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

Nov 11, 2017

$x = \frac{7}{4}$

#### Explanation:

Solve:

$x - \frac{1}{2} = 1 \frac{1}{4}$

Convert $1 \frac{1}{4}$ to an improper fraction by multiplying the denominator by the whole number $1$, and adding the numerator $1$. Set the result over the denominator $4$.

$\frac{4 \times 1 + 1}{4} = \frac{5}{4}$

Rewrite the equation.

$x - \frac{1}{2} = \frac{5}{4}$

Add $\frac{1}{2}$ to both sides.

$x = \frac{5}{4} + \frac{1}{2}$

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

Multiply $\frac{1}{2}$ by $\frac{2}{2}$.

$x = \frac{5}{4} + \frac{1}{2} \times \frac{2}{2}$

Simplify.

$x = \frac{5}{4} + \frac{2}{4}$

Simplify.

$x = \frac{7}{4}$

Nov 11, 2017

First, make the mixed fraction into improper fraction,
$x - \frac{1}{2} = \frac{5}{4}$
$x \cancel{- \frac{1}{2}} \cancel{+ \frac{1}{2}} = \frac{5}{4} + \frac{1}{2}$
Find LCM,
LCM is 4
$x = \frac{5}{4} + \frac{1 \cdot 2}{2 \cdot 2}$
$x = \frac{5}{4} + \frac{2}{4}$
$x = \frac{7}{4}$
Or,
$x = 1 \frac{3}{4}$
Or,
$x = 1.75$

Nov 21, 2017

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 $- \frac{1}{2}$

3) You end up with one dollar and one quarter $1 \frac{1}{4}$

$x$ . . . .$-$ . . . . . $\frac{1}{2}$ . . . . $=$ . . . . $1 \frac{1}{4}$
$. . . minus . . . 50ȼ . . . $=$. . .$1.25

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
$x = 1 \frac{3}{4}$ $\leftarrow$ one dollar and 3 quarters = \$1.75