Question

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

Answer 1

`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`

Answer 2

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`

Answer 3

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