What is 1/2 -: 3/4?

5 Answers
Mar 11, 2018

color (blue)(2/3)

Explanation:

Note that a/b÷c/d=a/b×d/c

So, 1/2÷3/4 = 1/2×4/3

1/cancel2×cancel4^2/3

2/3 ~~ 0.66

In decimal 0.bar6

Mar 11, 2018

2/3

Explanation:

=1/2/3/4

=1/2*4/3

=1*2/3

=2/3.

Mar 11, 2018

2/3

Explanation:

Because you use KFC... Keep Flip Change.

You keep the first fraction the same

1/4

then you flip the other fraction

1/4 ÷ 4/3

Finally, you change the symbol to a times

1/4 xx 4/3

You then multiply the fraction getting

4/6

Simplified makes

2/3

Mar 12, 2018

A fraction is actually a division problem so to divide two fractions set it up as a division problem or complex fraction. This makes the most sense.

1/2/ 3/4 = ( 1/2)/(3/4)

Now multiply both the top fraction and the bottom fraction by the inverse of the bottom fraction. This makes sense because multiply by (4/3)/(4/3) = 1 multiplying by one doesn't anything

Also multiplying by the inverse equals one

(3/4) xx ( 4/3) = 12/12 = 1

(1/2 xx 4/3)/ (3/4 xx 4/3) = ( 1/2 xx 4/3)/1 Which leaves.

1/2 xx 4/3 = 4/6 Divide both top and bottom by 2

(4/2)/( 6/2) = 2/3

Dividing a fraction by a fraction makes sense and is easier to remember, even thought it takes longer.

Mar 12, 2018

2/3

Explanation:

Here is another approach to understand WHY the method of Multiply and Flip works to divide by a fraction, rather than just HOW to do it.

The fraction 3/4 means 'three' quarters.

Quarters are obtained when a whole number is divided into four equal pieces, each is a quarter.

To find the number of quarters there are, multiply a number by 4

In 1 there will be 1xx4 = 4 quarters
In 2 there will be 2xx4=8 quarters
In 3 there will be 3xx4=12 quarters

In 11 there will be 11xx4=44 quarters

In 1/2 there will be 1/2xx4=2 quarters

However, when dividing by 3/4 we are actually asking "How many groups of 3/4 can be obtained ?"
(or how many times can 3/4 be subtracted?)

That means, once you have the total number of quarters, divide them into groups of three's - each group will be 'Three' quarters.

You do this by dividing the total number of quarters by 3

In 1 there will be 1xx4 = 4 quarters
4 div 3 = 1 1/3, so there are 1 1/3 groups of 3/4
Hence 3/4 divides into 1, a total of 1 1/3 times

(ie. once with a bit left over.)
.

In 2 there will be 2xx4=8 quarters

8div 3 = 2 2/3 so there are 2 2/3 groups of 3/4
Hence 3/4 divides into 2, a total of 2 2/3 times.

In 9 there will be 9 xx4 = 36 quarters.

36 div 3 = 12, so there are 12 groups of 3/4 in 9
.

In each case we are multiplying by 4 and dividing by 3.

4/3 is the reciprocal of 3/4

Hence the simple rule of Multiply and flip.

1/2 div 3/4

=color(blue)(1/2 xx4) div 3" "larr change into quarters

=2color(red)(div3)" "larr divide into groups of 3

=2/3
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Something like 6div 3/4 can be shown very nicely practically by taking 6 squares, cutting them into quarters and then then making groups of 3/4 ... there will be exactly 8. which nicely demonstrates:

6 div 3/4

=6xx4 div3

=6xx4/3

=8

3/4 fits into 6 a total of 8 times.
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