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calculations with fractions

Simplfying fractions

Lowest common multiple

Parts of a fraction

Key concepts

first, let's revise

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.

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DENOMINATOR

NUMERATOR

DENOMINATOR

NUMERATOR

Parts of a fraction

Drag the numerators and denominatorsto their corresponding images

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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.

Lowest common multiple

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

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

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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.

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.

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.

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

Simplifying fractions

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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.

Homogenous fractions are fractions that share the same denominator.

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calculations with homogenous fractions

EXAMPLES

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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.

Heterogenous fractions have different denominators.

calculations with heterogenous fractions

Multiply and divide

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

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.

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

Algorithm for addition and subtraction with heterogeneous fractions

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

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LCM de 4 y 3 = 12

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6 + 8

Finally we convert the result into an irreducible fraction.

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).

DIVISION

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

MULTIPLICAtion

Multiplication and division with heterogeneous fractions

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.

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Thanks!