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Fractions, Decimals, and Percentages - Adding and subtracting fractions

Grade 6IGCSE

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

πŸ”‘Concepts

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Like Denominators: When fractions have the same bottom number, add or subtract the numerators and keep the denominator the same.

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Unlike Denominators: Fractions must be converted to have a common denominator using the Least Common Multiple (LCM) before adding or subtracting.

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Equivalent Fractions: Multiplying the numerator and denominator by the same non-zero number to change the fraction's appearance without changing its value.

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Mixed Numbers: Convert mixed numbers into improper fractions before performing operations, or handle whole numbers and fractions separately (with care during subtraction regrouping).

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Simplification: Always reduce the final answer to its simplest form by dividing the numerator and denominator by their Greatest Common Divisor (GCD).

πŸ“Formulae

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

acβˆ’bc=aβˆ’bc\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

abΒ±cd=adΒ±bcbd\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}

πŸ’‘Examples

Problem 1:

Calculate \frac{3}{10} + rac{2}{5}

Solution:

710\frac{7}{10}

Explanation:

First, find a common denominator for 10 and 5. The LCM is 10. Convert 25\frac{2}{5} to tenths by multiplying the numerator and denominator by 2: 2Γ—25Γ—2=410\frac{2 \times 2}{5 \times 2} = \frac{4}{10}. Now add the numerators: 310+410=710\frac{3}{10} + \frac{4}{10} = \frac{7}{10}.

Problem 2:

Calculate 56βˆ’14\frac{5}{6} - \frac{1}{4}

Solution:

712\frac{7}{12}

Explanation:

The LCM of 6 and 4 is 12. Convert both fractions: 5Γ—26Γ—2=1012\frac{5 \times 2}{6 \times 2} = \frac{10}{12} and 1Γ—34Γ—3=312\frac{1 \times 3}{4 \times 3} = \frac{3}{12}. Subtract the numerators: 1012βˆ’312=712\frac{10}{12} - \frac{3}{12} = \frac{7}{12}.

Problem 3:

Solve 212βˆ’1342\frac{1}{2} - 1\frac{3}{4}

Solution:

34\frac{3}{4}

Explanation:

Convert mixed numbers to improper fractions: 212=522\frac{1}{2} = \frac{5}{2} and 134=741\frac{3}{4} = \frac{7}{4}. Find a common denominator (4): 52\frac{5}{2} becomes 104\frac{10}{4}. Subtract: 104βˆ’74=34\frac{10}{4} - \frac{7}{4} = \frac{3}{4}.