Question

What is the quotient? StartFraction 2 m + 4 Over 8 EndFraction divided by StartFraction m + 2 Over 6 EndFraction StartFraction 24 Over (m + 2) squared EndFraction StartFraction (m + 2) squared Over 24 EndFraction Two-thirds Three-halves

Answer 1

Answer:

Step-by-step explanation

Given that,

(2m+4) / 8 / (m+2) / 6

Then,

(2m+4) / 8 ÷ (m+2) / 6

[(2m+4) / 8] × [6 / (m+2)]

Simply the 2m+4

[2(m+2) / 8] × [6 / (m+2)]

Then, m+2 cancel out

We are left with

(2 / 8) × 6

12 / 8 =  3 / 2

So, the answer is three-halves

The last option is correct,

Check attachment for better understanding.

Answer 2

The quotient of an expression is the result of dividing the expressions

The quotient of $\mathbf{\frac{2m + 4}{8} \div \frac{m + 2}{6}}$ is three-halves

The expression is given as:

$\mathbf{\frac{2m + 4}{8} \div \frac{m + 2}{6}}$

Rewrite the expression as a product

$\mathbf{\frac{2m + 4}{8} \div \frac{m + 2}{6} = \frac{2m + 4}{8} \times \frac{6}{m + 2}}$

Factor out 2

$\mathbf{\frac{2m + 4}{8} \div \frac{m + 2}{6} = \frac{2(m + 2)}{8} \times \frac{6}{m + 2}}$

Cancel out m + 2

$\mathbf{\frac{2m + 4}{8} \div \frac{m + 2}{6} = \frac{2(1)}{8} \times \frac{6}{1}}$

Express 2(1) as 1

$\mathbf{\frac{2m + 4}{8} \div \frac{m + 2}{6} = \frac{2}{8} \times \frac{6}{1}}$

Multiply 2 by 6, and 8 by 1

$\mathbf{\frac{2m + 4}{8} \div \frac{m + 2}{6} = \frac{12}{8}}$

Divide 12 by 8

$\mathbf{\frac{2m + 4}{8} \div \frac{m + 2}{6} = 1.5}$

1.5 means three-halves.

Hence, the quotient of the expression is three-halves

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