Question

Find the following:
\[\dfrac{5}{6}\] of a year (in months)

Answer 1

Hint: To solve the given question, we will first find out how many months are there in a year. Then we will assume that there are 6 parts in a year. We will assume a variable x such that \[6\times x=12.\] From here, we will calculate the value of x. Then we will find out that if 6 parts of one year are 12 months, then what will be the 5 parts of one year. For this, we will multiply the value of x with 5. The product will be the answer of the given question.

Complete step-by-step answer:
Before we start to solve the above question, we must know that there are 12 months in a year. Now, it is given that there are 6 parts in a year. Now, we have to find 5 parts in one year. We will assume a variable x which when multiplied to 6 parts, we will get a year. Thus, we have,
\[6\times x=12\]
\[\Rightarrow 6x=12\]
Dividing the whole equation by 6, we will get,
\[\Rightarrow \dfrac{6x}{6}=\dfrac{12}{6}\]
\[\Rightarrow x=2\text{ months}\]
Now, we have to find 5 parts in one year. For this, we will multiply 5 parts to x. Thus, the total number of months in 5 parts of 6 will be,
\[\text{Total months in 5 parts of }6=5\times x\]
\[\Rightarrow \text{Total months in 5 parts of }6=5\times 2\text{ months}\]
\[\Rightarrow \text{Total months in 5 parts of }6=10\text{ months}\]
\[\Rightarrow \text{Total months in }\dfrac{5}{6}\text{ of a year}=10\text{ months}\]

Note: We can also solve the given question in an alternate way which is as shown. Now, we have to find \[\dfrac{5}{6}\] of a year. This means \[\dfrac{6}{6}\] will be one complete year. Now, one year has 12 months. Therefore,
1 year = 12 months
\[\Rightarrow \dfrac{6}{6}\text{ year}=12\text{ months}\]
\[\Rightarrow \dfrac{1}{6}\text{ year}=\dfrac{12}{6}\text{ months}\]
\[\Rightarrow \dfrac{5}{6}\text{ of year}=\dfrac{12}{6}\times \text{5 months}=10\text{ months}\]