Question

1. divide: \\(\frac{6}{7} \div \frac{4}{9}\\)\
2. evaluate: \\((+6)(-5) - (+7) + (-8)(-3)\\)

Explanation:

Problem 16: Divide $\boldsymbol{\frac{6}{7} \div \frac{4}{9}}$

Step1: Recall fraction division rule

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, $\frac{6}{7} \div \frac{4}{9} = \frac{6}{7} \times \frac{9}{4}$.

Step2: Multiply numerators and denominators

Multiply the numerators: $6 \times 9 = 54$. Multiply the denominators: $7 \times 4 = 28$. So we get $\frac{54}{28}$.

Step3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor, which is 2. $\frac{54 \div 2}{28 \div 2} = \frac{27}{14}$.

Step1: Calculate the products

First, calculate $(+6)(-5) = -30$ and $(-8)(-3) = 24$. The expression becomes $-30 - 7 + 24$.

Step2: Perform the subtractions and additions

First, $-30 - 7 = -37$. Then, $-37 + 24 = -13$.

Answer:

$\frac{27}{14}$

Problem 18: Evaluate $\boldsymbol{(+6)(-5) - (+7) + (-8)(-3)}$