1. The problem is to understand the process and effect of multiplying a number or expression by 36. 2. Multiplying by 36 means you are adding the number to itself 36 times. For example, if you have a number $x$, then multiplying by 36 is written as $36 \times x$. 3. The formula for multiplication is: $$a \times b = \text{sum of } a \text{ added } b \text{ times}$$ 4. When multiplying by 36, you can break 36 into factors to simplify calculations. For example, $36 = 6 \times 6$ or $36 = 4 \times 9$. 5. So, multiplying $x$ by 36 can be done as: $$36 \times x = (6 \times 6) \times x = 6 \times (6 \times x)$$ 6. This means you can first multiply $x$ by 6, then multiply the result by 6 again, which might be easier. 7. Another way is to multiply $x$ by 4, then multiply the result by 9: $$36 \times x = (4 \times 9) \times x = 4 \times (9 \times x)$$ 8. This factorization helps in mental math or simplifying algebraic expressions. 9. For example, if $x = 5$, then: $$36 \times 5 = 6 \times (6 \times 5) = 6 \times 30 = 180$$ 10. Or: $$36 \times 5 = 4 \times (9 \times 5) = 4 \times 45 = 180$$ 11. Both methods give the same result, confirming the correctness. 12. In summary, multiplying by 36 can be done directly or by breaking 36 into factors to simplify the multiplication process.