Question

What is the value of the expression (-8/9) divided by (-2/3) x (-4 1/2) ?

Answer 1

Answer:

B) $x=-\frac{8}{27}$

Step-by-step explanation:

$-\frac{8}{9}=-\frac{2}{3}x(-4\frac{1}{2})$

• To start things off, lets convert any mixed numbers like $-4\frac{1}{2}$ into improper fractions. In this case $-4\frac{1}{2}$ as an improper fraction is $-\frac{9}{2}$.

$-\frac{8}{9}=-\frac{2}{3}x(-\frac{9}{2})$

• Now let's multiply $-\frac{2}{3}x$ by $-\frac{9}{2}$. When multiplying fractions, all you need to do is multiply the numerators and denominators separately. Your final answer should be $\frac{18}{6}x$.
• *Note: a negative times a negative is a positive, so that's why we now have an even number in front of $x$ instead of a negative number.

$-\frac{8}{9}=\frac{18}{6}x$

• Now we want to isolate $x$, so we'll have to divide $-\frac{8}{9}$ by $\frac{18}{6}$, but dividing these two fractions seems like a pain. To make things a bit easier, let's turn our improper fraction into a whole number. To change this improper fraction into a whole number, we should ask ourselves what times $6$ is equal to $18$? In this case, the answer is 3, so $\frac{18}{6}$ is actually the same thing as the whole number $3$.
• *Note: In general, keeping fractions as either improper fractions or whole numbers will make doing math easier. Avoid mixed numbers like $-4\frac{1}{2}$ when trying to do math and simply change improper fractions into mixed numbers once you have your final solution.

$-\frac{8}{9}=3x$

• Now divide $-\frac{8}{9}$ by $3$. Think of it as multiplying the denominator of $-\frac{8}{9}$ by $3$.

$-\frac{8}{27}=x$