How do you solve #x - 1/2 = 1 1/4#?

3 Answers
Nov 11, 2017

Answer:

#x=7/4#

Explanation:

Solve:

#x-1/2=1 1/4#

Convert #1 1/4# to an improper fraction by multiplying the denominator by the whole number #1#, and adding the numerator #1#. Set the result over the denominator #4#.

#(4xx1+1)/4=5/4#

Rewrite the equation.

#x-1/2=5/4#

Add #1/2# to both sides.

#x=5/4+1/2#

In order to add or subtract fractions, the denominators must be the same. In this case the least common denominator (LCD) is #4#. Multiply #1/2# by a fraction equal to #1# in order to produce an equivalent fraction. For example #5/5=1#. This way the value of the fraction is not changed.

Multiply #1/2# by #2/2#.

#x=5/4+1/2xx2/2#

Simplify.

#x=5/4+2/4#

Simplify.

#x=7/4#

Nov 11, 2017

First, make the mixed fraction into improper fraction,
#x-1/2=5/4#
Add 1/2 on both sides
#x cancel(-1/2)cancel(+1/2)=5/4+1/2#
Find LCM,
LCM is 4
#x=5/4+(1*2)/(2*2)#
#x=5/4+2/4#
Add
#x=7/4#
Or,
#x=1 3/4#
Or,
#x=1.75#

Nov 21, 2017

Answer:

Sometimes fractions and decimals are easy if you think of them as money.

Explanation:

Thinking of it as money, the question says:

1) You have a certain amount of money which is called #x#.

2) You spend a half a dollar (two quarters), written as #- 1/2#

3) You end up with one dollar and one quarter #1 1/4#

#x# . . . .#-# . . . . . #1/2# . . . . #=# . . . . #1 1/4#
$ . . . minus . . . 50ȼ . . . #=# . . . $1.25

Maybe you already know the answer without doing any math.

You spend 50ȼ and end up with $1.25.
How much did you have to start?

Answer:
You must have started with "$1 and 3 quarters" ($1.75)

because spending "2 quarters" (half a dollar)

leaves you with "$1 and one quarter." ($1.25)

#$1.75 - $0.50 = $1.25#

Answer:
#x = 1 3/4# #larr# one dollar and 3 quarters = $1.75