Multiplication in real - life context:
\(\text{Multiplication}\) is an arithmetic operation that is known as a \(\text{repeated addition}\).
Example:
It takes \(30\) minutes for \(\text{Meena}\) to walk \(1 km\). How many minutes it will take for \(\text{Meena}\) to walk for \(3\) kms?
Solution:
It is given that,
\(\text{Meena}\) walk \(1 \text{km}\) within \(30\) \(\text{minutes}\).
\(\implies\) \(\text{Meena}\) walk \(3\) \(\text{km}\) within
\(= 3 \times 30\) \(\text{minutes}\)
\(=30+30+30\)
\(=90\) \(\text{minutes}\)
Answer:
It takes \(90\) \(\text{minutes}\) for \(\text{Meena}\) to walk \(3\)\(\text{km}\
From the above example, it is clear that \(\text{multiplication}\) is an arithmetic operation that is known as the \(\text{repeated addition}\).
Multiplying a whole number by a fraction:
Multiplying a \(\text{whole number}\) by a \(\text{fraction}\) is nothing but a \(\text{repeated addition}\) of that particular fraction.
Example:
It take pet dog to walk \(\frac{1}{2}\) \(\text{km}\) in \(1\) \(\text{hour}\). How far can it walk in \(5\) \(\text{hours}\)?
Solution:
It is given that,
It take pet dog to walk \(\frac{1}{2}\) \(\text{km}\) in \(1\) \(\text{hour}\)
Here the distance covered in an hour is in fraction.
The total distance covered in same way as multiplication.
Distance covered in \(1\) \(\text{hour}\) \(=\) \(\frac{1}{2}\) \(\text{km}\)
Therefore, the distance covered in \(5\) \(\text{hours}\)
\(= 5 \times \frac{1}{2}\)
\(=\) \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)
\(=\) \(\frac{5}{2}\)
The dog can walk \(\frac{5}{2}\) \(\text{km}\) in \(5\) \(\text{hours}\).