June 5th, 2023: Unlock Efficiency with Math Shortcuts and Techniques

   Unlock Efficiency with Math Shortcuts and Techniques

• Multiplying by Powers of 10: When multiplying a number by a power of 10, you can easily move the decimal point to the right by the number of zeros in the power. For example, multiplying 25 by 1,000 is the same as shifting the decimal point three places to the right: 25,000.
• Squaring Numbers Ending in 5: To quickly square a number ending in 5, multiply the digit formed by the tens place by its successor and append 25 to the result. For instance, to find the square of 35, multiply 3 (the tens digit) by its successor, 4, resulting in 12. Append 25 to obtain 1,225, the square of 35.
• Percentage Calculations: When calculating percentages, it’s often helpful to use mental math tricks. To find 10% of a number, divide it by 10. For example, to determine 10% of 80, divide 80 by 10, resulting in 8. To find 5% of a number, halve the 10% value. In this case, 5% of 80 is half of 8, or 4.Cross Multiplication: Cross multiplication is a handy shortcut for solving proportions. When faced with a proportion like a/b = c/d, you can cross multiply by multiplying a and d, and then multiply b and c. Setting the products equal, you have ad = bc. This equation can help you find unknown values in proportions quickly.
• Divisibility Tests: There are various divisibility tests to quickly determine if a number is divisible by another. For example, a number is divisible by 2 if it is even, divisible by 3 if the sum of its digits is divisible by 3, and divisible by 9 if the sum of its digits is divisible by 9.
• Estimation: Estimating can be a powerful tool when you need a quick approximation. Round numbers to the nearest whole number or significant digit to simplify calculations. For instance, if you need to calculate 31% of 82, you can round 82 to 80 and then find 30% (which is 24) and add 1% (which is 0.8) to get an approximate answer of 24.8.
• Adding Consecutive Numbers: The sum of consecutive numbers from 1 to n can be found using the formula n(n+1)/2. For example, the sum of numbers from 1 to 10 is (10 * 11) / 2 = 55.
• Multiplying by 11: To quickly multiply a two-digit number by 11, add the two digits together and place the result between them. For example, 11 * 27 = 297 (2 + 7 = 9, place 9 between 2 and 7).
• Subtracting from 1,000: To subtract a number from 1,000, subtract each digit from 9, except for the last digit, which is subtracted from 10. For example, 1,000 – 543 = 457 (9 – 5 = 4, 9 – 4 = 5, 10 – 3 = 7).
• Squaring Numbers Ending in 1: To square a number ending in 1, multiply the original number by the next consecutive number, then append 1 to the result. For example, 21 * 22 = 462, so 21^2 = 441.
• Multiplying Two-Digit Numbers: To multiply two-digit numbers, use the FOIL method (First, Outer, Inner, Last). Split each number into its tens and ones digits, multiply accordingly, and combine the results. For example, 23 * 45 = (20 * 40) + (20 * 5) + (3 * 40) + (3 * 5) = 1,035.Cubing Numbers: To quickly cube a number, multiply the number by itself twice. For example, 4^3 = 4 * 4 * 4 = 64.
• Dividing by 5: When dividing a number by 5, simply divide it by 10 and multiply the result by 2. For example, 80 ÷ 5 = (80 ÷ 10) * 2 = 16.
• Calculating Square Roots: For numbers ending in 1, 4, 5, 6, or 9, you can approximate the square root mentally. Find the closest perfect square and estimate the square root based on its proximity. For example, the square root of 26 is approximately between the square roots of 25 and 36, which are 5 and 6, respectively.
• Finding Percentages: To find 1% of a number, divide it by 100. To find 10%, divide it by 10. Then, multiply the result by the desired percentage. For example, to find 35% of 200, find 10% (20) and multiply by 3 (30) to get 60.
• Adding Numbers with the Same Units Digit: When adding numbers with the same units digit, focus only on the tens digit. Add the tens digits, keep the same units digit, and carry over any additional tens. For example, 34 + 74 = 108 (3 + 7 = 10, carry over 1).
• Squaring Numbers Ending in 9: To square a number ending in 9, subtract 1 from the tens digit, and append 1 to the resulting number. For example, 49^2 = 4,8 (4-1) 1 = 4,801.
• Multiplying by 5: When multiplying a number by 5, divide it by 2 and then multiply by 10. For example, 7 * 5 = (7 ÷ 2) * 10 = 3.5 * 10 = 35.
• Adding the Numbers 1 to 100: The sum of the numbers from 1 to 100 can be found using the formula (n(n+1))/2, where n is the highest number in the range. For this case, (100 * 101) / 2 = 5,050.
• Multiplying by 9: To multiply a number by 9, multiply it by 10 and then subtract the original number. For example, 6 * 9 = (6 * 10) – 6 = 60 – 6 = 54.
• Calculating Percentage Increases: To find the percentage increase between two numbers, subtract the original number from the final number, divide the result by the original number, and multiply by 100. For example, the percentage increase from 50 to 70 is ((70 – 50) / 50) * 100 = 40%.
• Squaring Numbers Ending in 0: To square a number ending in 0, remove the 0 and multiply the resulting number by itself, then append 0 to the result. For example, 30^2 = 3^2 * 10^2 = 900.
• Dividing by 4: When dividing a number by 4, divide it by 2 twice. For example, 36 ÷ 4 = (36 ÷ 2) ÷ 2 = 9 ÷ 2 = 4.5.
• Dividing by 11: To divide a two-digit number by 11, add the digits together and place the result between them. If necessary, carry over any tens. For example, 143 ÷ 11 = 13 with a remainder of 2, so the answer is 13 and 2/11.

By incorporating these additional math shortcuts and techniques into your repertoire, you’ll be well-equipped to tackle calculations efficiently and effectively. Remember, consistent practice and application will reinforce your skills and make these shortcuts second nature.