Question

How do you simplify `2 1/2 - 5 1/4 + .75`?

Answer 1

`-2`

Explanation:

You don't want to do calculations which involve a combination of fractions and decimals. Choose one or the other. IN this case decimals would work because both `1/2 and 1/4`are exact decimals.

However, many fractions do not give exact decimals, so it is better to change into fractions..

`2 1/2 -5 1/4 + 3/4" "larr` change to improper fractions

=`5/2-21/4+3/4`

=`(10-21+3)/4`

=`-8/4`

=`-2`
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Be careful with negative fractions!
Let's work with the whole numbers first:
`2 1/2 -5 1/4 + 3/4`

=`-3 +1/2-1/4+3/4`

=`-3 (2-1+3)/4`

=`-3 color(crimson)(+4/4) = -3color(crimson)(+1)" "larr "NOT"-3 4/4 rarr -(3 4/4)`

=`-2" "larr` luckily this one worked out to a whole number, but in another situation you might have positive and negative fractions which are much more tricky.`-2`

Answer 2

`-2`

Explanation:

The first step is to change the decimal fraction into a proper fraction.

`0.75=75/100=3/4`

`rArr2 1/2-5 1/4 +3/4color(red)" is now the calculation"`

Convert the fractions into `color(blue)"improper fractions. For example."`

`2 1/2=5/2`

That is : multiply the whole number 2 by the denominator of the fraction 2 and add the numerator of the fraction 1.

`(2xx2)+1=5`

`rArr5/2-21/4+3/4color(red)" is now the calculation"`

To add/subtract fractions we require them to have a `color(blue)"common denominator"` Two already have 4 but we require `5/2` to have a denominator of 4.

To do this multiply the numerator/denominator of `5/2` by 2

`(5xx2)/(2xx2)=10/4larr" now has a denominator of 4"`

`rArr10/4-21/4+3/4color(red)" is now the calculation"`

Now that they all have a common denominator we add/subtract the numerators together.

`rArr(10-21+3)/4=(-8)/4=-2`