The size of fractions

Japanese school year: Elementary 3

What you learn

You will learn the meaning of numerators and denominators, interpreting fractions as collections of unit fractions on a number line. This knowledge is useful for reading scale markings and comparing fractional quantities. A basic grasp of dividing whole objects equally will support this topic.

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Key points

This formula shows the structure of fraction $\frac{a}{b}$ . It defines $\frac{a}{b}$ as the quantity obtained by collecting $a$ units of $\frac{1}{b}$ .

\frac{a}{b} = a \times \frac{1}{b}

This equation shows when a fraction equals $1$ . For any non-zero number $a$ , a fraction whose numerator and denominator are both $a$ ( $\frac{a}{a}$ ) equals the integer $1$ .

\frac{a}{a} = 1 \quad (a \neq 0)

This rule compares fractions with a common denominator. When the positive denominator $c$ is the same, the fraction with the larger numerator ( $b$ when $a < b$ ) is greater.

\frac{a}{c} < \frac{b}{c} \quad (a < b, \, c > 0)

These are the names classifying fractions. A fraction with a numerator smaller than its denominator is a proper fraction, one with a numerator greater than or equal to its denominator is an improper fraction, and an integer combined with a proper fraction is a mixed number.

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Practice 1Coming soon