CALCULATIONS WITH FRACTIONS

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calculations with fractions

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Key concepts

Simplfying fractions

Parts of a fraction

Lowest common multiple

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Parts of a fraction

NUMERATOR

Using the classic example of a pizza, the is the number of slices we're talking about and the is the number of slices the pizza was cut into to begin with.

NUMERATOR

DENOMINATOR

DENOMINATOR

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Drag the numerators and denominators to their corresponding images

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Lowest common multiple

Often referred to as the least common multiple or LCM. It is the smallest multiple that several numbers have in common. In the following video you will learn two methods for finding the lowest common multiple of two or more numbers.

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Simplifying fractions

Fractions can be expressed in various ways that represent the same portion of the total, for example:

To simplify a fraction is to find a way to express it with the smallest possible numerator and denominator. To do this we must divide both by the same number until it is no longer possible to continue, the result of this process is called an irreducible fraction.

16

16

28

In the previous example we divided the numerator and denominator by 2, (4 : 2 = 2) ; (16 : 2 =8) -->

Repeat the process, this time dividing the numerator and denominator , we get

Since the only common number we can divide into 1 and 4 is 1, and the fraction would remain the same , we say that 1/4 is an irreducible fraction.

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When working with larger numbers, it is easiest to identify the greatest common divisor of the numerator and denominator and then divide both by it.

calculations with homogenous fractions

Homogenous fractions are fractions that share the same denominator.

To solve calculations with homogeneous fractions we simply keep the denominator the same and work with the numerators performing the operations in the normal way.

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EXAMPLES

calculations with heterogenous fractions

Heterogenous fractions have different denominators.

How we solve calculations with heterogeneous fractions will depend on the type of calculation to be performed. Let's see how they work in each case.

Multiply and divide

Add and subtract

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Algorithm for addition and subtraction with heterogeneous fractions

Convert heterogeneous fractions into homogeneous fractions, i.e., equalize their denominators.

LCM de 4 y 3 = 12

To do this we need to find the LCM of the denominators; this will be our new denominator.

12

14

Adjust the numerator so that the fraction still has the same value, this is done by dividing the LCM by the denominator of each fraction and multiplying the result by the numerator of the fraction.

6 + 8

12

12

We can solve the calculation as in the example, now we just have to convert the result into an irreducible fraction, by simplifying.

14

12

Multiplication and division with heterogeneous fractions

MULTIPLICAtion

DIVISION

To solve multiplication with heterogeneous fractions we simply multiply the denominators by the denominators and the numerators by the numerators as if they were two different calculations.

To solve division with heterogeneous fractions we simply multiply the numerator of the first by the denominator of the second, the result will be our new numerator, and then multiply the denominator of the first by the numerator of the second, the result will be our new denominator. (Cross multiplication).

20

40

35

24

Then we just have to convert the result into an irreducible fraction.

Finally we convert the result into an irreducible fraction.

20

40

35

24

Thanks!