Mahirap Tlga #Quipperschool ? Let us consider these two case Case I. 2 + (-3) Case II. 2 - (-3) We solve this using the number line. Case I: We begin at 2 then move 3 steps towards the left. The final position is -1. We move to the opposite direction because of the sign on 3.The emphasis here is that after definition a direction to be positive,(to the right), any movement in the opposite direction will be termed as positive. Hence, 2 + (-3) = -1 Case II: We begin at point two and wish to move to the negative direction (to the left) due to the negative on 3. We now consider the negative on (-3). Having established the negative direction, any further movement opposite to this negative direction is negative relative to it. That is the movement due to the negative on (-3). Hence we move 3 steps and get to point 5. Therefore, 2 - (-3) = 5 We can also approach negative numbers in another way. Let us consider a debt being a negative. Therefore, when somebody removes this debt from you, it is as if you have gained something that cannot be seen. For example, suppose you have $2 and someone has a debt of $3. The expression we are looking at is: 2 - (-3) Thus, you have 2 dollars with us and you have a debt of 3 dollars owed to you. The -(-3) implies somebody clearing this debt for you, hence you gain $3 that is not seen. This gain plus the initial $2 gives us $5. In summary, 2 - (-3) = 5 but this is equal to 2 + 3 = 5, hence 2 - (-3) = 2 + 3 = 5 We generalize this fact as a - (-b) = a + b For example, find the value of 10 - (-5) 10 - (-5) = 10 + 5 = 15 We can also observe something here that, subtracting negative 5 is the same as adding 5. But 5 and -5 are additive inverses, therefore, Subtracting a negative number implies addition of its additive inverse. L.C.M It is significant that we have an understanding of how to determine the L.C.M of two or more numbers since it will be required when subtracting negative fractions. Example 1 Simplify the following Solution Step 1 - the two negatives are substituted by positive sign as discussed above. Step 2 - Find the LCM of the denominators. This becomes the new denominator. LCM = 15 Step 3 - Re-write the fractions using the LCM as the denominator, which means we need to adjust each numerator. Therefore, to do this we must multiply each numerator by the respective value used to change the denominator to 15. For example, the first fraction denominator 3 X 5 = 15 and so 2 X 5 = 10 is the numerator. Similarly, we get 3 as the numerator for the second fraction. 2 3 −( − 1 5 )= 2 3 + 1 5 LCM=15 2 3 + 1 5 = (2×(15÷3))+(1×(15÷5)) 15 = (2×5)+(1×3) 15 2 3 + 1 5 = 10+3 15 = 13 15 Example 2 Simplify the following Solution Example 3 Simplify the following 2 1 3 −( −1 3 4 ) These are mixed fractions. There are many methods of solving this but we will consider the best one only. We change them into improper fractions, we carry out this process fraction by fraction, that is Multiply the denominator by the whole number then add the numerator then solve as usual
Posted on: Thu, 28 Aug 2014 05:42:32 +0000
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