Solve the Equation: If 35% Equals 7, What is the Whole?

Q: Why do I multiply by 100 in the formula?

You multiply by 100 because percentages are parts out of 100. When 35% = 7, you're finding what 100% equals, so you scale up: $ \frac{7 \times 100}{35} = 20 $

Q: Can I convert the percentage to a decimal first?

Absolutely! Convert 35% to 0.35, then divide: $ \frac{7}{0.35} = 20 $. Both methods work perfectly!

Q: What if the percentage doesn't divide evenly into the part?

No problem! You might get a decimal or fraction as your answer. For example, if 30% = 7, then the whole = $ \frac{700}{30} = 23.33... $

Q: How do I check my answer when the numbers are messy?

Use a calculator! Multiply your answer by the decimal form of the percentage. If 35% of your answer equals the original part, you're correct!

Q: Is there a faster way to solve this type of problem?

Yes! Set up a proportion: $ \frac{35}{100} = \frac{7}{x} $, then cross-multiply: $ 35x = 700 $, so $ x = 20 $

Percentage Problems with Whole Number Finding

Calculate the whole if 35 percent is equal to 7:

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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 Apply the formula to convert percentages to fractions

00:16 This fraction is equal to 35%

00:22 Multiply this fraction by the whole number in order to obtain 7 according to the given data

00:30 Multiply by the reciprocal fraction in order to isolate the whole number

00:53 Reduce wherever possible

01:09 Factor out and reduce wherever possible

01:16 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the whole if 35 percent is equal to 7:

Step-by-step solution

To solve this problem, we'll calculate the whole number using the provided percentage and part of that percentage.

Step 1: The given part is 7, which corresponds to 35% of the whole.
Step 2: Use the formula: $\text{whole} = \frac{\text{part} \times 100}{\text{percentage}}$
Step 3: Substitute the known values: $\text{whole} = \frac{7 \times 100}{35}$
Step 4: Calculate $7 \times 100 = 700$ .
Step 5: Divide by 35: $\text{whole} = \frac{700}{35}$
Step 6: Simplify the division: $\text{whole} = 20$

Therefore, the whole number when 35% is equal to 7 is 20.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Whole = Part × 100 ÷ Percentage for all problems
Technique: Calculate 7 × 100 ÷ 35 = 700 ÷ 35 = 20
Check: Verify 35% of 20 equals 7: 0.35 × 20 = 7 ✓

Common Mistakes

Avoid these frequent errors

Dividing part by 100 instead of multiplying
Don't calculate 7 ÷ 100 × 35 = 2.45! This gives a tiny decimal instead of the correct whole number. The part should be multiplied by 100, not divided. Always use: Part × 100 ÷ Percentage.

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 multiply by 100 in the formula?

You multiply by 100 because percentages are parts out of 100. When 35% = 7, you're finding what 100% equals, so you scale up: $\frac{7 \times 100}{35} = 20$

Can I convert the percentage to a decimal first?

Absolutely! Convert 35% to 0.35, then divide: $\frac{7}{0.35} = 20$ . Both methods work perfectly!

What if the percentage doesn't divide evenly into the part?

No problem! You might get a decimal or fraction as your answer. For example, if 30% = 7, then the whole = $\frac{700}{30} = 23.33...$

How do I check my answer when the numbers are messy?

Use a calculator! Multiply your answer by the decimal form of the percentage. If 35% of your answer equals the original part, you're correct!

Is there a faster way to solve this type of problem?

Yes! Set up a proportion: $\frac{35}{100} = \frac{7}{x}$ , then cross-multiply: $35x = 700$ , so $x = 20$

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