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# fraction Dividing

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why do you multiply fractions instead of dividing? cause my teacher always said to invert and multiply and i was confused why.

Jun 13, 2017

#1
+7350
+2

It is easier to multiply fractions.

For example:

$$\frac34\div\frac57=\frac34\,*\,\frac75$$

Then, just multiply straight across.

$$=\frac{3*7}{4*5}=\frac{21}{20}$$

It  is  true that

$$\frac34\div\frac57=\frac{3\div5}{4\div7}=\frac{21}{20}$$

But how are you going to evaluate   3 / 5    and   4 / 7    without using a calculator or long division?

And...to see why inverting and multiplying is the same as dividing, take a simple example:

$$10\div2=10\,*\,\frac12=\frac{10}{1}\,*\,\frac12=\frac{10}{2}$$

.
Jun 14, 2017

#1
+7350
+2

It is easier to multiply fractions.

For example:

$$\frac34\div\frac57=\frac34\,*\,\frac75$$

Then, just multiply straight across.

$$=\frac{3*7}{4*5}=\frac{21}{20}$$

It  is  true that

$$\frac34\div\frac57=\frac{3\div5}{4\div7}=\frac{21}{20}$$

But how are you going to evaluate   3 / 5    and   4 / 7    without using a calculator or long division?

And...to see why inverting and multiplying is the same as dividing, take a simple example:

$$10\div2=10\,*\,\frac12=\frac{10}{1}\,*\,\frac12=\frac{10}{2}$$

hectictar Jun 14, 2017