20% of what number is 7?
The Correct Answer and Explanation is:
To find out what number corresponds to 20% being equal to 7, we can set up the equation based on the percentage formula.
Understanding Percentages
The term “percentage” represents a part out of 100. Therefore, 20% can be expressed mathematically as:
[
20\% = \frac{20}{100} = 0.20
]
This means that when we say 20% of a number (let’s call it ( x )), we are essentially saying ( 0.20 \times x ).
Setting Up the Equation
According to the problem, 20% of ( x ) equals 7. We can write this as:
[
0.20 \times x = 7
]
Solving for ( x )
To find ( x ), we need to isolate it. We can do this by dividing both sides of the equation by 0.20:
[
x = \frac{7}{0.20}
]
Now we can perform the division:
[
x = 7 \div 0.20 = 7 \div \frac{20}{100} = 7 \times \frac{100}{20} = 7 \times 5 = 35
]
Conclusion
Thus, the number we are looking for is 35. To verify our result, we can calculate 20% of 35:
[
0.20 \times 35 = 7
]
This confirms that our solution is correct.
Key Takeaways
- Understanding Percentages: Always remember that percentages are fractions out of 100. To convert a percentage to a decimal, divide by 100.
- Setting Up Equations: When working with percentages, set up an equation based on the percentage definition, as shown above.
- Solving Algebraically: To isolate the variable, use inverse operations like division.
- Verification: After finding the solution, it’s a good practice to verify it by plugging it back into the original equation.
In summary, 20% of 35 is indeed 7, demonstrating the mathematical principles involved in percentage calculations.