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Fraction and proportionality examples

In this post we’re going to do some examples of exercises with fractions: Example 1 : If we have a cake divided in four parts and one of the parts was eaten we want to know: What fraction of the cake we would eat if we eat the half of one piece? How much of the cake lefts? First we must know how much cake we have: We have 3 pieces of cake left from the entire sweet, that was divided in four pieces. That means ¾ of the cake. Now we take one half of one piece. One piece is ¼ , that is the same that: So there are 2 pieces of cake with a size of 1/8 in one piece of cake ( 1/4 ). The answer to the first question is that we would eat a fraction of a value of 1/8 . Now the second question, how much of the cake lefts? We have eaten 1/8 of a quarter, and we had 3/4 of the cake, so we must differentiate them: To solve this we can use the least common multiple: So the least common multiple is 8. Now we multiply by 2 the nume...

Basis of the fractional calculus

First of all, we need to talk about the fractions. A fraction is a division between one number who’s going to be divided (dividend) that we call here numerator, and the number who divides (divider) that we call here denominator: Then, how to do a sum between fractions? You must have the same denominator if you want to sum the numerators. For this purpose we must know how to do the least common multiple.  The least common multiple is calculated when we have various denominators. We must calculate the prime numbers that obtain a number when you multiply them. A prime number is a number that can only be divided exatly by 1 and himself. For example 7 only can be divided by 1 and 7 so is a prime number. On the other hand 14 can be divided by 1,2,7 and 14 so it's not a prime number For example the numbers 70, 24,30: 70 is even so it´s divisible between 2 and we obtain 35. 35 ends in 5 so it’s divisible between 5 and we obtain 7 that it’s a prime number so that’s ...