Question

Add the following:
74 years 9 months and 12 years 4 months

Answer 1

Hint: First add the values of years separately, then go for addition of months. Finally, if months are getting converted into years then convert it. The conversion to be used here is 1 year = 12 months.

Complete step by step solution:
In the above question, we are given to add 74 years 9 months and 12 years 4 months.
We know that addition can be done only if both the values to be added are in the same unit, else we just represent different terms by adding the + symbol between them. For, example, if we are asked to add x and 2x, then we can add them as x+2x=3x. But if we are asked to add x and y, then we get the addition as x+y.
Here, we have months and years as units. So, first of all we will add the given year that is:
\[\begin{align}
  & \text{74 years }+\text{ 12 years} \\
 & \text{74}+\text{12 }=\text{ 86 years}. \\
\end{align}\]
Now, we will add the given months that is:
\[\begin{align}
  & \text{9 months }+\text{ 4 months} \\
 & \text{9}+\text{4 }=\text{ 13 months}. \\
\end{align}\]
Since, 1 year = 12 months, we can convert as shown below,
\[\begin{align}
  & \text{13 months }=\text{ 12 months }+\text{ 1 month} \\
 & \text{13 months }=\text{ 1 year }+\text{ 1 month} \\
\end{align}\]
Now, on adding all the values, we will get the answer as below,
\[\begin{align}
  & \text{86 years }+\text{ 1 year and 1 month} \\
 & \text{87 years and 1 month}. \\
\end{align}\]
Therefore, the sum of 74 years and 9 months and 12 years and 4 months will be 87 years and 1 month.

Note: The problem can also be solved by other methods like by converting the above value in either years or in months. We know that 1 year = 12 months, so we can convert 74 year 9 months to \[\left( 74\times 12 \right)+9\text{ months = 897 months}\] . Similarly, 12 years 4 months can be converted as \[\left( 12\times 12 \right)+4\text{ months = 148 months}\] Now adding then, we get \[897+148\text{ = 1045 months}\] . We can further express it in years and months as \[\left( 12\times 87 \right)+1\text{ month }\Rightarrow \text{ 87 years 1 month}\]