Solve for Original Value: Finding Whole Number When 40% Equals 2

Q: Why do I convert 40% to 0.40 instead of just using 40?

Percentages must be converted to decimals for calculations! 40% means 40 out of 100, which equals $ \frac{40}{100} = 0.40 $. Using 40 directly would give you the wrong answer.

Q: How do I remember the formula for finding the whole?

Think of it as reversing multiplication! If 40% × Whole = 2, then Whole = 2 ÷ 40%. It's like solving 0.40 × ? = 2 by dividing both sides by 0.40.

Q: What if I get a decimal answer instead of a whole number?

Check your work! In this problem, we expect a whole number answer. If you get a decimal, you likely forgot to convert the percentage to decimal form or made an arithmetic error.

Q: Can I solve this using a proportion instead?

Yes! Set up $ \frac{40}{100} = \frac{2}{x} $, then cross-multiply: 40x = 200, so x = 5. Both methods give the same answer!

Q: How do I check if 5 is really correct?

Calculate 40% of 5: $ 0.40 \times 5 = 2 $. Since this matches the given information that 40% equals 2, your answer is correct!

Percentage Problems with Decimal Division

Determine the whole number when 40% of its total is equal to 2:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the whole number

00:05 A fraction with a denominator equal to 100, equals the percentage (X)

00:11 Apply this formula to our exercise

00:21 Factor 40 into factors of 4 and 10, and 100 into factors 10 and 10

00:26 Reduce wherever possible

00:29 Factor 4 into factors of 2 and 2, and 10 into 2 and 5

00:34 Reduce wherever possible

00:39 This is the reduced fraction

00:46 Construct an appropriate equation, express the whole using unknown Y

00:56 Isolate Y

01:11 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine the whole number when 40% of its total is equal to 2:

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the given percentage to a decimal by dividing by 100.
Step 2: Use the formula to find the whole number based on the part and the percentage in decimal form.
Step 3: Verify that the calculated whole corresponds to the multiple choice answers provided.

Now, let's work through each step:
Step 1: Convert 40% to decimal form. This gives us $0.40$ .
Step 2: Use the formula for the whole:
$\text{Whole} = \frac{\text{Part}}{\text{Percentage in decimal}} = \frac{2}{0.40}$ Calculate this division: $\frac{2}{0.40} = 5$
Step 3: Verify: The whole number calculated is 5, a valid option in the multiple-choice answers.
Therefore, the solution to the problem is $5$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Whole = Part ÷ Percentage (as decimal)
Technique: Convert 40% to 0.40, then calculate 2 ÷ 0.40 = 5
Check: Verify that 40% of 5 equals 2: 0.40 × 5 = 2 ✓

Common Mistakes

Avoid these frequent errors

Using percentage as whole number in division
Don't divide 2 ÷ 40 = 0.05! This treats 40% as 40 instead of 0.40, giving a tiny decimal answer instead of the correct whole number. Always convert percentages to decimals by dividing by 100 first.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why do I convert 40% to 0.40 instead of just using 40?

Percentages must be converted to decimals for calculations! 40% means 40 out of 100, which equals $\frac{40}{100} = 0.40$ . Using 40 directly would give you the wrong answer.

How do I remember the formula for finding the whole?

Think of it as reversing multiplication! If 40% × Whole = 2, then Whole = 2 ÷ 40%. It's like solving 0.40 × ? = 2 by dividing both sides by 0.40.

What if I get a decimal answer instead of a whole number?

Check your work! In this problem, we expect a whole number answer. If you get a decimal, you likely forgot to convert the percentage to decimal form or made an arithmetic error.

Can I solve this using a proportion instead?

Yes! Set up $\frac{40}{100} = \frac{2}{x}$ , then cross-multiply: 40x = 200, so x = 5. Both methods give the same answer!

How do I check if 5 is really correct?

Calculate 40% of 5: $0.40 \times 5 = 2$ . Since this matches the given information that 40% equals 2, your answer is correct!

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