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Fractions, Decimals, and Percentages - Adding and subtracting fractions with different denominators

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Identifying the Least Common Multiple (LCM) to find a common denominator.

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Converting unlike fractions into equivalent fractions with the same denominator.

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Adding or subtracting only the numerators once the denominators are matched.

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Keeping the denominator constant during the addition or subtraction process.

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Simplifying the resulting fraction to its lowest terms (simplest form).

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Converting improper fractions to mixed numbers if necessary.

📐Formulae

ab±cd=a×db×d±c×bd×b=ad±bcbd\frac{a}{b} \pm \frac{c}{d} = \frac{a \times d}{b \times d} \pm \frac{c \times b}{d \times b} = \frac{ad \pm bc}{bd}

Equivalent Fraction: ab=a×nb×n\text{Equivalent Fraction: } \frac{a}{b} = \frac{a \times n}{b \times n}

Simplest Form: a÷GCD(a,b)b÷GCD(a,b)\text{Simplest Form: } \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)}

💡Examples

Problem 1:

Calculate 14+25\frac{1}{4} + \frac{2}{5}

Solution:

1320\frac{13}{20}

Explanation:

First, find the LCM of 4 and 5, which is 20. Convert both fractions: 1×54×5=520\frac{1 \times 5}{4 \times 5} = \frac{5}{20} and 2×45×4=820\frac{2 \times 4}{5 \times 4} = \frac{8}{20}. Now add the numerators: 5+8=135 + 8 = 13. The result is 1320\frac{13}{20}.

Problem 2:

Calculate 56−13\frac{5}{6} - \frac{1}{3}

Solution:

12\frac{1}{2}

Explanation:

The LCM of 6 and 3 is 6. Convert 13\frac{1}{3} to an equivalent fraction with denominator 6: 1×23×2=26\frac{1 \times 2}{3 \times 2} = \frac{2}{6}. Subtract the numerators: 56−26=36\frac{5}{6} - \frac{2}{6} = \frac{3}{6}. Simplify by dividing both numerator and denominator by 3 to get 12\frac{1}{2}.

Problem 3:

Calculate 23+12\frac{2}{3} + \frac{1}{2}

Solution:

1161 \frac{1}{6}

Explanation:

The LCM of 3 and 2 is 6. Convert fractions: 2×23×2=46\frac{2 \times 2}{3 \times 2} = \frac{4}{6} and 1×32×3=36\frac{1 \times 3}{2 \times 3} = \frac{3}{6}. Add them: 4+36=76\frac{4+3}{6} = \frac{7}{6}. Since this is an improper fraction, convert it to a mixed number: 1161 \frac{1}{6}.