6th Grade Math Flashcards: Divide Fractions By Fractions

What this deck covers

This deck focuses on Divide Fractions By Fractions, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Compute $\frac{1}{2} \div 3$.

Answer: $\frac{1}{6}$. $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$.

Flashcard 2: What is $3 \div $$\frac{1}{4}$ $?

Answer: $12$. $3 \times \frac{4}{1} = 12$ by the reciprocal rule.

Flashcard 3: Compute $\frac{2}{5} \div 4$.

Answer: $\frac{1}{10}$. $\frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10}$.

Flashcard 4: Identify the missing factor: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \underline{\ \ \ }$.

Answer: $\frac{d}{c}$. The reciprocal of the divisor completes the multiplication.

Flashcard 5: What is the reciprocal of $\frac{c}{d}$ (with $c,d\ne 0$)?

Answer: $\frac{d}{c}$. Flip the numerator and denominator.

Flashcard 6: What is $\frac{6}{7} \div \frac{3}{14}$?

Answer: $4$. $\frac{6}{7} \times \frac{14}{3} = \frac{84}{21} = 4$.

Flashcard 7: Find the width: area $\frac{1}{2}$ sq mi and length $\frac{3}{4}$ mi.

Answer: $\frac{2}{3}$ mi. $\text{Width} = \text{Area} \div \text{Length} = \frac{1}{2} \div \frac{3}{4}$

Flashcard 8: State the general rule for dividing fractions: $(\frac{a}{b}) \div (\frac{c}{d})$ equals what?

Answer: $\frac{ad}{bc}$. Multiply by the reciprocal: $\frac{a}{b} \times \frac{d}{c}$

Flashcard 9: What is $\frac{5}{6} \div \frac{1}{3}$?

Answer: $\frac{5}{2}$. $\frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2}$.

Flashcard 10: Compute $\frac{3}{4} \div \frac{1}{2}$.

Answer: $\frac{3}{2}$. $\frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2}$.

Flashcard 11: How many $\frac{3}{4}$-cup servings are in $\frac{2}{3}$ cup?

Answer: $\frac{8}{9}$ serving. $\frac{2}{3} \div \frac{3}{4} = \frac{8}{9}$ of a serving.

Flashcard 12: Compute $\frac{1}{2} \div \frac{3}{4}$.

Answer: $\frac{2}{3}$. $\frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}$.

Flashcard 13: What is $$ $\frac{1}{2} \div 3$ $?

Answer: $\frac{1}{6}$. $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$ since $3 = \frac{3}{1}$.

Flashcard 14: Which expression matches "Each person's share of $\frac{1}{2}$ lb split among $3$ people"?

Answer: $\frac{1}{2} \div 3$. Total amount divided by number of people.

Flashcard 15: What operation is equivalent to $$ $\frac{a}{b} \div \frac{c}{d}$ $?

Answer: $\frac{a}{b} \times \frac{d}{c}$. Division by a fraction equals multiplication by its reciprocal.

Flashcard 16: Compute $\frac{4}{9} \div \frac{2}{3}$.

Answer: $\frac{2}{3}$. $\frac{4}{9} \times \frac{3}{2} = \frac{12}{18} = \frac{2}{3}$.

Flashcard 17: Compute $\frac{7}{8} \div \frac{7}{16}$.

Answer: $2$. $\frac{7}{8} \times \frac{16}{7} = \frac{112}{56} = 2$.

Flashcard 18: What division expression represents "How many $$ $\frac{3}{4}$ $-cup servings fit in$ $\frac{2}{3}$ cup"?

Answer: $\frac{2}{3} \div \frac{3}{4}$. Total amount divided by size of each serving.

Flashcard 19: What is $1 \div \frac{3}{4}$?

Answer: $\frac{4}{3}$. $\frac{1}{1} \times \frac{4}{3} = \frac{4}{3}$.

Flashcard 20: Identify the correct equation for rectangle width $w$: $A=\frac{1}{2}$, $L=\frac{3}{4}$.

Answer: $w = \frac{1}{2} \div \frac{3}{4}$. Area = Length $\times$ Width, so Width = Area $\div$ Length.

Flashcard 21: What is $\frac{2}{5} \div 2$?

Answer: $\frac{1}{5}$. $\frac{2}{5} \times \frac{1}{2} = \frac{2}{10} = \frac{1}{5}$ simplified.

Flashcard 22: What is the missing number $x$ in $$ $\frac{3}{4} \times x = \frac{2}{3}$ $?

Answer: $\frac{8}{9}$. $x = \frac{2}{3} \div \frac{3}{4} = \frac{8}{9}$ by division.

Flashcard 23: What is $\frac{9}{10} \div \frac{3}{5}$?

Answer: $\frac{3}{2}$. $\frac{9}{10} \times \frac{5}{3} = \frac{45}{30} = \frac{3}{2}$.

Flashcard 24: What is $$ $\frac{5}{12} \div \frac{5}{6}$ $?

