Math Problem Statement

What is the result of 5/6 ÷ 2/3?

Solution

The equation shown in the image is:

56÷23\frac{5}{6} \div \frac{2}{3}

To divide fractions, we use the rule:

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Applying this rule to the given problem:

56÷23=56×32\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2}

Now, multiply the numerators and the denominators:

5×36×2=1512\frac{5 \times 3}{6 \times 2} = \frac{15}{12}

To simplify, divide both the numerator and the denominator by their greatest common divisor, which is 3:

1512=54\frac{15}{12} = \frac{5}{4}

Thus, the solution is:

54\frac{5}{4}

This is equivalent to 1.25 in decimal form.

Would you like further details or have any questions? Here are some related questions for practice:

  1. How would you multiply 34×75\frac{3}{4} \times \frac{7}{5}?
  2. What is the reciprocal of 78\frac{7}{8}?
  3. How do you convert an improper fraction like 94\frac{9}{4} into a mixed number?
  4. How would you add 56+23\frac{5}{6} + \frac{2}{3}?
  5. Can you simplify 1428\frac{14}{28}?

Tip: When dividing fractions, always remember to multiply by the reciprocal of the second fraction!

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Math Problem Analysis

Mathematical Concepts

Fractions
Division of Fractions
Simplification

Formulas

a/b ÷ c/d = a/b × d/c

Theorems

Reciprocal Rule in Division of Fractions

Suitable Grade Level

Grades 5-6