Tipo test mates II

In order to solve multiplications of decimal numbers removing dots,. We only have one technique…. We have two techniques, and both avoid the use of D10, 100…. One technique consists in considering 10, 100… times the initial rectangle, and the other technique consists in considering smaller units of measurement.

Situations of the division involving decimal numbers. There are as many situations as kind of magnitudes. There are three, and in two of them there is only one magnitude involved. There are three.

The rule D100 says that, when you divide a number by 100, you just have to shifts the dot to the left. It works if you all the situations of the division. It only works if you are dividing by 100 parts. It does not work if both the dividend and the divisor are amounts on the same magnitude.

In the situation of dividing by the same magnitude, in the interpretation of the multiplication table of the divisor. The left column refers to the amount of magnitude used. The left column refers to number of parts (of the size given by dividend) you can do with the amount given by the divisor. The left column refers to number of parts (of the size given by the divisor) you can do with the amount given by dividend.

Imagine we know that 45 times 7m = 315m. ¿How to use it in order to prove that 45 times 0,7m = 31,5 m?. By using D10 we know that it amounts to prove that 45 times 0,7m is the tenth part of 315m or, equivalently, that 10 time 4 times 0,7m =315m. After that, we just have to use the commutativity property, M10 and the fact that 45 times 7m = 315m. According to D10, if you shift the dot once to the left in one factor of a multiplications (going from 7 to 0,7), then you have to move the dot once to the left in the result of that multiplication (going from 315 to 31.5). We just make the multiplication 45 times 0,7m by using first the distributivity property and them solving the smaller multiplications 40 times 0.7m and 5 times 0,7m.

On different interpretations of fractions: 2/3m can be regarded as one third of two meters, on one hand, or as two meters divided by three, on the other hand. 2/3m can be regarded as tyo times one third of a meter, on one hand, or as the multiplication by two of the quotient of the division of one by three, on the other. 2/3m can be regarded as two times one third of one meter but also as one third of to meters.

One third of two meters equals two times one third of one meter because: 1/3 of 2m = 1/3 of 2 times 3 times 1/3 m = 1/3 of 3 times 2 times 1/3 m= 2 times 1/3 m. The multiplication of fraction and natural numbers satisfies the commutative property. The numbers 2 and 3 do not have common divisors other than 1.

Why 2/3m and 7x2/7x3 m are equivalent?. Because 2/3 is irreducible. If you reduce 7 times the parts into which you split 1m (being each part 1/7x3 m instead of 1/3 m), then you have to take 7 times mor parts (7x2 parts instead of 2 parts) to get the same of length. Because 7 is a prime number, and so you get a decomposition into a product of prime numbers both in the numerator and in the denominator.

To find an irreducible fraction equivalent to a given one: We can divide both the numerator and the denominator by their least common multiple. We check whether the fraction is a decimal one, because in this case it would be equivalent to a fraction with a power of ten in the denominator. We can divide both the numerator and the denominator by their greatest common divisor.

How many divisors have 210 (including 1 and 210 itself)?. By using M10, we know that it has 10 times the number of divisors of 21. 16. The number of divisors has to be a muttiple of 3, because 3 divides 210.

The cross-product method says that: If the cross-product of two fractions provide the same number, then the fractions are equivalent. If the fractions are equivalent, then their cross-product provide the same number. Both (a) and (b) are true.

in order to add two fractions with different denominators: We have to check whether one of this fractions is a decimal one. We can replace those fractions with fractions having a common denominator. We need to transform those fractions into decimal numbers.

We can "multiplication" of two fractions to the process we follow in order to: Calculate the amount of area of a rectangle such that amount of length of the sides is given by fractions. Calculate a fraction of a fraction. Both (a) and (b).

The decimal number corresponding to the fraction 5/6 is: 0,83 periodico. 0,883 periodico el 8 y el 3. 0,83 periodico el 3.

The fraction corresponding to the decimal number 3,14159 is: Called PI by ancient Greeks. The fraction whose numerator is the length of the circumference, and whose denominator is the corresponding diameter. 314159-314/99900.