What is #1/2 -: 3/4#?

Question

Gianna Caruso · Accepted Answer

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.

Gabriel Agustin · Answer

#color (blue)(2/3)# 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#

Autumn Arnold · Answer

#2/3# #=1/2/3/4# #=1/2*4/3# #=1*2/3# #=2/3#.

Luna Angel · Answer

#2/3#

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#

Jeremiah Andrews · Answer

#2/3#

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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mila Anderson · Answer

undefined To divide fractions, you can multiply the first fraction by the reciprocal of the second fraction.

So, 1/2 ÷ 3/4 is the same as 1/2 × 4/3.

When you multiply these fractions, you multiply the numerators together and the denominators together.

1/2 × 4/3 = (1 × 4) / (2 × 3) = 4/6.

Now, you can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

4/6 simplifies to 2/3.

Therefore, 1/2 ÷ 3/4 equals 2/3.