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Adding Fractions
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Foundational skills
Recognise when fractions are ready to be added
\[ \frac{3}{8} + \frac{5}{8} \text{ — ready?} \]
Decide if two fractions have the same denominator.
Find the LCM of two coprime numbers
\[ \text{LCM of } 4 \text{ and } 7 \]
LCM when numbers share no common factors.
Find the LCM when one is a multiple of the other
\[ \text{LCM of } 4 \text{ and } 8 \]
LCM when one divides into the other.
Find the LCM when two numbers share a factor
\[ \text{LCM of } 6 \text{ and } 9 \]
LCM when numbers share a common factor.
Integer plus proper fraction
\[ 3 + \frac{1}{5} = \square \]
Add a whole number to a proper fraction.
Integer plus improper fraction
\[ 3 + \frac{7}{5} = \square \]
Add a whole number to an improper fraction.
Same denominators
Same denominator — proper result
\[ \frac{1}{5} + \frac{2}{5} = \square \]
Add fractions with same denominator, answer < 1.
Same denominator — improper result
\[ \frac{3}{5} + \frac{4}{5} = \square \]
Add fractions with same denominator, answer > 1.
Fraction plus its complement to one whole
\[ \frac{3}{8} + \frac{5}{8} = \square \]
Add two fractions that make exactly 1.
Find the complement to one whole
\[ \frac{2}{7} + \square = 1 \]
Find the fraction needed to make 1.
Different denominators — multiples
One denominator is a multiple — proper result
\[ \frac{1}{4} + \frac{3}{8} = \square \]
One denominator divides into the other, answer < 1.
One denominator is a multiple — improper result
\[ \frac{3}{4} + \frac{5}{8} = \square \]
One denominator divides into the other, answer > 1.
Different denominators — coprime
Coprime denominators — proper result
\[ \frac{1}{3} + \frac{2}{5} = \square \]
Denominators share no common factors, answer < 1.
Coprime denominators — improper result
\[ \frac{2}{3} + \frac{4}{5} = \square \]
Denominators share no common factors, answer > 1.
Unit fractions with coprime denominators
\[ \frac{1}{3} + \frac{1}{4} = \square \]
Add two unit fractions with coprime denominators.
Different denominators — shared factor
Shared factor denominators — proper result
\[ \frac{1}{6} + \frac{2}{9} = \square \]
Denominators share a factor, answer < 1.
Shared factor denominators — improper result
\[ \frac{5}{6} + \frac{7}{9} = \square \]
Denominators share a factor, answer > 1.
Unit fractions with shared factor denominators
\[ \frac{1}{4} + \frac{1}{6} = \square \]
Add two unit fractions with shared factor denominators.
Mixed number + proper fraction
Same denominator — no regrouping
\[ 2\frac{1}{5} + \frac{3}{5} = \square \]
Mixed + proper, same denominator, no regrouping.
Same denominator — with regrouping
\[ 3\frac{4}{5} + \frac{3}{5} = \square \]
Mixed + proper, same denominator, with regrouping.
One denominator multiple of other
\[ 2\frac{1}{4} + \frac{5}{8} = \square \]
Mixed + proper, one denominator is a multiple.
Coprime denominators
\[ 2\frac{1}{3} + \frac{2}{5} = \square \]
Mixed + proper, coprime denominators.
Shared factor denominators
\[ 2\frac{1}{6} + \frac{2}{9} = \square \]
Mixed + proper, shared factor denominators.
Two mixed numbers
Same denominator — no regrouping
\[ 2\frac{1}{7} + 3\frac{2}{7} = \square \]
Two mixed numbers, same denominator, no regrouping.
Same denominator — with regrouping
\[ 2\frac{4}{7} + 3\frac{5}{7} = \square \]
Two mixed numbers, same denominator, with regrouping.
One denominator multiple of other
\[ 2\frac{1}{4} + 3\frac{1}{8} = \square \]
Two mixed numbers, one denominator is a multiple.
Coprime denominators
\[ 2\frac{1}{3} + 3\frac{1}{4} = \square \]
Two mixed numbers, coprime denominators.
Shared factor denominators
\[ 2\frac{1}{6} + 3\frac{1}{9} = \square \]
Two mixed numbers, shared factor denominators.
Special cases
Adding three fractions — same denominator
\[ \frac{1}{7} + \frac{2}{7} + \frac{3}{7} = \square \]
Add three fractions with the same denominator.
Adding three fractions — different denominators
\[ \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = \square \]
Add three fractions with different denominators.
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