what is 70 of 120

2 min read 22-12-2024

Finding percentages is a common task in many areas of life, from calculating discounts to determining grades. This article will show you how to easily calculate what 70% of 120 is, and provide some helpful tips for solving similar problems.

Understanding Percentages

Before we dive into the calculation, let's quickly review what percentages represent. A percentage is a fraction out of 100. So, 70% means 70 out of 100, or 70/100.

Method 1: Using Decimal Conversion

This is arguably the easiest method. We convert the percentage to a decimal and then multiply it by the number.

Step 1: Convert the percentage to a decimal.

To convert 70% to a decimal, divide 70 by 100:

70 ÷ 100 = 0.70

Step 2: Multiply the decimal by the number.

Now, multiply the decimal (0.70) by 120:

0.70 x 120 = 84

Therefore, 70% of 120 is $\boxed{84}$ .

Method 2: Using Fractions

This method involves converting the percentage to a fraction and then simplifying before multiplying.

Step 1: Convert the percentage to a fraction.

70% can be written as the fraction 70/100.

Step 2: Simplify the fraction (if possible).

Both 70 and 100 are divisible by 10, simplifying the fraction to 7/10.

Step 3: Multiply the fraction by the number.

Now, multiply the simplified fraction (7/10) by 120:

(7/10) x 120 = (7 x 120) / 10 = 840 / 10 = 84

Again, we find that 70% of 120 is $\boxed{84}$ .

Method 3: Proportion Method

This method sets up a proportion to solve for the unknown value.

Step 1: Set up a proportion.

We can set up a proportion like this:

70/100 = x/120

where 'x' represents the value we want to find (70% of 120).

Step 2: Cross-multiply.

Cross-multiplying gives us:

70 x 120 = 100 x

Step 3: Solve for x.

8400 = 100x

x = 8400 / 100

x = 84

Once again, we arrive at the answer: 70% of 120 is $\boxed{84}$ .

Practical Applications

Understanding how to calculate percentages is crucial in various real-world scenarios:

Sales and discounts: Calculating the final price after a discount.
Taxes: Determining the amount of tax on a purchase.
Grades and scores: Converting raw scores to percentages.
Statistics: Analyzing data and interpreting results.

Conclusion

Calculating percentages is a fundamental mathematical skill. Whether you use the decimal, fraction, or proportion method, the answer remains the same: 70% of 120 is 84. Choose the method that you find most comfortable and apply it to solve similar percentage problems. Remember to practice regularly to master this important skill!