Ask a New Question
Menu

(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.

5 answers

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.

Your friend incorrectly says that the quotient
3
8
÷
1
8
=
1
3
8
3
​
÷
8
1
​
=
3
1
​
. What is the correct quotient?

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.

do it with no cancil out

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.