how to multiply fractions

In the previous section we have discussed about how to add fractions and In today's session we are going to discuss about how to multiply fractions, All mathematical operators can be performed on the fraction numbers. We will learn about how to multiply fractions. For multiplying the fraction numbers, we say that in order to multiply the fraction numbers, we say that a fraction number is expressed in the form of a / b, then we say that the if we have two fraction numbers, say a1/b1 and a2/b2, then we say that the product of two fraction numbers can be calculated in the form, such that the numerators of both the fraction numbers are multiplied and the denominators of both the fractions are subtracted. So we get the fraction such that the result appears as follows:
    ( a1 * a2 ) / ( b1 * b2 )
 Now let us look at the following example: If we have two fractions such that a1/b1 = 2/5 and a2 / b2 = 10/15. Then we say that the product of the two numbers is ( a1/b1 ) * ( a2/b2 ) and its result will be :
( a1/b1 ) * ( a2/b2 ) = ( 2/5 ) * ( 10 / 15 )
 = ( 2 * 10 ) / ( 5 * 15 )
= 20 / 75
 Now we will divide both the numerators and the denominators by 5 and we get :
= ( 20 ÷ 5 ) / ( 75 ÷ 5 )
= 4 / 15
 So we observe that the product of the two numbers  2/5 and 10 /15  is  4 / 15.
  The product of the fractions is converted into their lowest form to get the result of multiplication in the standard form.

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how to add fractions

Adding fractions is very easy. Before learning how to add fractions, we need to revise like & unlike fractions. We will quickly recall here that that a fraction has two parts, a numerator & a denominator. The fractions with same denominators are called like fractions; while the fractions with different denominators are called unlike fractions.

Now, when we have to add fractions, we must always remember that the fractions can be added or even subtracted; only when they are likewise., they have same denominators. If in any case, the denominators are different, we first make them same.

We can convert unlike fractions into like or in simple words, make the denominators of fractions same by finding the LCM of the denominators of the fractions to be added & then getting the equivalent fractions with such denominator, as is the LCM. Then, we continue addition of fractions by adding only the numerators of the addendent fractions. It is worth mentioning here that the denominators of the fractions are not added, rather it is written only once after being the LCM of denominators. It is always advisable to change the answer fraction to its mixed form; in case it is in improper fraction.

We will see some examples here.

To add 2/7 & 3/5 , we observe that the fractions are unlike. So, we will find the LCM of the denominators, 7 & 5 which is 35. Now, we will change the addendents to their equivalent forms with denominator 35 & we get, 2/7=(2*5)/(7*5)=10/35.

 Also, 3/5=(3*7)/(5*7)=21/35

Now, adding these two fractions, we get 2/7+3/5=10/35+21/35 =(10+21)/35=31/35

In another example, 7/5+3/6+8/15. Here, the LCM of 5,6,15 is 30.

So, the fractions will be written as:

7/5=(7*6)/(5*6) =42/30

3/6=(3*5)/(6*5)=15/30

8/15=(8*2)/(15*2)=16/30

Adding these, we get 7/5+3/6+8/15 = (42+15+16)/30 = 73/30.

Since 73/30 is improper fraction, we’ll convert it to mixed fraction & the final sum of the given fractions is 2 13/30.

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adding and subtracting integers worksheets

In previous blog we talked about adding decimal calculator, in this post we will focus on adding and subtracting integers worksheets. While studying about the Adding and Subtracting Integers Worksheets, we simply need to understand the concept of Adding and Subtracting Integers, which is quite different from the addition and subtraction of the two numbers.
If we have two integers, whom we need to add or subtract, we need to first check, if the two integers are positive integers or the negative integers. There exist the series of rules for the addition and the subtraction of the integers. Let us first look at the addition of the two integers:
1.      If the two integers are positive, then the simple addition will be performed, and the result is a positive number. Eg : + 3 + 4 = + 7
2.      In case the two integers are to be added and the two numbers are negative numbers, then we will perform the addition of the two digits and the result will be a negative number.  – 2 + ( -4 ) = -6
3.      In case we are adding one positive and one negative number, then we will find the difference of the two digits and the sign of the larger number will be the sign of the resultant number.  +4 + ( -2 ) = +2 and   -4 + ( +2 ) = -2
Now if we subtract the two digits, which are integers, then simply we need to change the sign of the number to be subtracted and then it becomes the simple sum of addition and all the rules prevailing for addition will be applied on it. So if the problem is subtract  4 from -3, it is written as
-3 -4 and the result is  = -7 Ans.
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adding decimal calculator

We know that a decimal number is a number with a decimal or a point. This decimal divides the decimal number into two parts , a decimal part & a whole part . While the whole part shows the things in complete , the decimal part shows the same as a part of the whole. Now that we know decimals are numbers & also that we can do any mathematical operation on numbers; so we can add , subtract , multiply or even divide decimal numbers as well .
Let us learn how to add decimal numbers or what is adding decimal calculator.
While learning to add simple numbers, we learnt that each digit of a number has its place & for adding different numbers , the digits of all the addendents must be written at their proper places ; one under the other .
Similarly, we have to do while adding the decimal numbers. In decimal numbers also, each digit has an assigned place & the digits of each number representing a particular place must be written one under the other vertically. By this, we mean that to add decimal numbers, the digits at tens place of each number should be written vertically one under the other & those at ones place & similarly at tenth, at hundredth place & so on for all the places. This would finally result in the decimal of each of the decimal numbers being written in a line, one under the other.
Example : 234.67 + 32.098 + 1875.9 + 5.65
We will write these decimal numbers vertically taking care of the places as follows:
   234.67
     32.098
1875.9
 +    5.650
 2148.318
Thus, the sum is 2148.318

Next blog will be focused on adding and subtracting integers worksheets, algebra problem solver & even Tamilnadu Board Sociology Sample Paper online.