but she got 11.090 after placing the decimal point.
Conclusion Therefore, the errors Tori made are:
She did not correctly align the place values of the partial products.
She did not place the decimal point correctly.
She added the partial products incorrectly.
Examples
Understanding decimal multiplication is crucial in everyday life. For instance, when calculating the sale price of an item with a discount, you need to multiply the original price by a decimal (e.g., 0.20 for a 20% discount). If a shirt costs $25.50 and is 20% off, you multiply $25.50 by 0.20 to find the discount amount ($5.10). Subtracting this from the original price gives the sale price ($20.40). Accurate decimal multiplication ensures you pay the correct amount.
