Solve for the Whole: Finding Total When 60 Percent Equals 4

Q: Can I solve this using proportions instead?

Absolutely! Set up the proportion: $ \frac{4}{x} = \frac{60}{100} $ where x is the whole. Cross-multiply: 4 × 100 = 60 × x, so 400 = 60x, giving x = 6.67.

Q: What if my answer doesn't match the given choices exactly?

Check if your answer needs to be rounded or expressed as a fraction. $ \frac{20}{3} $ = 6.666... which rounds to 6.67 or 6.66 depending on decimal places required.

Q: How can I check my answer makes sense?

Ask yourself: "Is my whole number larger than the part?" Since 4 represents only 60% (more than half), the whole should be larger than 4. Our answer 6.67 > 4, so it makes sense!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, find the whole number we need to work with.

00:10 Next, let's convert the percent to a fraction. Here's how: sixty percent becomes sixty over one hundred.

00:18 Notice that this fraction stands for sixty percent.

00:24 Now, multiply the fraction by the whole number. This should give us four, based on what we're told.

00:32 Then, multiply by the reciprocal of the fraction. This helps us find the whole number.

00:43 Remember to simplify or reduce the fraction whenever you can.

01:00 Factor and reduce again, if possible.

01:04 And there you have it, that's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Calculate the whole if 60 percent is equal to 4:

2

Step-by-step solution

To solve this problem, we'll proceed with the following steps:

Step 1: Identify the given information.
Step 2: Apply the appropriate formula for the percentage calculation.
Step 3: Perform the necessary calculations to find the whole number.

Now, let's work through each step:

Step 1: The problem states that 60% of a number is equal to 4. We need to find this number, denoted as the whole.

Step 2: We'll use the percentage formula: $\text{whole} = \frac{\text{part} \times 100}{\text{percentage}}$

Step 3: Plugging in the values, we have: $\text{whole} = \frac{4 \times 100}{60}$ $\text{whole} = \frac{400}{60}$ $\text{whole} = \frac{20}{3}$

Simplifying further, $\text{whole} \approx 6.66$

Therefore, the solution to the problem is $6.66$ .

3

Final Answer

6.66

Key Points to Remember

Essential concepts to master this topic

Formula: Whole = (Part × 100) ÷ Percentage
Technique: Given 60% = 4, calculate (4 × 100) ÷ 60 = 6.67
Check: Verify by calculating 60% of 6.67: 0.60 × 6.67 = 4 ✓

Common Mistakes

Avoid these frequent errors

Confusing which number is the part vs. whole
Don't think 4 is the whole number and try to find 60% of 4 = 2.4! This gives the wrong direction. Always identify what you're looking for: when given that 60% equals 4, you're finding the whole that 4 represents 60% of.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

How do I know which formula to use for percentage problems?

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Look at what you're given and what you need to find! If you know the percentage and the part (like 60% = 4), use: Whole = (Part × 100) ÷ Percentage. If you know the whole and percentage, multiply to find the part.

Why do I multiply by 100 in the formula?

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Because percentages are out of 100! When you have 60%, it really means $\frac{60}{100}$ . To reverse this and find the whole, you need to multiply by 100 and divide by the percentage.

Can I solve this using proportions instead?

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Absolutely! Set up the proportion: $\frac{4}{x} = \frac{60}{100}$ where x is the whole. Cross-multiply: 4 × 100 = 60 × x, so 400 = 60x, giving x = 6.67.

What if my answer doesn't match the given choices exactly?

+

Check if your answer needs to be rounded or expressed as a fraction. $\frac{20}{3}$ = 6.666... which rounds to 6.67 or 6.66 depending on decimal places required.

How can I check my answer makes sense?

+

Ask yourself: "Is my whole number larger than the part?" Since 4 represents only 60% (more than half), the whole should be larger than 4. Our answer 6.67 > 4, so it makes sense!

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Solve for the Whole: Finding Total When 60 Percent Equals 4

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