Question

Using 7 1/2 / 3/4 = 60/6=10 interpret the meaning of the quotient in terms of the two fractions given

Answer 1

$\bf \cfrac{~~7\frac{1}{2}~~}{\frac{3}{4}}\implies \cfrac{~~\frac{7\cdot 2+1}{2}~~}{\frac{3}{4}}\implies \cfrac{~~\frac{15}{2}~~}{\frac{3}{4}}\implies \cfrac{\stackrel{5}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 10$

if we divide 7½ by 3/4, we get 10, namely, 3/4 + 3/4 +3/4 +3/4 +3/4 +3/4 +3/4 +3/4 +3/4 +3/4 = 7½.

or put differently, 3/4 goes into 7½ 10 times.

Answer 2

Answer:

Here's what I get.

Step-by-step explanation:

$x = 7\frac{1}{2} \div \frac{3}{4}$

1. Convert the mixed number to an improper fraction

$x = \dfrac{15}{2} \div \dfrac{3}{4}$

2. Invert the proper fraction and change division to multiplication

$x = \dfrac{15}{2} \times \dfrac{4}{3}$

3. Multiply numerators and denominators

$x = \dfrac{60}{6}$

4. Divide the numerator and the denominator

$x = 10$

The quotient is what you get after you invert the denominator in Step 2 and then multiply the two fractions in Step 3.