Understanding and Calculating 100 x 45 x 35 x 35: A Guide to Multiplication

The expression 100 x 45 x 35 x 35 might seem daunting at first, but once broken down, it becomes a manageable problem. This guide will walk you through the process of solving this equation, focusing on the principles of multiplication and providing step-by-step instructions to help you understand the solution.

Step-by-Step Solution

Let's start by breaking down the factors and applying the rules of multiplication:

First, break down the numbers:

100 x 9 / 2 x 10 x 7 / 2 x 10 x 7 / 2 x 10 10 - 1 x 49 / 8 x 100000 490 - 49 x 100000 / 8 441 x 100000 / 8

Now, let's simplify the expression using multiplication properties:

The order of multiplication does not alter the result. Therefore, we can group the factors in a way that simplifies the calculation:

Grouping Factors:

100 x 45 x 35 x 35 4500 x 1225

By grouping the factors this way, we break down the problem into simpler steps that are easier to compute manually or with a calculator.

Carrying Out the Multiplication:

Now, let's perform the multiplication step-by-step:

Step 1:

4500 x 1225

1225 can be further broken down as 1225 1250 - 25.

Step 2:

4500 x 1250 - 4500 x 25

This simplifies to:

4500 x 1250 5625000 4500 x 25 112500

Step 3:

Now subtract the second result from the first:

5625000 - 112500 5512500

Thus, the final result of 100 x 45 x 35 x 35 is 5512500.

Learning from Practice

Multiplication is a fundamental skill in mathematics, and solving problems like this can be a great way to learn or refresh your arithmetic skills. It's always beneficial to practice and understand the underlying principles. This process, although tedious when done manually, can be a valuable learning exercise, especially when dealing with larger numbers and complex calculations.

Conclusion

The expression 100 x 45 x 35 x 35 evaluates to 5512500. By breaking it down and simplifying the multiplication, we can see that even seemingly complex calculations can be managed with a bit of patience and perseverance.

Frequently Asked Questions

Q: Can I use a calculator for this?
A: Absolutely! A calculator can be a helpful tool for verifying your calculations quickly and accurately.

Q: Is this type of calculation useful in real life?
A: Yes, understanding multiplication is crucial in many real-life scenarios, such as budgeting, construction, engineering, and more. It forms the basis for more complex mathematical concepts.