Dividing a Fraction by a Fraction
This Grade 6 math skill from Pengi Math (Grade 6) teaches students the procedure for dividing one fraction by another fraction. Students learn to apply the keep-change-flip method (multiply by the reciprocal) and simplify the result, building fluency with fraction division.
Key Concepts
Property To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction. $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$.
Examples $\frac{2}{3} \div \frac{1}{5} = \frac{2}{3} \times \frac{5}{1} = \frac{10}{3}$ $\frac{3}{4} \div \frac{9}{8} = \frac{3}{4} \times \frac{8}{9} = \frac{24}{36} = \frac{2}{3}$.
Explanation Dividing by a fraction is the same as multiplying by its reciprocal. To solve a fraction division problem, you keep the first fraction the same, change the division sign to a multiplication sign, and flip the second fraction to find its reciprocal. After rewriting the problem as multiplication, multiply the numerators and the denominators, and simplify the result if necessary.
Common Questions
How do you divide a fraction by a fraction?
Keep the first fraction, change the division sign to multiplication, and flip the second fraction (use its reciprocal). Then multiply the numerators and denominators.
What is the keep-change-flip method?
Keep the first fraction unchanged, change the division to multiplication, and flip the second fraction to its reciprocal. For example, 2/3 ÷ 4/5 = 2/3 × 5/4.
Should you simplify before or after multiplying fractions?
You can simplify by cross-canceling before multiplying, which makes the numbers smaller and easier to work with. Then simplify the final answer if needed.
What is the result of dividing a fraction by itself?
Any non-zero fraction divided by itself equals 1, just like any non-zero number divided by itself.
Where is dividing a fraction by a fraction taught?
This operation is covered in the Grade 6 Pengi Math textbook under fraction computation skills.