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

3 Answers
Aug 10, 2016

Answer:

#x=1/2#

Explanation:

We start with #3/4+x=5/4#. Our goal is to solve for #x#, which means that we need to subtract #3/4# on both sides, leaving us with #x=5/4-3/4#. 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 #2/4#. That can be simplified to #1/2#, which means that #x=1/2#.

Aug 13, 2016

Answer:

#x=1/2#

#color(purple)("Solution split into 2 parts.")#
#color(purple)("Part 1: Detailed explanation about adding and subtracting fractions.")#

#color(purple)("Part 2: Answering your question.")#

Explanation:

#color(blue)("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 #1/2# it takes 2 of them to make a whole but we have got a count of 1 of them.

For #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 #6/1-2/1" "larr" not normally done this way"#

The denominators (size indicators) are the same so we can #ul("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.

#2/("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.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

#3/4+x=5/4#

Subtract #color(blue)(3/4)# from both sides

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

But #3/4-3/4=0#

#0+x=5/4-3/4#

#x=5/4-3/4#

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

#x=(5-3)/4 = 2/4#

But #2/4# is equivalent to #1/2#

#x=1/2#

Aug 26, 2016

Answer:

#x =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:

#8/3 xx6 = 8/cancel3 xxcancel6^2 =16#

#2/5 xx15 = 2/cancel5xxcancel15^3 = 6#

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

#color(red)(4xx) 3/4 +color(red)(4xx)x = color(red)(4xx)5/4#

#color(red)(cancel4xx) 3/cancel4 +color(red)(4xx)x = color(red)(cancel4xx)5/cancel4#

#3+4x = 5#

#4x = 5-3 = 2#

#x = 1/2#