gloryyy3
Answered

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What is the quotient of the fractions below?

[tex]\[ \frac{1}{3} \div \frac{5}{8} \][/tex]

A. [tex]\[ \frac{8}{15} \][/tex]

B. [tex]\[ \frac{5}{24} \][/tex]

C. [tex]\[ \frac{24}{5} \][/tex]

D. [tex]\[ \frac{15}{8} \][/tex]

Sagot :

GinnyAnswer
To find the quotient of the fractions [tex]\(\frac{1}{3} \div \frac{5}{8}\)[/tex], follow these steps:

1. Identify the operation: We need to divide [tex]\(\frac{1}{3}\)[/tex] by [tex]\(\frac{5}{8}\)[/tex].

2. Division of fractions: Division by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{5}{8}\)[/tex] is [tex]\(\frac{8}{5}\)[/tex].

3. Set up the multiplication:
[tex]\[ \frac{1}{3} \div \frac{5}{8} = \frac{1}{3} \times \frac{8}{5} \][/tex]

4. Multiply the numerators: Multiply the numerators of both fractions.
[tex]\[ 1 \times 8 = 8 \][/tex]

5. Multiply the denominators: Multiply the denominators of both fractions.
[tex]\[ 3 \times 5 = 15 \][/tex]

6. Resulting fraction: Combine the results from the numerators and the denominators into a fraction.
[tex]\[ \frac{8}{15} \][/tex]

7. Simplify the fraction if possible: In this case, [tex]\(\frac{8}{15}\)[/tex] is already in its simplest form.

Thus, the quotient of [tex]\(\frac{1}{3} \div \frac{5}{8}\)[/tex] is [tex]\(\frac{8}{15}\)[/tex].

Therefore, the correct answer is:

A. [tex]\(\frac{8}{15}\)[/tex]
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