What is the answer to 3/4 divided by 2/5

The Correct Answer and Explanation is :

To solve the problem of dividing ( \frac{3}{4} ) by ( \frac{2}{5} ), you can follow these steps:

Step 1: Understand Division of Fractions

Dividing fractions is not as straightforward as dividing whole numbers. Instead of dividing directly, we can use the rule that states:

[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
]

In this case, you will multiply by the reciprocal of the second fraction.

Step 2: Find the Reciprocal

The reciprocal of ( \frac{2}{5} ) is ( \frac{5}{2} ). This means you will rewrite the division problem as a multiplication problem:

[
\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2}
]

Step 3: Multiply the Fractions

Now you can multiply the fractions together. To multiply fractions, you simply multiply the numerators together and the denominators together:

[
\frac{3 \times 5}{4 \times 2} = \frac{15}{8}
]

Step 4: Simplify if Necessary

In this case, ( \frac{15}{8} ) is already in its simplest form. However, you can also express it as a mixed number. To convert ( \frac{15}{8} ) into a mixed number, divide the numerator by the denominator:

( 15 \div 8 = 1 ) with a remainder of ( 7 ).

Thus,

[
\frac{15}{8} = 1 \frac{7}{8}
]

Final Answer

The result of ( \frac{3}{4} \div \frac{2}{5} ) is ( \frac{15}{8} ) or ( 1 \frac{7}{8} ).

Conclusion

Understanding how to divide fractions by using the reciprocal can make the process straightforward. Always remember to simplify your final answer where possible, and converting to a mixed number can provide a clearer understanding of the quantity represented by the fraction.