What is 3/4 divided by 2/5?
Understand the Problem
The question is asking to calculate the result of dividing the fraction 3/4 by the fraction 2/5. This involves using the rule for dividing fractions, which is to multiply by the reciprocal of the second fraction.
Answer
The result is \( \frac{15}{8} \).
Answer for screen readers
The result of dividing ( \frac{3}{4} ) by ( \frac{2}{5} ) is ( \frac{15}{8} ).
Steps to Solve
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Identify the fractions We are given two fractions: ( \frac{3}{4} ) and ( \frac{2}{5} ). We need to divide ( \frac{3}{4} ) by ( \frac{2}{5} ).
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Find the reciprocal of the second fraction The reciprocal of a fraction is obtained by swapping its numerator and denominator. The reciprocal of ( \frac{2}{5} ) is ( \frac{5}{2} ).
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Multiply by the reciprocal Now, instead of dividing ( \frac{3}{4} ) by ( \frac{2}{5} ), we multiply ( \frac{3}{4} ) by ( \frac{5}{2} ): $$ \frac{3}{4} \times \frac{5}{2} $$
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Multiply the numerators and denominators Perform the multiplication: Numerator: ( 3 \times 5 = 15 )
Denominator: ( 4 \times 2 = 8 )
Putting it all together: $$ \frac{15}{8} $$
- Simplify if needed In this case, ( \frac{15}{8} ) is already in its simplest form.
The result of dividing ( \frac{3}{4} ) by ( \frac{2}{5} ) is ( \frac{15}{8} ).
More Information
The answer ( \frac{15}{8} ) can also be expressed as a mixed number, which is ( 1 \frac{7}{8} ). This division of fractions is an important concept in algebra, particularly in dealing with ratios and proportions.
Tips
- Forgetting to use the reciprocal: Remember, to divide fractions, you must multiply by the reciprocal of the second fraction.
- Incorrect multiplication of the numerators/denominators: Always double-check your multiplication to ensure accuracy.
