For positive fractions with a/b < c/d, which number always lies between them?

a+c/b+d. Adding tops and adding bottoms (the mediant) always gives a number in between, e.g. 1/3, 2/5, 1/2. The product ac/bd can be smaller than both (1/3 × 1/2 = 1/6).

For positive fractions with $\frac{a}{b} < \frac{c}{d}$ , which number always lies between them?

Class 7Rational Numbers Between Two NumbersRational Numbers

A $\frac{a + c}{b + d}$
B $\frac{a + c}{b \times d}$
C $\frac{a \times c}{b \times d}$
D $\frac{b + d}{a + c}$

Step-by-Step Solution

Adding tops and adding bottoms (the mediant) always gives a number in between, e.g.

\frac{1}{3}, \frac{2}{5}, \frac{1}{2}

. The product

\frac{a c}{b d}

can be smaller than both

(\frac{1}{3} \times \frac{1}{2} = \frac{1}{6})

Answer: A)

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

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For positive fractions with $\frac{a}{b} < \frac{c}{d}$ , which number always lies between them?