Adding & subtracting unlike fractions

Japanese school year: Elementary 5

What you learn

You will learn how to add and subtract fractions with different denominators by finding a common denominator first. This skill is useful for combining quantities measured in the same unit but expressed with different denominators. Proficiency in finding least common multiples and simplifying fractions will ensure your success.

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Key points

This formula is used to add two fractions $\frac{a}{b}$ and $\frac{c}{d}$ with different denominators. You first find a common denominator $bd$ , and then add the adjusted numerators ( $ad + bc$ ).

\frac{a}{b} + \frac{c}{d} = \frac{a d + b c}{b d}

This formula is used to subtract the fraction $\frac{c}{d}$ from $\frac{a}{b}$ when denominators differ. You first find a common denominator $bd$ , and then subtract the numerators ( $ad - bc$ ).

\frac{a}{b} - \frac{c}{d} = \frac{a d - b c}{b d}

This is a rule for finding a common denominator (finding common multiples). Choosing the least common multiple (LCM) of the denominators keeps the numbers small and simplifies calculations.

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Practice 1Coming soon