Simplify 7/9 ÷ 5/6.
Understand the Problem
The question is asking to simplify the expression which consists of a fraction divided by another fraction.
Answer
The simplified fraction is \( \frac{14}{15} \).
Answer for screen readers
The simplified expression is ( \frac{14}{15} ).
Steps to Solve
- Rewrite the Division as Multiplication
To simplify ( \frac{7}{9} \div \frac{5}{6} ), we rewrite the division of fractions as multiplying by the reciprocal. Thus, it becomes: $$ \frac{7}{9} \times \frac{6}{5} $$
- Multiply the Numerators and Denominators
Next, multiply the numerators together and the denominators together: $$ \frac{7 \times 6}{9 \times 5} $$
This gives: $$ \frac{42}{45} $$
- Simplify the Fraction
To simplify ( \frac{42}{45} ), identify the greatest common divisor (GCD) of 42 and 45, which is 3. Now, divide both the numerator and the denominator by 3: $$ \frac{42 \div 3}{45 \div 3} = \frac{14}{15} $$
The simplified expression is ( \frac{14}{15} ).
More Information
The process of simplifying fractions involves multiplying by the reciprocal and finding the GCD to reduce the fraction. This technique is useful in many mathematical applications, such as solving equations.
Tips
- Forgetting to multiply by the reciprocal when dividing fractions.
- Not simplifying the fraction completely. Always check for common factors.
