Simplification and Expansion of Simple Fractions

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Simplification and Expansiono f Simple Fractions

To amplify fractions

We will perform the same multiplication operation on the numerator and the denominator: the value of the fraction will be preserved.

You can expand as many times as you want and by any number.

To simplify fractions:

We will perform the same division operation on the numerator and the denominator: the value of the fraction will be preserved.

This can only be done with a number that is completely divisible by both the numerator and the denominator.

It is possible to simplify only until reaching a fraction in which it is not possible to find a number that divides without remainder both in the numerator and the denominator.

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Simplify the following fraction by a factor of 1:

\( \frac{3}{10}= \)

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Simplify and expand simple fractions

Simplifying and amplifying fractions is an easy and enjoyable topic that will accompany you in almost all exercises with fractions.

Simplifying and amplifying a fraction is actually a multiplication or division operation that is performed on the fraction so that the real value of the fraction does not change and simply looks different.

Expansion: a multiplication operation (which is performed on both the numerator and the denominator).

Simplification: a division operation (which is performed on both the numerator and the denominator).


Expansion of Fractions

A daily example

Think of a pizza with 88 slices: a normal family-sized pizza sold at pizzerias.

You call to place the order and ask the seller to put olives on half of the pizza.

You will receive 121 \over 2 pizza with olives.

But, what if you told the seller, please put olives on 44 triangles of the pizza?

Let's see:

Even then you would get half a pizza with olives.

That is to say: 484 \over 8 -> four slices out of 88 is equal to 121 \over 2

Now let's see this in the exercise

We expand the fraction 121 \over 2 by 44
Solution:

We multiply by 22 both in the numerator and the denominator and we get:

3 - We amplify the fraction

Note the sign that is usually used to expand.

If we multiply both the numerator and the denominator by the same number, the value of the fraction will not change and the fractions will be equal, exactly as in the pizza.

Important note: we can expand the fraction as many times as we want and by any number we want and still the value will not change!

For example, even if instead of being expanded by 44 we would expand by 22, we would get:

4 - if instead of being amplified by (4) we would amplify by (2)


which is also equal to 484 \over 8


More exercises of another type

Complete the missing number

28=4□\frac{2}{8}=\frac{4}{□}

Solution:

We see that 22 in the numerator becomes 44. That is, it is multiplied by 22. Therefore, we also multiply the denominator 88 by the number 22 to reach the correct result.

After all, we learned that fractions will be equal only if we perform the operation on both the numerator and the denominator.

We obtain:

5 - We see that (2) in the numerator becomes (4)


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Now we move on to the simplification of fractions

Simplifying fractions is a division operation that is performed on both the numerator and the denominator and preserves the value of the fraction.

It is possible to simplify only by a number that is divisible without remainder in both the numerator and the denominator.

When can we not simplify a fraction?

When the numerator and the denominator are not completely divisible by the same number.

Exercise

Simplify the fraction 6126 \over 12 by 66.
Solution:
We divide both the numerator and the denominator by 66 and we get:
12=612\frac{1}{2}=\frac{6}{12}

Extra section:

We simplify the fraction 6126 \over 12 by the number you choose (except for 66)

Solution:

We must choose a number that divides both the numerator and the denominator without remainder.

We are asked: What number can you divide 66 and 1212 by?
The answer can be: 22 or 33. For example
We choose: 33 and simplify:
24=12=612\frac{2}{4}=\frac{1}{2}=\frac{6}{12}


Another exercise

We simplify the fraction: 353 \over 5

Solution:

This exercise has no solution. This fraction cannot be simplified further since there is no number that is divisible by 33 and also by 55 without a remainder.


Another exercise

Complete the missing number

810=4□\frac{8}{10}=\frac{4}{□}

Solution:
We see that 88 in the numerator becomes 44. That is, it is divided by 22. Therefore, we also divide in the denominator 1010 by the number 22 to arrive at the correct result since we learned that fractions will be equal only if we perform the operation both in the numerator and in the denominator.
We obtain:

6 - fractions will be equal

Note: Expansion does not mean that the fraction gets bigger and simplification does not mean that the fraction gets smaller!


Do you know what the answer is?
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