Question

Mohit travels 380 km per day. How much will he travel in 120 days?

Answer 1

Hint: Here, we need to find the distance Mohit travels in 120 days. We will use the concept of multiplication to get the distance travelled by Mohit in 120 days. Multiplication is the repeated addition of equal groups.

Complete step-by-step answer:
Multiplication helps in adding multiple equal groups quickly. It is denoted by the symbol \[ \times \]. Brackets may also be used to denote multiplication.
For example: Suppose that the number 2 is added repeatedly 15 times, that is \[2 + 2 + \ldots \ldots + 2\] 15 times. This can be represented using multiplication as \[2 \times 15\].
Now in the question, it is given that the distance travelled by Mohit in 1 day is 380 km.
We can multiply the distance travelled in 1 day by any number \[x\], to get the distance travelled by Mohit in \[x\] days.
Multiplying the distance travelled in 1 day by 120, we can find the distance travelled by Mohit in 120 days.
Therefore, we get
Distance travelled by Mohit in 120 days \[ = 380 \times 120\]km
Simplifying the expression, we get
Distance travelled by Mohit in 120 days \[ = 45600\]km
Therefore, Mohit travels 45,600 km in 120 days.

Note: We can solve the product \[380 \times 120\] more using the algebraic identity \[{a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)\].
Rewriting \[380 \times 120\] as a product of sum and difference of two numbers, we get
\[380 \times 120 = \left( {250 + 130} \right)\left( {250 - 130} \right)\]
Applying the algebraic identity \[{a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)\], we get
\[ \Rightarrow 380 \times 120 = {250^2} - {130^2}\]
Simplifying the expression, we get
\[ \Rightarrow 380 \times 120 = 62500 - 16900\]
Subtracting the terms of the expression, we get
\[ \Rightarrow 380 \times 120 = 45600\]
Thus, distance travelled by Mohit in 120 days \[ = 45600\]km
Therefore, Mohit travels 45,600 km in 120 days.