2/5 divided by 1 7/8 in the as a fraction in it simplest form
The Correct Answer and Explanation is:
To divide 25\frac{2}{5}52 by 1781 \frac{7}{8}187, we first need to convert the mixed number into an improper fraction and then apply the division rule for fractions.
Step 1: Convert 1781 \frac{7}{8}187 to an improper fraction
A mixed number like 1781 \frac{7}{8}187 can be written as an improper fraction. The formula to convert a mixed number to an improper fraction is:Improper fraction=(whole number×denominator+numerator)/denominator\text{Improper fraction} = \left( \text{whole number} \times \text{denominator} + \text{numerator} \right) / \text{denominator}Improper fraction=(whole number×denominator+numerator)/denominator
For 1781 \frac{7}{8}187, the whole number is 1, the numerator is 7, and the denominator is 8. So:178=(1×8)+78=8+78=1581 \frac{7}{8} = \frac{(1 \times 8) + 7}{8} = \frac{8 + 7}{8} = \frac{15}{8}187=8(1×8)+7=88+7=815
Step 2: Divide 25\frac{2}{5}52 by 158\frac{15}{8}815
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So:25÷158=25×815\frac{2}{5} \div \frac{15}{8} = \frac{2}{5} \times \frac{8}{15}52÷815=52×158
Step 3: Multiply the fractions
Multiply the numerators and denominators:2×85×15=1675\frac{2 \times 8}{5 \times 15} = \frac{16}{75}5×152×8=7516
Step 4: Simplify the fraction
The fraction 1675\frac{16}{75}7516 is already in its simplest form because 16 and 75 have no common factors other than 1.
Thus, the final answer is:1675\frac{16}{75}7516
Explanation
When dividing fractions, the key concept is flipping the second fraction (reciprocal) and multiplying it by the first fraction. We then simplify the resulting fraction if possible. In this case, the improper fraction conversion and multiplication were straightforward, and no further simplification was necessary. The result is 1675\frac{16}{75}7516, a proper fraction in its simplest form.
