Question
(a)
Error Analysis:
Your friend incorrectly says that the quotient
3
8
÷
1
8
=
1
3
8
3
÷
8
1
=
3
1
. What is the correct quotient?
3
8
÷
1
8
=
8
3
÷
8
1
=
24/8
(b)
What mistake did your friend likely make?
A
Your friend multiplied 83×8\frac{8}{3}\times 8
3
8
×8
B
Your friend multiplied with the reciprocal of the first fraction, not the second fraction.
C
Your friend multiplied 38×18\frac{3}{8}\times \frac{1}{8}
8
3
×
8
1
D
Your friend added the fractions instead of dividing.
Answers
Answer
Your friend incorrectly says that the quotient
3
8
÷
1
8
=
1
3
8
3
÷
8
1
=
3
1
. What is the correct quotient?
3
8
÷
1
8
=
1
3
8
3
÷
8
1
=
3
1
. What is the correct quotient?
Answer
do it with no cancil out
Answered by
GPT-4o mini
To correct your friend's calculation, let's first find the correct quotient of the fractions given.
(a) To calculate \( \frac{3}{8} \div \frac{1}{8} \), you multiply by the reciprocal of the second fraction:
\[
\frac{3}{8} \div \frac{1}{8} = \frac{3}{8} \times \frac{8}{1}
\]
Now, multiply:
\[
\frac{3 \times 8}{8 \times 1} = \frac{24}{8} = 3
\]
So the correct quotient is \( 3 \).
(b) Now, let's analyze what mistake your friend likely made. The options provided are:
A. Your friend multiplied \( \frac{8}{3} \times 8 \)
B. Your friend multiplied with the reciprocal of the first fraction, not the second fraction.
C. Your friend multiplied \( \frac{3}{8} \times \frac{1}{8} \)
D. Your friend added the fractions instead of dividing.
From your friend's claim that \( \frac{3}{8} \div \frac{1}{8} = \frac{1}{3} \) and that it equals \( 1 \frac{3}{8} \), it seems that they did not apply the correct operation. Since they ended up with an incorrect quotient of \( 1 \frac{3}{8} \), it indicates they may have tried to add or misunderstood how to divide fractions.
The best fit among the options is:
**D. Your friend added the fractions instead of dividing.**
This error would lead to a different outcome, as addition of the two fractions would not yield the correct division result.
(a) To calculate \( \frac{3}{8} \div \frac{1}{8} \), you multiply by the reciprocal of the second fraction:
\[
\frac{3}{8} \div \frac{1}{8} = \frac{3}{8} \times \frac{8}{1}
\]
Now, multiply:
\[
\frac{3 \times 8}{8 \times 1} = \frac{24}{8} = 3
\]
So the correct quotient is \( 3 \).
(b) Now, let's analyze what mistake your friend likely made. The options provided are:
A. Your friend multiplied \( \frac{8}{3} \times 8 \)
B. Your friend multiplied with the reciprocal of the first fraction, not the second fraction.
C. Your friend multiplied \( \frac{3}{8} \times \frac{1}{8} \)
D. Your friend added the fractions instead of dividing.
From your friend's claim that \( \frac{3}{8} \div \frac{1}{8} = \frac{1}{3} \) and that it equals \( 1 \frac{3}{8} \), it seems that they did not apply the correct operation. Since they ended up with an incorrect quotient of \( 1 \frac{3}{8} \), it indicates they may have tried to add or misunderstood how to divide fractions.
The best fit among the options is:
**D. Your friend added the fractions instead of dividing.**
This error would lead to a different outcome, as addition of the two fractions would not yield the correct division result.
Answered by
GPT-4o mini
To find the correct quotient of the division \( \frac{3}{8} \div \frac{1}{8} \), we will multiply by the reciprocal of the second fraction.
The operation is:
\[
\frac{3}{8} \div \frac{1}{8} = \frac{3}{8} \times \frac{8}{1}
\]
Now, we can perform the multiplication:
\[
\frac{3 \times 8}{8 \times 1} = \frac{24}{8} = 3
\]
So, the correct quotient is **3**.
The operation is:
\[
\frac{3}{8} \div \frac{1}{8} = \frac{3}{8} \times \frac{8}{1}
\]
Now, we can perform the multiplication:
\[
\frac{3 \times 8}{8 \times 1} = \frac{24}{8} = 3
\]
So, the correct quotient is **3**.
Answered by
GPT-4o mini
Certainly! Let's compute \( \frac{3}{8} \div \frac{1}{8} \) without canceling out any terms during the multiplication.
To divide fractions, we multiply by the reciprocal of the second fraction:
\[
\frac{3}{8} \div \frac{1}{8} = \frac{3}{8} \times \frac{8}{1}
\]
Now, we multiply the numerators together and the denominators together:
\[
\frac{3 \times 8}{8 \times 1} = \frac{24}{8}
\]
Now we'll divide 24 by 8 without canceling:
\[
24 \div 8 = 3
\]
Thus, the correct quotient is **3**.
To divide fractions, we multiply by the reciprocal of the second fraction:
\[
\frac{3}{8} \div \frac{1}{8} = \frac{3}{8} \times \frac{8}{1}
\]
Now, we multiply the numerators together and the denominators together:
\[
\frac{3 \times 8}{8 \times 1} = \frac{24}{8}
\]
Now we'll divide 24 by 8 without canceling:
\[
24 \div 8 = 3
\]
Thus, the correct quotient is **3**.
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