# How do you solve 3/4+x=5/4?

Aug 10, 2016

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

#### Explanation:

We start with $\frac{3}{4} + x = \frac{5}{4}$. Our goal is to solve for $x$, which means that we need to subtract $\frac{3}{4}$ on both sides, leaving us with $x = \frac{5}{4} - \frac{3}{4}$. To subtract equations, we first must make sure the demoninators are the same. In our case they are, so now we just deal with the numerators. Treat it like $5 - 3$, which is $2$. Now we slap on the denominator and get $\frac{2}{4}$. That can be simplified to $\frac{1}{2}$, which means that $x = \frac{1}{2}$.

Aug 13, 2016

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

$\textcolor{p u r p \le}{\text{Solution split into 2 parts.}}$
$\textcolor{p u r p \le}{\text{Part 1: Detailed explanation about adding and subtracting fractions.}}$

$\textcolor{p u r p \le}{\text{Part 2: Answering your question.}}$

#### Explanation:

$\textcolor{b l u e}{\text{Insight into addition and subtraction of fractions}}$

Hold the thought for a moment that when you apply the process of, say, $6 - 2$ you are manipulating counts.

Now consider a fraction (rational number). We have the structure of:

" "("count")/("size indicator of what you are counting")

Using the proper names for these we have:

" " ("numerator")/("denominator")

Size indicator tells you how many of what you are counting are needed to make a whole of something (a complete 1)

So
For $\frac{1}{2}$ it takes 2 of them to make a whole but we have got a count of 1 of them.

For $\frac{2}{16}$ it takes 16 of them to make a whole but we have got a count of 2 of them

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ok! Lets go back to $6 - 2$

Write this as $\frac{6}{1} - \frac{2}{1} \text{ "larr" not normally done this way}$

The denominators (size indicators) are the same so we can $\underline{\text{directly}}$ apply the subtraction of the counts

,...............................................................................................................
So if you wish to add subtract the counts you need to make the size indicators the same. Otherwise you are trying to do the equivalent operation as the following example.

$\frac{2}{\text{box of apples")" "-" "3/("single apples}}$

You need to convert the size indicator of "box of apples" to the size indicator of "single apples" before you can determine how many apples you are left with.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

$\frac{3}{4} + x = \frac{5}{4}$

Subtract $\textcolor{b l u e}{\frac{3}{4}}$ from both sides

color(brown)(3/4color(blue)(-3/4)+x=5/4color(blue)(-3/4)

But $\frac{3}{4} - \frac{3}{4} = 0$

$0 + x = \frac{5}{4} - \frac{3}{4}$

$x = \frac{5}{4} - \frac{3}{4}$

The size indicators (denominators) are the same so we can directly subtract the counts.

$x = \frac{5 - 3}{4} = \frac{2}{4}$

But $\frac{2}{4}$ is equivalent to $\frac{1}{2}$

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

Aug 26, 2016

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

#### Explanation:

Fractions are numbers which many students find difficult to work with. Luckily with equations which have fractions, we can get rid of any fractions immediately by a multiplying by the LCM of the denominators. (same as the LCD)

Note that: if you multiply a fraction by a multiple of the denominator, the denominator can cancel.
For example:

$\frac{8}{3} \times 6 = \frac{8}{\cancel{3}} \times {\cancel{6}}^{2} = 16$

$\frac{2}{5} \times 15 = \frac{2}{\cancel{5}} \times {\cancel{15}}^{3} = 6$

In this question both the denominators are 4
.
Multiply the WHOLE equation by 4

$\textcolor{red}{4 \times} \frac{3}{4} + \textcolor{red}{4 \times} x = \textcolor{red}{4 \times} \frac{5}{4}$

$\textcolor{red}{\cancel{4} \times} \frac{3}{\cancel{4}} + \textcolor{red}{4 \times} x = \textcolor{red}{\cancel{4} \times} \frac{5}{\cancel{4}}$

$3 + 4 x = 5$

$4 x = 5 - 3 = 2$

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