Which expression equals -2/3 × (5/7 - 4/9 ) by the distributive property?

Which expression equals $- \frac{2}{3} \times (\frac{5}{7} - \frac{4}{9})$ by the distributive property?

Class 8Rational NumbersRational Numbers

A $- \frac{2}{3} \times \frac{5}{7} - \frac{4}{9}$
B $- \frac{2}{3} \times \frac{5}{7} + (- \frac{2}{3}) \times \frac{4}{9}$
C $- \frac{2}{3} \times \frac{5}{7} - (- \frac{2}{3}) \times \frac{4}{9}$
D $(- \frac{2}{3} - \frac{5}{7}) \times (- \frac{2}{3} - \frac{4}{9})$

Step-by-Step Solution

The rule is

a \times (b - c) = a \times b - a \times c

, so the factor

- \frac{2}{3}

must multiply BOTH terms and the minus between them stays a minus. Option 1 forgets to multiply the second term at all; option 2 turns the subtraction into an addition. (Both the question and the correct option evaluate to

- \frac{34}{189} .

)

Answer: C)

- \frac{2}{3} \times \frac{5}{7} - (- \frac{2}{3}) \times \frac{4}{9}

Key idea: Closure of rationals

Rationals are **closed under addition, subtraction, and multiplication** — the result is always rational.

But **division is closed only if you exclude division by 0**: for any rationals a and b ≠ 0, a ÷ b is rational.

This is more than integers (which weren't closed under division at all) and more than fractions (which sometimes had subtraction lead outside the fractions). Rationals form the smallest 'nice' number system that supports all four basic operations (with the 0-divisor exception).

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The reciprocal of a rational number x is -5/12. What is x?How many rational numbers with denominator 63 lie strictly between 2/7 and 3/7?Between which two consecutive integers does -11/4 lie on the number line?The sum of two rational numbers is -1/3. If one of them is 5/6, find the other.Use the properties (not brute force) to compute 3/8 × (-4/5 ) + (-4/5 ) × 5/8.

Which expression equals −32​×(75​−94​) by the distributive property?

Step-by-Step Solution

Key idea: Closure of rationals

Master this chapter in 30 minutes a day.

More Class 8 Rational Numbers practice

Which expression equals $- \frac{2}{3} \times (\frac{5}{7} - \frac{4}{9})$ by the distributive property?