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 15% of 100:

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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