What number is 120% of 70?
The Correct Answer and Explanation is :
To find 120% of 70, we can use a simple calculation. First, we convert the percentage to a decimal by dividing by 100. So, 120% as a decimal is (1.2). Next, we multiply this decimal by the number we want to find the percentage of:
[
1.2 \times 70 = 84
]
Thus, 120% of 70 is 84.
Verification Using Proportion
To check our answer using a proportion, we can set up the following relationship:
[
\frac{120}{100} = \frac{x}{70}
]
Here, (x) represents the number we are trying to find, which is 120% of 70. We can cross-multiply to solve for (x):
[
120 \times 70 = 100 \times x
]
Calculating the left side gives:
[
8400 = 100x
]
Now, to isolate (x), divide both sides by 100:
[
x = \frac{8400}{100} = 84
]
This confirms that our initial calculation was correct. The value of (x), which is 120% of 70, is indeed 84.
Explanation of Steps
- Convert Percentage to Decimal: Understanding how to convert percentages to decimals is crucial. By dividing the percentage by 100, we can use it in mathematical operations.
- Multiplication: Multiplying the decimal by the original number provides the desired result directly.
- Proportion Method: Setting up a proportion allows us to cross-multiply, providing a different method to verify our result. This method is particularly useful in scenarios where direct multiplication may seem less intuitive.
- Cross-Multiplication: This technique is effective for solving proportions and can be applied to various mathematical problems involving ratios and percentages.
Using both methods gives a solid understanding of how percentages work, reinforces mathematical principles, and ensures accuracy in calculations. Thus, whether through direct calculation or verification via proportion, we arrive at the same conclusion that 120% of 70 is 84.