Math Problem Statement

Simplify. Write your answer as a proper or improper fraction in simplest form: 8/5 ÷ 7/6

Solution

The expression in the image is a division of two fractions:

85÷76\frac{8}{5} \div \frac{7}{6}

To simplify this, we multiply the first fraction by the reciprocal of the second fraction:

85×67=8×65×7=4835\frac{8}{5} \times \frac{6}{7} = \frac{8 \times 6}{5 \times 7} = \frac{48}{35}

Since 4835\frac{48}{35} is already in its simplest form (it cannot be simplified further), the final answer is:

4835\frac{48}{35}

This is an improper fraction, as the numerator is greater than the denominator. You could leave it like this or convert it to a mixed number:

48÷35=1 remainder 1348 \div 35 = 1 \text{ remainder } 13

So, as a mixed number:

113351 \frac{13}{35}

Would you like more details on these steps?

Here are 5 related questions:

  1. How do you multiply two fractions in general?
  2. How do you convert an improper fraction into a mixed number?
  3. Can you explain why we use the reciprocal when dividing fractions?
  4. How would the process change if you were asked to divide a fraction by a whole number?
  5. How can you simplify fractions before multiplying?

Tip: Always check if the fractions can be simplified before multiplying to make the calculation easier.

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Math Problem Analysis

Mathematical Concepts

Fractions
Division of Fractions
Reciprocal
Multiplication of Fractions

Formulas

Division of Fractions: a/b ÷ c/d = a/b × d/c

Theorems

Reciprocal of a Fraction

Suitable Grade Level

Grades 5-7