Answer :
Ruby made an error in the division of fractions. Let's go through the correct process step by step.
When you divide fractions, you actually multiply by the reciprocal of the second fraction. Here’s how you can do it correctly:
1. Write the problem:
[tex]\(\frac{4}{5} \div \frac{2}{15}\)[/tex]
2. Find the reciprocal of the second fraction:
The reciprocal of [tex]\(\frac{2}{15}\)[/tex] is [tex]\(\frac{15}{2}\)[/tex].
3. Change the division to multiplication using the reciprocal:
[tex]\(\frac{4}{5} \times \frac{15}{2}\)[/tex]
4. Multiply the numerators:
[tex]\(4 \times 15 = 60\)[/tex]
5. Multiply the denominators:
[tex]\(5 \times 2 = 10\)[/tex]
6. Combine the result into a new fraction:
[tex]\(\frac{60}{10}\)[/tex]
7. Simplify the fraction:
[tex]\(\frac{60}{10} = 6\)[/tex]
So, the correct answer is [tex]\(6\)[/tex]. Ruby made a mistake by not correctly calculating the division as multiplication by the reciprocal, leading to an incorrect answer of [tex]\(\frac{14}{15}\)[/tex].
When you divide fractions, you actually multiply by the reciprocal of the second fraction. Here’s how you can do it correctly:
1. Write the problem:
[tex]\(\frac{4}{5} \div \frac{2}{15}\)[/tex]
2. Find the reciprocal of the second fraction:
The reciprocal of [tex]\(\frac{2}{15}\)[/tex] is [tex]\(\frac{15}{2}\)[/tex].
3. Change the division to multiplication using the reciprocal:
[tex]\(\frac{4}{5} \times \frac{15}{2}\)[/tex]
4. Multiply the numerators:
[tex]\(4 \times 15 = 60\)[/tex]
5. Multiply the denominators:
[tex]\(5 \times 2 = 10\)[/tex]
6. Combine the result into a new fraction:
[tex]\(\frac{60}{10}\)[/tex]
7. Simplify the fraction:
[tex]\(\frac{60}{10} = 6\)[/tex]
So, the correct answer is [tex]\(6\)[/tex]. Ruby made a mistake by not correctly calculating the division as multiplication by the reciprocal, leading to an incorrect answer of [tex]\(\frac{14}{15}\)[/tex].
