The rules of operations like multiplication and addition of fractions is different from the rules of operation of whole numbers. However, the rule of multiplying fractions is very easy, and you can solve the multiplication of a fraction by another fraction. The rule of multiplication in the case of fractions is to multiply the numerators of both the fractions. Then, you have to multiply the denominators as well of both the fractions. It will explain further in details, but you firstly know about the fractions. For performing different operations on fractions like addition and multiplication operation, you must know about the fractions. What are the different types of fractions? Commonly, there are three main kinds of fractions found in practice. They include the mixed fraction, the proper fraction and also the improper fraction. The proper fractions are the fractions in which numerators are less than the denominators, like 2/3, 5/16. On the other hand, it is opposite in the case of the improper fraction. The improper fractions are the fractions in which denominators are less than the numerators like 3/2, 7/3. Mixed fraction has the fraction with a whole number and is in the form of the quotient, remainder, and divisor. Another important concept in the fraction is like and unlike fractions. The like fractions are the fractions having the numerators common, whereas the unlike fractions are the fraction having uncommon numerators. How to multiply a fraction by another fraction? If you want to multiply a fraction that is a proper or improper with another fraction, it is so easy. However, if one of that fraction, you found as a mixed fraction, so convert that fraction into the simple fraction. There are only three simple steps regarding multiplying fractions and it is applicable for both the proper and improper fractions. Step 1: Multiply the numerator of the first fraction with the numerator of the second fraction. Step2: Multiply the denominator of the first fraction correctly by the denominator of the second fraction. Step 3: If needed, convert the fraction you will get after both the multiplication into reduced form. It is necessary to convert the fraction to the simple form, or it can also be called as the lowest form of the fraction. Go through the example illustrated further So, multiply the top numbers that are the numerators and then multiply the bottom numbers of both these fractions correctly. 10/28 If you carefully look at this fraction, you will find that it can be simplified. Simplification is also important in all the multiplying fractions related problems. Here, you can reduce this fraction to the lowest form, and it is the correct solution. Why is this operation important in the fractions?
So, you should solve the problems of multiplying fractions to be perfect in the fractions. Another interesting fact is that the multiplication operation is also needed if you have to perform the division of fractions. Similarly, if at many problems, you have to deal with algebraic fractions. There you may have to multiply the algebraic fraction as well. You can also learn the multiplying fractions involving algebraic expressions very easily.
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There are many different subjects under mathematics. Mathematics is known to be a collection of various formula and methods which guide you towards the right answers of the questions. Quadratic equations are some of the most important parts of algebraic math. There are many students who find difficulty in solving quadratic equations. Therefore in this content we will be talking about some simple ways of learning to solve such equations. Quadratic equation is also known as a polynomial equation with a single variable, in this equation the variable with highest exponent is always 2. Usually when it comes to the methods of solving these equations, there can be mainly three ways of doing this. These are 1.) By factoring the quadratic equation, 2.) Using the quadratic formula, and 3.) By completing the square. Therefore this content will be covering some of these for you. Quadratic formula is known to be one of the easiest ways of solving quadratics. However we will be starting by factoring the equation. Let’s solve something
It is very important to know about how to factor a quadratic equation as this is going to hold great importance further in this topic. You are told to find the values of x for a given equation to be true. For example: solve (x-3)(x-4)= 0 Actually, this equation has been already factored. So then how will you get the answers to the equation? According to the zero factor principle, at least one of the factors in the equation s should be equal to zero. Thus, x-3= 0 Or x-4= 0 Thus now they are in the form of a simple linear equation and can now be easily solved. Now we get, x = 3 or x = 4 Here the “or” indicates that the value of x can be either 3 or 4. And this is the correct solution you were looking for. Therefore it can be said that solving quadratic equations is easy by factoring the equation. Now an important thing to be discussed here is the verification of the solution that you’ve got from the above steps. Sometimes, factoring is not able to bring out the correct solutions for the equations. Therefore it is very important to cross check these in order to ensure accuracy. Foe the example solved above you needs to follow the following steps: Check x =3 in (x – 3) (x – 4) = 0: ([3] – 3) ([3] – 4)? =? 0 {putting the value of x in the equation as 3} (3 – 3)(3 – 4)? =? 0 Then solving these further we get, (0)(- 1)? =? 0 thus, 0=0 Hence proved correct (LHS = RHS) Now similarly check x = 4 in (x – 3)(x – 4) = 0: It will be solved like: ([4] – 3) ([4] – 4)? =? 0 We will solve it further to get: (4 – 3) (4 – 4) ?=? 0 Which will further be: (1) (0)? =? 0 and 0=0. Here LHS = RHS and hence proved correct. The example mentioned above would have surely helped you in solving quadratic equations very easily by factoring method. |
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