Answer: $\frac{1}{2}$. $\frac{5}{12} \times \frac{6}{5} = \frac{30}{60} = \frac{1}{2}$ simplified.

Flashcard 25: Find and correct the error: $\frac{2}{3} \div \frac{3}{4} = \frac{2}{3} \times \frac{3}{4}$.

Answer: Correct: $\frac{2}{3} \times \frac{4}{3}$. Should multiply by reciprocal $\frac{4}{3}$, not $\frac{3}{4}$.

Flashcard 26: Compute $\frac{5}{6} \div \frac{1}{2}$.

Answer: $\frac{5}{3}$. $\frac{5}{6} \times \frac{2}{1} = \frac{10}{6} = \frac{5}{3}$.

Flashcard 27: What multiplication equation checks $\frac{2}{3} \div \frac{3}{4} = \frac{8}{9}$?

Answer: $\frac{3}{4} \times \frac{8}{9} = \frac{2}{3}$. Check by multiplying quotient by divisor to get dividend.

Flashcard 28: Compute $4 \div \frac{2}{3}$.

Answer: $6$. $4 \times \frac{3}{2} = \frac{12}{2} = 6$.

Flashcard 29: What is $\frac{3}{4} \div 2$?

Answer: $\frac{3}{8}$. $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$.

Flashcard 30: What is $\frac{7}{8} \div \frac{7}{4}$?

Answer: $\frac{1}{2}$. $\frac{7}{8} \times \frac{4}{7} = \frac{28}{56} = \frac{1}{2}$.

Flashcard 31: What does $\frac{2}{3} \div \frac{3}{4}$ mean in words?

Answer: How many $\frac{3}{4}$ are in $\frac{2}{3}$. Division asks how many groups of the divisor fit in the dividend.

Flashcard 32: What is the reciprocal of $\frac{c}{d}$?

Answer: $\frac{d}{c}$. Flip the numerator and denominator.

Flashcard 33: What does $\frac{2}{3} \div \frac{3}{4}$ represent in words?

Answer: How many $\frac{3}{4}$ are in $\frac{2}{3}$. Division asks how many groups of the divisor fit in the dividend.

Flashcard 34: What operation is equivalent to dividing by a fraction $c/d$?

Answer: Multiply by the reciprocal: $\times \frac{d}{c}$. Division by a fraction equals multiplication by its reciprocal.

Flashcard 35: How many $\frac{3}{4}$-cup servings are in $\frac{2}{3}$ cup of yogurt?

Answer: $\frac{8}{9}$ serving. Divide total by serving size: $\frac{2}{3} \div \frac{3}{4}$.

Flashcard 36: What is the reciprocal of $3/4$?

Answer: $\frac{4}{3}$. Flip the numerator and denominator to find the reciprocal.

Flashcard 37: Compute $\frac{5}{6} \div \frac{1}{3}$.

Answer: $\frac{5}{2}$. $\frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2}$.

Flashcard 38: Which expression matches "How many $\frac{3}{4}$-cup servings are in $\frac{2}{3}$ cup"?

Answer: $\frac{2}{3} \div \frac{3}{4}$. Total amount divided by size of each serving.

Flashcard 39: What is the width if area is $$ $\frac{1}{2}$ $mi$^2$and length is$ $\frac{3}{4}$ mi?

Answer: $\frac{2}{3}$ mi. Width = Area ÷ Length = $\frac{1}{2} \div \frac{3}{4} = \frac{2}{3}$ mi.

Flashcard 40: What multiplication equation is equivalent to $x \div \frac{c}{d}$?

Answer: $x \times \frac{d}{c}$. Division by a fraction equals multiplication by its reciprocal.

Flashcard 41: What is $\frac{3}{5} \div \frac{2}{5}$?

Answer: $\frac{3}{2}$. $\frac{3}{5} \times \frac{5}{2} = \frac{15}{10} = \frac{3}{2}$.

Flashcard 42: How much chocolate does each get if $3$ people share $\frac{1}{2}$ lb equally?

Answer: $\frac{1}{6}$ lb each. Divide total amount by number of people: $\frac{1}{2} \div 3$.

Flashcard 43: What is $\frac{4}{9} \div \frac{2}{3}$?

Answer: $\frac{2}{3}$. $\frac{4}{9} \times \frac{3}{2} = \frac{12}{18} = \frac{2}{3}$.

Flashcard 44: What is $\frac{2}{3} \div \frac{3}{4}$?

Answer: $\frac{8}{9}$. $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$ by the reciprocal rule.

Flashcard 45: Find the width if area is $\frac{1}{2}$ sq mi and length is $\frac{3}{4}$ mi: $w=\frac{1}{2} \div \frac{3}{4}$.

Answer: $\frac{2}{3}$ mi. $\text{Area} \div \text{length} = \text{width}$: $\frac{1}{2} \times \frac{4}{3} = \frac{2}{3}$

Flashcard 46: What is $\frac{5}{6} \div \frac{1}{2}$

Answer: $\frac{5}{3}$. $\frac{5}{6} \times \frac{2}{1} = \frac{10}{6} = \frac{5}{3}$ simplified.

