What number is 120% of 70

Use a proportion to check your answer. What number is 120% of 70?

The Correct Answer and Explanation is :

To find 120% of 70, we can use a simple calculation involving proportions and percentages.

Calculation Steps

1. Understanding Percentages:
   A percentage represents a fraction of 100. Therefore, 120% can be expressed as:
   [
   120\% = \frac{120}{100} = 1.2
   ]
2. Calculating 120% of 70:
   To find 120% of 70, multiply 70 by 1.2:
   [
   1.2 \times 70 = 84
   ]
   So, 120% of 70 is 84.

Using a Proportion to Check the Answer

To verify our answer using a proportion, we can set up a relationship based on percentages.

• Let ( x ) represent the unknown number (which we found to be 84).
• We can establish a proportion based on the definition of percentages:
  [
  \frac{x}{70} = \frac{120}{100}
  ]

1. Cross-Multiplying:
   Cross-multiplying gives us:
   [
   100x = 120 \times 70
   ]
2. Calculating the Right Side:
   First, calculate ( 120 \times 70 ):
   [
   120 \times 70 = 8400
   ]
   Then, the equation becomes:
   [
   100x = 8400
   ]
3. Solving for ( x ):
   Now, divide both sides by 100:
   [
   x = \frac{8400}{100} = 84
   ]

Conclusion

The proportion method confirms our initial calculation. Therefore, the answer is 84, and it validates the understanding of how percentages work. Using proportions provides a solid check on calculations and helps reinforce the concept of relationships between numbers in percentage form. This method can be applied to various situations where percentages need to be calculated or verified, ensuring accuracy in mathematical computations.