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Dividing Fractions
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Foundational skills
Find the reciprocal of a unit fraction
\[ \text{Reciprocal of } \frac{1}{5} \]
Find the reciprocal of a unit fraction.
Find the reciprocal of a proper fraction
\[ \text{Reciprocal of } \frac{3}{7} \]
Flip numerator and denominator.
Find the reciprocal of an improper fraction
\[ \text{Reciprocal of } \frac{7}{3} \]
Flip numerator and denominator.
Find the reciprocal of an integer
\[ \text{Reciprocal of } 5 \]
Find the reciprocal of a whole number.
Find the reciprocal of a mixed number
\[ \text{Reciprocal of } 2\frac{1}{3} \]
Convert to improper first, then flip.
Convert a mixed number to an improper fraction
\[ 3\frac{2}{5} = \frac{?}{5} \]
Preparation for division.
Rewrite division as multiplication by reciprocal
\[ \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{?}{?} \]
Without calculating.
Integer ÷ fraction
Integer ÷ unit fraction
\[ 6 \div \frac{1}{3} = \square \]
Divide a whole number by a unit fraction.
Integer ÷ proper fraction — whole number result
\[ 6 \div \frac{2}{3} = \square \]
Answer is a whole number.
Integer ÷ proper fraction — fraction result
\[ 5 \div \frac{2}{3} = \square \]
Answer is not a whole number.
Integer ÷ improper fraction — whole number result
\[ 6 \div \frac{3}{2} = \square \]
Answer is a whole number.
Integer ÷ improper fraction — fraction result
\[ 5 \div \frac{3}{2} = \square \]
Answer is not a whole number.
Integer ÷ mixed number
\[ 6 \div 1\frac{1}{2} = \square \]
Divide a whole number by a mixed number.
Fraction ÷ integer
Unit fraction ÷ integer
\[ \frac{1}{3} \div 4 = \square \]
Divide a unit fraction by a whole number.
Proper fraction ÷ integer — no simplifying
\[ \frac{2}{5} \div 3 = \square \]
No simplifying needed.
Proper fraction ÷ integer — with simplifying
\[ \frac{2}{3} \div 4 = \square \]
The answer simplifies.
Improper fraction ÷ integer
\[ \frac{7}{3} \div 2 = \square \]
Divide an improper fraction by a whole number.
Mixed number ÷ integer
\[ 2\frac{1}{3} \div 2 = \square \]
Divide a mixed number by a whole number.
Proper ÷ proper fraction
Proper ÷ proper — result less than 1
\[ \frac{1}{3} \div \frac{2}{3} = \square \]
Answer is less than one.
Proper ÷ proper — result equals 1
\[ \frac{2}{5} \div \frac{2}{5} = \square \]
Divide a fraction by itself.
Proper ÷ proper — result greater than 1
\[ \frac{2}{3} \div \frac{1}{4} = \square \]
Answer is greater than one.
Proper ÷ proper — whole number result
\[ \frac{2}{3} \div \frac{1}{3} = \square \]
Answer is a whole number.
Proper ÷ proper — with cross-cancelling
\[ \frac{3}{4} \div \frac{9}{8} = \square \]
Cross-cancelling is possible.
Involving improper fractions
Proper ÷ improper
\[ \frac{2}{5} \div \frac{7}{3} = \square \]
Divide a proper by an improper fraction.
Improper ÷ proper
\[ \frac{7}{3} \div \frac{2}{5} = \square \]
Divide an improper by a proper fraction.
Improper ÷ improper — result less than 1
\[ \frac{5}{3} \div \frac{7}{2} = \square \]
Smaller ÷ larger improper.
Improper ÷ improper — result greater than 1
\[ \frac{7}{2} \div \frac{5}{3} = \square \]
Larger ÷ smaller improper.
Improper ÷ improper — whole number result
\[ \frac{9}{4} \div \frac{3}{4} = \square \]
Same denominator, whole number result.
Involving mixed numbers
Mixed number ÷ unit fraction
\[ 2\frac{1}{3} \div \frac{1}{4} = \square \]
Divide a mixed number by a unit fraction.
Mixed number ÷ proper fraction
\[ 2\frac{1}{2} \div \frac{3}{4} = \square \]
Divide a mixed number by a proper fraction.
Mixed number ÷ improper fraction
\[ 3\frac{1}{2} \div \frac{7}{4} = \square \]
Divide a mixed number by an improper fraction.
Proper fraction ÷ mixed number
\[ \frac{2}{3} \div 1\frac{1}{4} = \square \]
Divide a proper fraction by a mixed number.
Mixed number ÷ mixed number — result less than 1
\[ 1\frac{1}{3} \div 2\frac{1}{2} = \square \]
Smaller ÷ larger mixed number.
Mixed number ÷ mixed number — result greater than 1
\[ 3\frac{1}{2} \div 1\frac{1}{4} = \square \]
Larger ÷ smaller mixed number.
Mixed number ÷ mixed number — whole number result
\[ 2\frac{1}{2} \div 1\frac{1}{4} = \square \]
Answer is a whole number.
Special cases
Fraction ÷ 1
\[ \frac{3}{5} \div 1 = \square \]
Identity property of division.
Fraction ÷ itself
\[ \frac{3}{5} \div \frac{3}{5} = \square \]
Divide a fraction by itself.
Fraction ÷ its reciprocal
\[ \frac{2}{3} \div \frac{3}{2} = \square \]
Result is the square of the fraction.
Dividing equal fractions with different forms
\[ \frac{1}{2} \div \frac{2}{4} = \square \]
Equivalent fractions divide to give 1.
1 ÷ fraction (finding reciprocal)
\[ 1 \div \frac{3}{4} = \square \]
Divide 1 by a fraction to find its reciprocal.
Dividing by a fraction equal to one half
\[ \frac{6}{7} \div \frac{1}{2} = \square \]
Equivalent to doubling the fraction.
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