Flashcard 47: Compute $\frac{3}{5} \div \frac{9}{10}$.

Answer: $\frac{2}{3}$. $\frac{3}{5} \times \frac{10}{9} = \frac{30}{45} = \frac{2}{3}$.

Flashcard 48: Find the width: area $=\frac{1}{2}$ sq mi and length $=\frac{3}{4}$ mi.

Answer: $\frac{2}{3}$ mi. Width = Area ÷ Length = $\frac{1}{2} \div \frac{3}{4} = \frac{2}{3}$.

Flashcard 49: State the rewrite rule for fraction division: $\frac{a}{b} \div \frac{c}{d}$.

Answer: $\frac{a}{b} \times \frac{d}{c}$. Division becomes multiplication by the reciprocal.

Flashcard 50: What is each person's share if $3$ people split $\frac{1}{2}$ lb equally?

Answer: $\frac{1}{6}$ lb. $\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$.

Flashcard 51: What is $$ $\frac{7}{8} \div \frac{7}{4}$ $?

Answer: $\frac{1}{2}$. $\frac{7}{8} \times \frac{4}{7} = \frac{28}{56} = \frac{1}{2}$ simplified.

Flashcard 52: State the general rule for dividing fractions: $a/b c/d$.

Answer: $\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$. Multiply the first fraction by the reciprocal of the second.

Flashcard 53: What is each share if $3$ people split $\frac{1}{2}$ lb equally?

Answer: $\frac{1}{6}$ lb. $\frac{1}{2} \div 3 = \frac{1}{6}$ lb per person.

Flashcard 54: What is the rule for dividing fractions: $\frac{a}{b} \div \frac{c}{d}$?

Answer: $\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$. Multiply by the reciprocal: flip the second fraction and multiply.

Flashcard 55: What is $2 \div \frac{1}{5}$?

Answer: $10$. $\frac{2}{1} \times \frac{5}{1} = 10$.

Flashcard 56: Which equation matches "How many $\frac{3}{4}$-cup servings are in $\frac{2}{3}$ cup"?

Answer: $\frac{2}{3} \div \frac{3}{4}$. Total amount divided by serving size gives number of servings.

Flashcard 57: How much chocolate does each person get if $3$ people share $\frac{1}{2}$ lb equally?

Answer: $\frac{1}{6}$ lb. $\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$.

Flashcard 58: Which equation matches "Each person's share of $\frac{1}{2}$ lb among $3$ people"?

Answer: $\frac{1}{2} \div 3$. Total amount divided by number of people gives each share.

Flashcard 59: What is $\frac{4}{9} \div \frac{2}{3}$?

Answer: $\frac{2}{3}$. $\frac{4}{9} \times \frac{3}{2} = \frac{12}{18} = \frac{2}{3}$ simplified.

Flashcard 60: What is the reciprocal of $\frac{c}{d}$ (with $c,d \ne 0$)?

Answer: $\frac{d}{c}$. Flip the numerator and denominator.

Flashcard 61: Compute $\frac{2}{3} \div \frac{3}{4}$.

Answer: $\frac{8}{9}$. $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$ by the reciprocal rule.

Flashcard 62: What is $$ $\frac{3}{5} \div \frac{2}{3}$ $?

Answer: $\frac{9}{10}$. $\frac{3}{5} \times \frac{3}{2} = \frac{9}{10}$ by the reciprocal rule.

Flashcard 63: What is $$ $\frac{2}{3} \div \frac{3}{4}$ $?

Answer: $\frac{8}{9}$. $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$ by the reciprocal rule.

Flashcard 64: Compute $\frac{2}{5} \div 3$.

Answer: $\frac{2}{15}$. $\frac{2}{5} \times \frac{1}{3} = \frac{2}{15}$.

Flashcard 65: Compute $3 \div \frac{1}{2}$.

Answer: $6$. $3 \times \frac{2}{1} = 6$ by the reciprocal rule.

Flashcard 66: What is $1 \div $$\frac{3}{7}$ $?

Answer: $\frac{7}{3}$. $1 \times \frac{7}{3} = \frac{7}{3}$ by the reciprocal rule.

Flashcard 67: What is $$ $\frac{9}{10} \div \frac{3}{5}$ $?

Answer: $\frac{3}{2}$. $\frac{9}{10} \times \frac{5}{3} = \frac{45}{30} = \frac{3}{2}$ simplified.

Flashcard 68: Compute $3 \div \frac{2}{5}$.

Answer: $\frac{15}{2}$. $3 \times \frac{5}{2} = \frac{15}{2}$.

Flashcard 69: State the general rule for dividing fractions: $\frac{a}{b} \div \frac{c}{d}$

Answer: $\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$. Multiply by the reciprocal: flip the second fraction and multiply.

Flashcard 70: What is $\frac{3}{4} \div \frac{3}{8}$?

Answer: $2$. $\frac{3}{4} \times \frac{8}{3} = \frac{24}{12} = 2$ simplified.