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Subtracting Fractions
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Foundational skills
Recognise when fractions are ready to be subtracted
\[ \frac{5}{8} – \frac{3}{8} \text{ ready?} \]
Decide whether two fractions already have the same denominator.
Find the LCM of two coprime numbers
\[ \text{LCM of } 4 \text{ and } 7 \]
Find the lowest common multiple of two numbers that share no common factors.
Find the LCM when one number is a multiple of the other
\[ \text{LCM of } 4 \text{ and } 8 \]
Find the LCM of two numbers where one divides exactly into the other.
Find the LCM when two numbers share a common factor
\[ \text{LCM of } 6 \text{ and } 9 \]
Find the LCM when numbers share a factor but neither is a multiple.
One whole minus a proper fraction
\[ 1 – \frac{2}{5} = \square \]
Subtract a proper fraction from one whole.
Integer minus proper fraction
\[ 5 – \frac{2}{7} = \square \]
Subtract a proper fraction from a whole number greater than one.
Integer minus improper fraction
\[ 5 – \frac{9}{7} = \square \]
Subtract an improper fraction from a whole number.
Same denominators
Same denominator — proper result
\[ \frac{4}{7} – \frac{2}{7} = \square \]
Subtract two fractions that already have the same denominator.
Same denominator — result is zero
\[ \frac{3}{7} – \frac{3}{7} = \square \]
Subtract two identical fractions to get zero.
Subtract from one whole to leave a target
\[ 1 – \square = \frac{2}{5} \]
Find the fraction to subtract from one whole to leave a given amount.
Find what was subtracted
\[ \frac{5}{8} – \square = \frac{3}{8} \]
Find the fraction that was subtracted.
Different denominators — multiples
One denominator is a multiple — proper result
\[ \frac{5}{8} – \frac{1}{4} = \square \]
Subtract fractions where one denominator is a multiple of the other.
One denominator is a multiple — result is zero
\[ \frac{1}{4} – \frac{2}{8} = \square \]
Subtract two equivalent fractions with different denominators.
Different denominators — coprime
Coprime denominators — proper result
\[ \frac{2}{3} – \frac{1}{5} = \square \]
Subtract fractions whose denominators share no common factors.
Unit fractions with coprime denominators
\[ \frac{1}{3} – \frac{1}{4} = \square \]
Subtract two unit fractions with coprime denominators.
Different denominators — shared factor
Shared factor denominators — proper result
\[ \frac{5}{6} – \frac{1}{4} = \square \]
Subtract fractions whose denominators share a common factor.
Unit fractions with shared factor denominators
\[ \frac{1}{4} – \frac{1}{6} = \square \]
Subtract unit fractions with shared factor denominators.
Mixed number − proper fraction
Same denominator — no regrouping
\[ 3\frac{4}{5} – \frac{2}{5} = \square \]
Subtract a proper fraction from a mixed number, no borrowing needed.
Same denominator — with regrouping
\[ 3\frac{1}{5} – \frac{3}{5} = \square \]
Subtract a proper fraction from a mixed number, borrowing needed.
One denominator multiple of other
\[ 3\frac{1}{4} – \frac{3}{8} = \square \]
Mixed number minus proper fraction, one denominator is a multiple.
Coprime denominators
\[ 3\frac{1}{3} – \frac{1}{5} = \square \]
Mixed number minus proper fraction with coprime denominators.
Shared factor denominators
\[ 3\frac{1}{6} – \frac{1}{9} = \square \]
Mixed number minus proper fraction with shared factor denominators.
Two mixed numbers
Same denominator — no regrouping
\[ 5\frac{4}{7} – 2\frac{1}{7} = \square \]
Subtract two mixed numbers, same denominator, no borrowing.
Same denominator — with regrouping
\[ 5\frac{2}{7} – 2\frac{4}{7} = \square \]
Subtract two mixed numbers, same denominator, borrowing needed.
One denominator multiple of other
\[ 5\frac{1}{4} – 2\frac{1}{8} = \square \]
Subtract two mixed numbers, one denominator is a multiple.
Coprime denominators
\[ 5\frac{1}{3} – 2\frac{1}{4} = \square \]
Subtract two mixed numbers with coprime denominators.
Shared factor denominators
\[ 5\frac{1}{6} – 2\frac{1}{9} = \square \]
Subtract two mixed numbers with shared factor denominators.
Special cases
Improper minus proper — same denominator
\[ \frac{9}{5} – \frac{2}{5} = \square \]
Subtract a proper fraction from an improper fraction.
Improper minus improper — same denominator
\[ \frac{11}{5} – \frac{7}{5} = \square \]
Subtract one improper fraction from another.
Subtracting from an improper fraction — different denominators
\[ \frac{7}{4} – \frac{2}{3} = \square \]
Subtract a proper fraction from an improper fraction, different denominators.
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