How do you insert a pair of brackets to make each statement true #1/2+ 2/3 - 1/4 * 2/5 ÷ 1/6 = 6 2/5#?

1 Answer
Jul 4, 2015

Answer:

#(1/2+ 2/3 - 1/4 * 2/5) ÷ 1/6 = 6 2/5#

Explanation:

#1/2+ 2/3 - 1/4 * 2/5 ÷ 1/6 = 6 2/5#

I first rewrote #-:1/6 # as #*6/1#

#1/2+ 2/3 - 1/4 * 2/5 * 6/1 = 6 2/5#

Now that mixed number on the right confuses me, so write:

#1/2+ 2/3 - 1/4 * 2/5 * 6/1 = 32/5#

That looks better but there are too many denominators especially in the addition and subtraction. So let's write:

#30/60 + 40/60 - 15/60 * 2/5 *6 = 384/60#

Keeping the factors # 15/60 * 2/5 *6# together means we'll need to do something with
#-15/60*2/5*6 = -3/60 * 2/3*6 = -36/60#

But the first two only sum to #70/60#, so that won't work.

Next, I divided #384# by #6# to see what we'd need #1/2+ 2/3 - 1/4 * 2/5# to be, if multiply by #6# was the last step.

#384 -: 6 = 64#

And, (Bonus)

#30/60 + 40/60 - 15/60 * 2/5 = 30/60 + 40/60 - (3/60 * 2/1)#

# = 30/60 + 40/60 - 6/60 = 64/60#

Last check:

#(1/2+ 2/3 - 1/4 * 2/5) ÷ 1/6 #

# = (1/2 + 2/3 -(1/4*2/5)) -: 1/6#

# = (1/2 + 2/3 -1/10) -: 1/6#

# = (15/30 + 20/30 -3/30) -: 1/6#

# = (35/30 - 3/30)-: 1/6#

# = 32/30 -: 1/6#

# = 32/30 * 6/1 = 32/5 = 6 2/5#

It works!