Some problems involving fractions:
There are many word problems that involve fractions and use arithmetic operations like addition, subtraction, multiplication, and division.
We are going to see some real-life problems involving multiplication and division of fractions.
Steps to work on word problems involving fractions:
- First, understand the information given in the question.
- Consider all the fractions and numbers given in the question.
- Identify the arithmetic operation suitable for the given content.
- Solve the fractions and write the answer with the given units.
Example:
1. A farmer had 10 grandchildren. She distributed \(\frac{2}{4}\) acre of land to each of her grandchildren. How much land in all did she give to her grandchildren?
Solution:
Total acre of land a farmer had initially is \(10\) times of \(\frac{2}{4}\) acre of land.
\(=\frac{10}{1} \times \frac{2}{4}\)
Using the formula below, we get,
\(\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\)
\(=\frac{10 \times2}{1 \times 4}\)
\(=\frac{20}{4}\)
\(=\frac{5}{1}\)
Thus, initally a farmer had \(\frac{5}{1}\) acre of land
Example:
2. Maria bought \(20 litres\) of curd to make buttermilk to sell in a school competition. She used \(\frac{1}{3} litres\) of curd for each cup of buttermilk. How many cups of buttermilk did she make?
Solution:
Maria has 20 litres of curd. Each cup of butter milk needs \(\frac{1}{3}\) \(\text{litres of curd}\)
Number of cups of butter milk \(=\) \(20\) \(\div\) \(\frac{1}{3}\)
\(=\) \(\frac{20}{1}\) \(\div\) \(\frac{1}{3}\)
Using the formula below, we get,
\(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}\)
\(=\) \(20\) \(\times\) \(3\)
\(=\) \(60\) \(\text{cups}\)
Maria made \(60\) \(\text{cups of butter milk}\).