Evaluate 1/5 divided by 3/4 Give your answer as a fraction in its simplest form.
The correct answer and explanation is:
To evaluate the expression 15÷34\frac{1}{5} \div \frac{3}{4}, follow these steps:
Step 1: Convert Division to Multiplication
When dividing by a fraction, you multiply by the reciprocal of that fraction. The reciprocal of 34\frac{3}{4} is 43\frac{4}{3}. So, the division becomes: 15÷34=15×43\frac{1}{5} \div \frac{3}{4} = \frac{1}{5} \times \frac{4}{3}
Step 2: Multiply the Fractions
To multiply two fractions, multiply the numerators and multiply the denominators: 15×43=1×45×3=415\frac{1}{5} \times \frac{4}{3} = \frac{1 \times 4}{5 \times 3} = \frac{4}{15}
Step 3: Simplify the Fraction
In this case, 415\frac{4}{15} is already in its simplest form because the numerator (4) and the denominator (15) have no common factors other than 1.
Final Answer:
The result of 15÷34\frac{1}{5} \div \frac{3}{4} is 415\frac{4}{15}.
Explanation:
Division of fractions can be simplified by converting it to multiplication. Instead of dividing, you multiply by the reciprocal of the divisor. This operation maintains the equality of the expression. The process involves straightforward multiplication of the numerators and denominators, and the final fraction is reduced to its simplest form if necessary. In this case, the fraction is already in its simplest form.