# What is a quarter plus five eighths

Why is?
Just as you have to constantly add and subtract normal numbers, you also want to calculate with fractions of plus and minus.

A quarter liter of paint from this bucket, a third from that and two fifths from another bucket are poured together. How much color does that make in total?

 In this lesson you will learn: 1. Adding and subtracting fractions with the same denominator. 2. Adding and subtracting fractions with different denominators. 3. Adding and subtracting mixed numbers.
Adding and subtracting with the same denominator.
Easy! Super easy !!!

Three eighths and four eighths equals? N / A???
Seven eighths, of course, what else?

If both fractions have the same denominator, i.e. if the fragments are the same size, you just have to add the number of pieces together. You just have to add the numerators, the denominator remains as it was.

+   =

+   =

The same is true, of course, if you subtract:

–   =

–   =

 Note: If both fractions have the same denominator, only the numerators have to be added or subtracted.

Fractions with the same denominator are called "same name".
Adding and subtracting with different denominators.
Not so easy anymore!

Fractions with different denominators cannot simply be added together, because the fragments are no longer the same size!

A quarter and two thirds? Difficult!

+   = ???

 Note: If the fractions have different denominators, they are first reduced to thesame Denominator. The counters can then be added or subtracted.

The main denominator

is the LCM, the lowest common multiple of the two denominators.

(see 5th grade)

There is onlyone Way: Both fractions must be reshaped in such a way that they are counted in equal pieces.

So you have to expand them so that they get the same denominator. Then you can add:

+   =   +   =

Further examples:

+   = ???

First bring to the same denominator (the main denominator), then add the numerators:

+   =   +   =

–   =   –   =

At the end of a calculation, you always check whether the result can still be reduced. You also check whether the numerator is perhaps greater than the denominator. In this case the fraction is written as a mixed number.

+   =   +   =   = 1
Adding and subtracting mixed numbers
Mixed numbers are added or subtracted by calculating the natural numbers and the remaining fractions separately.

 Note: In the case of mixed numbers, the natural numbers and the fractions are calculated separately.

3  + 2  = 3  + 2  = 5

4  + 3  = 4  + 3  = 7  = 7

Of course, you also have to look here to see whether the fraction in the result can be reduced again, or whether the numerator in the fraction is greater than the denominator.

5  – 4  = 1  = 1

+ 1  =   + 1  = 1  = 2

Ten tenths became a whole again.

It becomes uncomfortable when the first fraction is smaller than the second when subtracting. In this case you have to "borrow" something from the integer:

7  – 1  = 6  – 1  = 5  = 5

Because the one quarter is too small to subtract, we borrowed four quarters from the total of 7.