NCERT Solutions for Chapter: Ways to Multiply and Divide, Exercise 7: Fun with multiplication

Each letter $\mathrm{a}, \mathrm{b}, \mathrm{c}$ here stands for a number.

$\underline{\begin{array}{ccccc}& & \mathrm{a}& \mathrm{a}& \mathrm{a}\\ & \times & \mathrm{a}& \mathrm{a}& \mathrm{a}\\ & & \mathrm{a}& \mathrm{a}& \mathrm{a}\\ & \mathrm{a}& \mathrm{a}& \mathrm{a}& +\\ \mathrm{a}& \mathrm{a}& \mathrm{a}& +& +\\ \mathrm{a}& \mathrm{b}& \mathrm{c}& \mathrm{b}& \mathrm{a}\end{array}}$

Take $\mathrm{a}=1$, then find what the numbers $\mathrm{b}$ and $\mathrm{c}$ will be.

Tricks with your age.
Write your age_____
Multiply it by $7$ _____
Again multiply the answer by $13$ _____
Multiply again that answer by $11$_____
Now look at your last answer. Can you find your age in that answer?
How many times does your age show in the answer?

Going round and round!

Do you find a pattern in all these answers?$$