How to solve operations combined with fractions

To correctly develop an operation with fractional numbers we must understand:

  1. That these are numbers formed by a numerator and a denominator.
  2. That the numerators represent the number of parts taken from the unit.
  3. Also, the denominators represent the amount in which the unit has been divided.

Just as we can take a Pizza and split it into several pieces, we can also perform different mathematical operations and combine them with those pieces, that is, with the fractions of the Pizza.

How to solve operations combined with fractions:

In case of operations with fractions, first we must proceed to solve the mixed products and numbers that are inside the parentheses.


After this a simplification will be made. Always executing the operations inside the parentheses first.


Finally we will perform the operations of the numerator, dividing and then simplifying the result, we can observe this in the following example:


 Next, let’s see other operations exercises combined with fractions:


Let’s review what we studied facing some problems of fractions:

1. You had saved $ 18. To buy a toy you have taken 4/9 of the money from your savings. How much has the toy cost you?

To solve problems you have to read the statement well until you know what you are asking, in this case we try to calculate the fraction of a number.

You need 4/9 of the $ 18 you have for the toy.

4/9 of 18 = $ 8 has cost you the toy.

Another way: You can calculate what corresponds to 1/9 and multiply by 4.

1/9 of 18 = $ 2

2×4 = $ 8

2. Between three brothers, $ 120 must be distributed. The first one takes 7/15 of the total, the second 5/12 of the total and the third the rest. How much money has each one taken?

First we reduce the fractions to a common denominator; mcm (15, 12) = 60


The first one gets 7/15 = 28/60

The second one gets 5/12 = 25/60

We add what they carry between the two 28/60 + 25/60 = 53/60

The third will be in fraction: 60/60 – 53/60 = 7/60

Second, we calculate the fraction of the number that corresponds to each one:

The first one will take 28/60 of 120 = $ 56

The second one will take 25/60 of 120 = $ 50

The third one will take 7/60 of 120 = $ 14

Finally we can verify that the operation is correctly solved adding the amount that each one takes, that is to say; 56 + 50 + 14 = 120

Then the answer is: The three brothers have taken $ 56, $ 50, and $ 14 respectively. We can observe in the results that each one corresponds to the quantities of the fractions from highest to lowest.

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