The multiplication and division of common fractions . Widely used in practical life in situations usually given to share and / or distribute something.
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Summary
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- 1 Historical Review
- 1 Graphic example
- 2 Multiplication of common fractions
- 3 Division of common fractions
- 1 Reciprocal of a fraction
- 1.1 Examples of reciprocal
- 1.2 Examples of division
- 4 Sources
- 1 Reciprocal of a fraction
Historical review
The theory and calculation of fractions as we use it today is attributed to the Hindu mathematician Brahmagupta (600 years old). Thanks to the Indian mathematicians, who revolutionized the art of calculating, we can now express and calculate with fractions in a simpler way.
Graphible example
If Jaime walks 8/3 of an mile, how much does he travel in half an hour? The answer is simple: half the proposed distance, this is 8 / 3×1 / 2 = 8×1 / 3×2 = 4/3 of a mile.
Multiplication of common fractions
Like natural numbers , fractions can be multiplied.
For example:
If you want to know the time you spend practicing spelling dedicating ¼ (a quarter) of an hour 3 times a week, how do you put it?
Do you need to know how many buttons represent ¾ (three quarters) of a set of 8 buttons?
Do you want to know what part of the cake your little sister ate if she was served ¼ (a quarter) of half the cake?
In the previous examples you have seen different representations for the multiplication of fractions, in all cases the product is calculated in the same way:
Note that:
In all cases, the fractions have been multiplied by multiplying numerator by numerator and denominator by denominator.
Let’s see other examples:
Find the product of the following fractions:
How do we solve them ?:
In summary:
- Multiplication of fractions is done by multiplying the numerators and multiplying the denominators together. It is convenient, before calculating the product, simplify as much as possible otherwise you should do it in the resulting fraction.
Generally:
Division of common fractions
Reciprocal of a fraction
Before starting the study of the division of fractions, it is necessary that you learn what is the reciprocal of a fraction, you will need it in the procedure to follow to divide .
Definition 1
The reciprocal of a fraction is the fraction where .
Given a fraction, to form its reciprocal, it is enough to invert its terms.
Examples of reciprocal
Find the reciprocal of:
- a) 1/3 (one out of three)
- b) 2
- c) 7/4 (seven out of four)
- d) 0.5
Answers :
- a) 1/3 (one over three) equals 3/1 (three over one). Reversing the numerator and the denominator. The reciprocal of 1/3 (one over three) equals 3.
- b) 2 equals ½. The reciprocal of 2 is ½ (one-half).
- c) 7/4 (seven out of four) equals 4/7 (four out of seven). The reciprocal of 7/4 (seven out of four) is 4/7 (four out of seven).
- d) 0.5 equal to 5/10 (five out of ten). The decimal expression is written as a fraction. The reciprocal of 5/10 (five out of ten) is 10/5 (ten out of five) which equals 2.
In natural numbers division means dividing equally, with fractions you can also give that interpretation and solve practical situations, for example:
You have 5 oranges and you chop them exactly half how many parts do you have now?
You divide half of a school garden into four equal parts to plant lettuces in one of them, what part of the land will be dedicated to this type of vegetables?
To find which part is one set of another, you must divide. Then we can also give this meaning to the division of fractions, for example:
What part is ½ m of fabric of ¾ m?
Regardless of the different interpretations that division can have, to calculate there is a single procedure as we can see below:
In all cases, the fractions have been divided, reducing them to a multiplication where the second factor is the reciprocal of the divisor.
Examples of division
Find the quotient:
To solve them:
In summary:
- The division of fractions is carried out by transforming it into a multiplication in which the first factor is the dividend and the second is the reciprocal of the divisor. Then proceed as in multiplication.
