Begin by identifying the fraction of the number you are working with. For example, if you want to find out what 20% of 250 is, multiply 250 by 0.20 (20/100). This method is direct and efficient for quick results.
Another common scenario is determining the change in a value due to an increase or decrease. If a price goes up by 15%, multiply the original price by 1.15. If the price goes down by 15%, multiply it by 0.85. This approach simplifies many real-world situations like shopping discounts or salary adjustments.
When dealing with multiple steps or compound operations, break down each calculation into manageable parts. For instance, when working with more than one percentage change, apply each percentage change sequentially on the original value to get the accurate outcome.
Calculating Fractions of a Number with Basic Exercises
To find a specific fraction of a total: Multiply the number by the fraction. For example, if you need to calculate 25% of 120, multiply 120 by 0.25. The result is 30.
For determining the total from a given fraction: If you know that 15% of a number is 45, divide 45 by 0.15. This gives you the original number, which is 300.
To calculate increases or decreases: If a price increases by 10%, multiply the original value by 1.10. If it decreases by 10%, multiply the original value by 0.90. For instance, for a $200 item with a 10% increase, the new price will be 200 * 1.10 = 220.
How to Quickly Find Fractions of a Given Number
For a quick calculation: Convert the percentage into a decimal by dividing it by 100. Multiply the decimal by the given number to get the result. For example, to find 30% of 200, convert 30% to 0.30 and then multiply 200 by 0.30. The result is 60.
For 10%, 20%, 50%, and other common values: These are easy to calculate without a calculator. For 10%, just divide the number by 10. For 20%, divide the number by 5. For 50%, simply divide the number by 2. For instance, to find 50% of 80, divide 80 by 2, which equals 40.
Using the “double and halve” trick: If you need 25% or 75%, first find 50% (half the number). For 25%, divide that result by 2. For 75%, add the 50% result to the 25% result. For example, for 25% of 80, halve 80 to get 40, and then halve 40 to get 20.
Understanding the Process of Increasing or Decreasing by a Percentage
To increase a value: First, convert the percentage to a decimal by dividing it by 100. Then, multiply the decimal by the original number to find the increase. Finally, add the increase to the original number. For example, to increase 150 by 20%, convert 20% to 0.20, multiply 150 by 0.20 (resulting in 30), and then add this to 150 to get 180.
To decrease a value: Follow the same process but subtract the result instead of adding it. For example, to decrease 200 by 15%, convert 15% to 0.15, multiply 200 by 0.15 (resulting in 30), and then subtract this from 200 to get 170.
Another method for both increases and decreases: Multiply the original number by (1 + decimal value) to increase, or (1 – decimal value) to decrease. For example, to increase 120 by 25%, multiply 120 by 1.25 (resulting in 150). To decrease 120 by 25%, multiply 120 by 0.75 (resulting in 90).