Explain Why (7÷4)÷(1÷2)=7÷4÷1×2 | Fractions

[eddie159]

Can someone please explain why the following equation is true:

(7 \div 4) \div (1 \div 2) = 7 \div 4 \div 1 \times 2

As in, why does the division become multiplication when the parentheses are removed?Thanks

 

[mfb]

Dividing by something is the same as multiplying by the inverse (by definition), and the inverse of 1/2 is 2/1. Therefore, (7/4)/(1/2) = (7/4) * (2/1) = (7/4)*2/1 = ((7/4)/1)*2.

 

[eddie159]

Thanks!

Dividing by something is the same as multiplying by the inverse (by definition), and the inverse of 1/2 is 2/1. Therefore, (7/4)/(1/2) = (7/4) * (2/1) = (7/4)*2/1 = ((7/4)/1)*2.

 

[member 587159]

Thanks!

I can't resist to say that $a \div b$ is an ugly and often confusing notation. Rather, we use $\frac{a}{b}$

 

[rahul_26]

When we divide a fraction by another fraction, we have to multiply first fraction by the reciprocal of second fraction.
i.e. $$\dfrac{a}{b}\div \dfrac{m}{n}=\dfrac{a}{b}\times \dfrac{n}{m}$$
so $$(7\div 4)\div (1\div 2)=\dfrac{7}{4}\div \dfrac{1}{2}=\dfrac{7}{4}\times \dfrac{2}{1}$$

 

[Mark44]

I can't resist to say that $a \div b$ is an ugly and often confusing notation. Rather, we use $\frac{a}{b}$

I totally agree.

 

[Deepak suwalka]

Dividing a fraction by another fraction is same as multiplying reciprocal of another fraction. So,

$\dfrac{7}{4}\div\dfrac{1}{2}=\dfrac{7}{4}\times\dfrac{2}{1}=\dfrac{\dfrac{7}{4}}{1}\times2$

$\implies\dfrac{7}{4}\div\dfrac{1}{2}=\dfrac{14}{4}$

$\implies\dfrac{7}{4}\times\dfrac{2}{1}=\dfrac{14}{4}$

$\implies\dfrac{\dfrac{7}{4}}{1}\times2=\dfrac{14}{4}$

 

[Mark44]

You have a lot of extra work here that isn't needed.

Dividing a fraction by another fraction is same as multiplying reciprocal of another fraction. So,

$\dfrac{7}{4}\div\dfrac{1}{2}=\dfrac{7}{4}\times\dfrac{2}{1}$

$=\frac 7 2$
Done...

$=\dfrac{\dfrac{7}{4}}{1}\times2$

$\implies\dfrac{7}{4}\div\dfrac{1}{2}=\dfrac{14}{4}$

$\implies\dfrac{7}{4}\times\dfrac{2}{1}=\dfrac{14}{4}$

$\implies\dfrac{\dfrac{7}{4}}{1}\times2=\dfrac{14}{4}$

With all of this extra, unnecessary work, you at least could have simplfied your final result.