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Simplifying & common denominators

Fractions

Japanese school year: Elementary 5

What you learn

You will learn how to simplify fractions and find common denominators by using equivalent fraction properties. These techniques are crucial for comparing fractions and preparing for addition and subtraction. Prior mastery of finding common factors and multiples will make these procedures straightforward.

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Key points

This formula is used for finding a common denominator. Multiplying both numerator aa and denominator bb by the same non-zero number cc does not change the fraction's value.

ab=a×cb×c(c≠0)\frac{a}{b} = \frac{a \times c}{b \times c} \quad (c \neq 0)

This formula is used for simplifying (reducing) fractions. Dividing both numerator aa and denominator bb by a common divisor cc (c≠0c \neq 0) does not change the fraction's value.

ab=a÷cb÷c(c≠0)\frac{a}{b} = \frac{a \div c}{b \div c} \quad (c \neq 0)

Use this method to reduce a fraction to its simplest form. Dividing both numerator and denominator by their greatest common divisor yields an irreducible fraction.

Use this procedure when adding or subtracting fractions with different denominators. Find the least common multiple of the denominators to rewrite them with a common denominator before calculating.

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