Question

Translate to an equation and solve. \(40 \%\) of 350 is what number?

Short answer

Answer: 140

Step-by-step solution

Write the equation

To find out what number is equal to 40% of 350, we can write the equation like this: $$0.40 * x = 0.40 * 350$$ Here, x represents the number we are trying to find.

Convert percentage to a decimal

Since we are working with percentages, we should convert 40% to a decimal. To do this, we divide 40 by 100: $$40 \% = \frac{40}{100} = 0.40$$ Now we can rewrite our equation using the decimal form of 40%: $$0.40 * x = 0.40 * 350$$

Multiply both sides of the equation by the same number

To solve the equation, we need to multiply both sides by the same number. In this case, we should multiply both sides by 350: $$0.40 * x = 0.40 * 350$$

Solve the equation

Now we can solve the equation: $$0.40 * x = 140$$ To find x, we need to divide both sides of the equation by 0.40: $$x = \frac{140}{0.40} = 350$$

Interpret the result

Our result tells us that 40% of 350 is equal to 140. Therefore, the number we are looking for is 140.

Key concepts

Equation Solving

Solving equations is like solving a puzzle, where you work towards finding a specific number that fits. In percentage problems, we often translate a problem into an equation. This helps us find the missing number we are looking for. Let's start by looking at the problem: "40% of 350 is what number?" Our aim is to find "what number." To do this, we set up an equation:

• Start with what you know: 40% of 350
• Use the formula: \( x = 0.40 \times 350 \)
• \( x \) is the number we want to find

Here, \( x \) stands for the unknown number. Setting it up this way allows you to see what you need to do next. The equation states that some number \( x \) equals \( 0.40 \times 350 \). This approach makes it easier to understand what the solution requires.

Decimal Conversion

Converting percentages to decimals is a crucial step in solving many math problems, including percentage problems. A percentage shows a number as part of 100. For instance, 40% means 40 out of 100 parts. To use this in calculations, converting the percentage into a decimal makes operations simpler.
To convert a percentage into a decimal:

• Remove the percent symbol \(\%\)
• Divide the number by 100

For 40%, this means:\[40\% = \frac{40}{100} = 0.40\]Now, you can use the decimal 0.40 in any math equations. Decimals are easier to work with because it's straightforward to multiply, divide, or add them in calculations. By converting 40% to 0.40, the problem becomes simpler when creating equations and finding solutions.

Basic Arithmetic

Basic arithmetic skills are key to solving percentage problems. In these problems, common operations like multiplication and division are frequently used. Let’s see how they help in the exercise problem you are working on.
Once you've set up the equation \(0.40 \times x = 140\):

• Multiply: \(0.40 \times 350 = 140\)
• Next, solve for \( x \): divide both sides of the equation by 0.40

To do this calculation:\[x = \frac{140}{0.40} = 350\]Through multiplication, you could figure out that 140 is 40% of 350. Then, division was used to confirm that 140 is indeed the result. Mastery of these basic arithmetic operations enables you to unlock solutions with confidence!