Example of Addition of Fractions with Integers

Math / by admin / July 04, 2021

Fractions are numerical values that are not enough to complete the unit, and are made up of two main parts: denominator, what does it tell us what are we talking about: halves, thirds, fourths, etc. Y numerator, which indicates how many there are of those means, thirds, fourths, etc. Fractions, since they are values, participate in arithmetic operations like addition.

For a sum of fractions to be carried out, there are two main requirements:

That all are in proper or improper form (not mixed)
That they all have the same denominator

However, sometimes the sums include both fractions and whole numbers, so it is difficult in the first instance to get an idea of how to solve them.

Sum of fractions with integers

A sum of fractions with integers it's a different operation of a sum of mixed fractions. The difference is explained because we can get confused about it:

Sum of mixed fractions

All terms are mixed fractions (fractions with a whole part and a proper part). If this is the operation that interests you, you can find out about it here: Example of Sum of Mixed Fractions.

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$Sum of mixed fractions$

Sum of fractions with integers

In this operation, there are terms that are fractions (proper, improper, or mixed) and terms that are whole numbers.

$Sum of fractions with integers$

Next, we will study the steps to solve a sum of fractions with integers:

Convert all terms into proper or improper fractions
Find the common denominator for all terms
Accumulate the numerators with the common denominator
Present the result as an improper or mixed fraction

Example of adding fractions with integers

There is a group of fractions that must be added:

$Sum of fractions with integers$

Convert all terms into proper or improper fractions

$Conversion to proper and improper fractions$

Find the common denominator for all terms

The denominators found in the problem are: 1, 4, 5, 8, 10. To find a common denominator for all of them, you can start by multiplying the smallest ones, to see if we can find it:

4*5 = 20. The number 20 is a multiple of all but 8.
4*8 = 32. The number 32 is a multiple of 1, 4, and 8, but not 5 or 10.
5*8 = 40. The number 40 is a multiple of 1, 4, 5, 8 and 10: of all.

It is determined that 40 is the common denominator for all of them. Now, you just need to multiply both the numerators and the denominators, by a multiple that takes them to the denominator 40.