## 40 is What percent of 400?

*40 is 10% of 400. To find the percentage, divide the part (40) by the whole (400) and multiply by 100: (40 / 400) * 100 = 10%. So, 40 is 10% of 400.*

## Finding the Percent When Given Part and Total

Word problems involving percentages often require finding what percentage one number represents out of a larger total. For example, if you earned $40 out of a $400 paycheck, what percent of the total paycheck was your amount? This involves setting up and solving a proportion to determine the percentage. Let’s look at the step-by-step method for finding what percent one number is of a total amount.

## Understand the Relationship

The first step is to make sure you understand the relationship between the numbers provided. Here, we are given two key pieces of information:

- The part amount: $40
- The total amount: $400

We need to determine what percent $40 is of the total $400. Rephrasing the question can help solidify the relationship: 40 is what percent of 400?

## Set Up a Proportion

To find an unknown percentage, we can set up a proportion equation. The proportion will be:

Part/Total = Percent/100

Plugging in the amounts from our word problem gives us:

40/400 = Percent/100

The part and total form the left side of the equation. The unknown percent over 100 gives us the right side.

## Solve the Proportion for Percent

Now we can use algebraic techniques to solve this proportion for the unknown percent value:

40/400 x 100/1 = Percent/100 x 100/1 (40 x 100) / 400 = Percent 4000/400 = Percent Percent = 10

So if 40 is a part of a total of 400, then 40 represents 10% of 400.

## Double Check the Solution

It’s always smart to double check your solution when solving word problems. We can verify that 10% of 400 is 40 to confirm we have the right percentage value.

Finding unknown percentages is a useful life skill with many real-world applications in personal finances, taxes, and more. Setting up proportions compares the part to the total and allows you to solve for the percent systematically. Practicing these crucial steps will give you confidence in unlocking unknown percentages when only given a clue like the part and total amounts. With this technique under your belt, percentages will seem much more straightforward!

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