Adding Fractions Breakdown
1. Foundations & Same Denominator
Recognise readiness
\[ \frac{3}{8} + \frac{5}{8} \]
Identify if denominators match
Integer + proper fraction
\[ 3 + \frac{1}{5} \]
Combine whole number and fraction
Same denominator (Proper)
\[ \frac{1}{5} + \frac{2}{5} \]
Add numerators, sum < 1
Same denominator (Improper)
\[ \frac{3}{5} + \frac{4}{5} \]
Add numerators, sum > 1
2. Different Denominators (Proper Result)
One multiple of other
\[ \frac{1}{4} + \frac{3}{8} \]
Convert smaller denominator
Coprime denominators
\[ \frac{1}{3} + \frac{2}{5} \]
No common factors. LCM = product
Common factor
\[ \frac{1}{6} + \frac{2}{9} \]
Share factor, not multiples
3. Different Denominators (Improper Result)
One multiple of other
\[ \frac{3}{4} + \frac{5}{8} \]
Convert, sum > 1
Coprime denominators
\[ \frac{2}{3} + \frac{4}{5} \]
No common factors. Sum > 1
Common factor
\[ \frac{5}{6} + \frac{7}{9} \]
Share factor. Sum > 1
4. Mixed Numbers (Same Denominator)
Mixed + Proper (Basic)
\[ 2\frac{1}{5} + \frac{3}{5} \]
No regrouping needed
Mixed + Proper (Regroup)
\[ 3\frac{4}{5} + \frac{3}{5} \]
Fractions sum > 1
Two Mixed (Basic)
\[ 2\frac{1}{7} + 3\frac{2}{7} \]
No regrouping needed
Two Mixed (Regroup)
\[ 2\frac{4}{7} + 3\frac{5}{7} \]
Fractions sum > 1
5. Mixed Numbers (Different Denominators)
Mixed + Proper (Multiple)
\[ 2\frac{1}{4} + \frac{5}{8} \]
One denom multiple of other
Mixed + Proper (Coprime)
\[ 2\frac{1}{3} + \frac{2}{5} \]
Denominators coprime
Mixed + Proper (Common)
\[ 2\frac{1}{6} + \frac{2}{9} \]
Denominators share factor
Two Mixed (Multiple)
\[ 2\frac{1}{4} + 3\frac{1}{8} \]
One denom multiple of other
Two Mixed (Coprime)
\[ 2\frac{1}{3} + 3\frac{1}{4} \]
Denominators coprime
Two Mixed (Common)
\[ 2\frac{1}{6} + 3\frac{1}{9} \]
Denominators share factor
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