Question

Explain in step by step procedure, how we one can use mental maths to calculate the sum given below;
 $ 74 + 2.6 + 1.4 $

Answer 1

Hint: Mental math is basically being able to solve a given problem without writing it down or without using an external help like a calculator. Remember to finish off the easy calculations first. Remember multiplication tables, it makes addition quick. Keep in mind basic decimal addition; especially remember the different combinations which add up to $ 1 $ in decimals and $ 10 $ in whole numbers.

Complete step by step solution:
As step $ 1 $ , we can first write down the question;
We are asked to find the sum of these terms by using mental math; $ 74 + 2.6 + 1.4 $
It helps for us to know every combination where we get;
 $ 1 $ while adding decimal points
 $ 10 $ while adding whole numbers
While dealing with whole numbers let us list out all the possibilities of reaching $ 10 $ after addition of whole numbers. The combinations are as follows;
 $ 1 + 9 = 10 $ , equivalent to this combination we have $ 9 + 1 = 10 $
 $ 2 + 8 = 10 $
 $ 3 + 7 = 10 $
 $ 4 + 6 = 10 $
 $ 5 + 5 = 10 $
Similarly since addition of whole numbers is commutative, the order of addition does not matter so each combination has two ways of being written just as is demonstrated in the case of $ 1,9 $ .
While dealing with numbers with decimal points let us list out all the possibilities of reaching $ 1 $ after addition. The combinations are as follows;
 $ 0.1 + 0.9 = 1.0 $
 $ 0.2 + 0.8 = 1.0 $
 $ 0.3 + 0.7 = 1.0 $
 $ 0.4 + 0.6 = 1.0 $
 $ 0.5 + 0.5 = 1.0 $
Here also, we have the commutative property, so order of terms in addition does not matter, it will give the same answer.
Now that we have kept some points in mind, let us see how to solve the addition of the given rational numbers;
 $ 74 + 2.6 + 1.4 $
First we finish off the easy calculations, that is adding all the whole number parts of the rational numbers;
Consider: $ 2 $ from $ 2.6 $ , keep the remaining aside $ 0.6 $
And consider: $ 1 $ from $ 1.4 $ , keep the remaining aside $ 0.4 $
So now we can calculate this easily in our minds; $ 74 + 2 + 1 = 77 $
Let us add the remaining decimal part we kept aside;
  $ 0.6 + 0.4 = 1.0 $
This was easily calculated since we know the combination tables.
Now the easiest task is to add the whole part and decimal parts;
 $ 77 + 1 = 78 $
This is how we solve the question of addition of rational numbers using mental maths.
So, the correct answer is “78”.

Note: Mental maths is an easy and faster way to solve questions but it is not always possible. Some patterns allow us to perform mental summing but for big numbers and difficult operations we would not opt for this method. On the other hand, mental maths also helps improve our brain efficiency and makes us more alert to situations. So practicing this is not always easy but it is worth the effort.