why is the fraction being reciprocated? please read above!?

Question

for example when 1/2 is multiplied by 3/4, the fraction is reciprocated and it becomes like 1/2 by 4/3. why is it like that? any specific answer!

oops sorry guys its when 1/2 is DIVIDED by 3/4

Answer 1

What you mentioned is a general property of fractions. If (x/y) and (a/b) are two fractions, they give the same answers when they are multiplied and when the reciprocal of the divisor is taken and divided. This is because when two fractions are divided, the process is equivalent to the reciprocal of the divisor being taken and then multiplied.

So, (x/y) * (a/b) = (xa/yb)

(x/y) / (b/a) = (x/y) * (a/b) = (xa/yb)

Hope that makes sense. Mail me if you need any more clarifications.

Answer 2

Yes, you meant 1/2 divided by 3/4 didn't you ?

Anyway to explain this there is one thing that you should understand before we start. This is it: you are allowed to multiply the top and bottom of any fraction without changing its value, so;

for example,

2/3 is the same as (2 x 7) / (3 x 7) = 14/21 {we multiplied top and bottom by 7}
and, very importantly ! 2/3 = 14/21.

Technically, we say that 2/3 and 14/21 are EQUIVALENT fractions.

How does understanding this help ?

Well, take your original problem. Follow these steps carefully, we are going to write a sort of double-decker fraction !

Write down 1/2 (use a – rather than a / when writing fractions).
Draw a longer horizontal line underneath the 1/2.
Below the horizontal line write 3/4

You have now written 1/2 divided by 3/4 as a very large double-decker fraction !

This next step will help you understand your original problem.

Remembering that we are allowed to multiply top and bottom by the same number, we are going to multiply the top and bottom of our double-decker fraction by the same number – we will choose 4/3, your "reciprocated" fraction

So, the top row of the double-decker will now be 1/2 x 4/3, and the bottom row will be 3/4 x 4/3. Look carefully at the bottom one; 3/4 x 4/3 ! It is 12/12, in other words it is exactly 1. Your teacher has probably told you dividing by 1 is very easy because any number divided by 1 is that same number.

So 45 divided by 1 is 45,
8.78 divided by 1 is 8.78.
7/8 divided by 1 is 7/8 and, in your example . . . .

1/2 x 4/3 divided by 1 is just 1/2 x 4/3

Look what happened !
You wrote down 1/2 divided by 3/4 as a double-decker fraction.
You multiplied top and bottom by 4/3.
This gave you an equivalent answer of 1/2 x 4/3

So 1/2 ÷ 3/4 = 1/2 x 4/3

Similarly 2/5 divided by 7/9 = 2/5 x 9/7, and so on.

So, the second fraction appears to turn upside-down, and the division becomes multiplication.

Hope it helps !

P.S. If you are doing 2/3 divided by 1¾, be careful ! Make sure that you change the 1¾ into 7/4 before inverting it (i.e reciprocating it)

So . . . 2/3 ÷ 1¾ = 2/3 ÷ 7/4 = 2/3 x 4/7 = 8/21

Answer 3

Example 1
1/2 x 3/4 = 3 / 8 (no reciprocating when multiplying)

Example 2
4 ÷ 1/2 = 4 /1 x 2 / 1 = 8 (i.e. reciprocate when dividing by a fraction)

Example 3
3/4 ÷ 1/8 = 3 / 4 x 8 / 1 = 24 / 4 = 6

Answer 4

To do a fraction division. For example:

1/2 divided by 1/2 will become 1/2 times 2/1
The product will be 2/2 or simply 1

Answer 5

Although multiplication of fractions may seem complicated, the fraction is not actually reciprocated.

When writing the fractions down, to multiply the fractions, multiply the top numbers (numerators), then multiply the bottom numbers (denominators).

For your example: Multiply the top numbers of each fraction

1*3 = 3

Now multiply the bottom numbers

2*4 = 8

So 1/2 multiplied by 3/4 = 3/8

You may be confusing multiplication with division of fractions, where the latter fraction is reciprocated. Don't worry multiplication of fractions isn't as confusing as you might think.

Cheers!

Answer 6

oooops - when 1/2 is DIVIDED by 3/4 the equation becomes

1/2 times 4/3 = 4/6 = 2/3

division not multiplication

1/2 times 3/4 = 3/8 that is multiplication

Answer 7

1/2*3/4
=1/2*(4/3)^-1
because (4/3)^-1=(3/4)
anything power minus one is the same as 1 upon that number so it becomes:
1/2*1/(4/3)
=(1/2)/(4/3)

Answer 8

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Answer 9

can't understand ur q.