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Educational Psychology: Tutoring Solution9 chapters | 335 lessons

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*Ravinder Sandhu*

Mental math allows children to solve mathematical problems without using a calculator or paper and pencil. This lesson presents tricks that allow you to solve multiplication problems in a matter of seconds.

**Mental math** occurs when we use nothing but our own brains to solve a math problem. Kids usually start learning how to solve math problems using tools such as a number line or by writing out the problem using pen and pencils. With time, they learn to solve mathematical problems mentally, eventually with great ease and speed. Conquering mental math provides a satisfaction that fosters a love for math, which can be beneficial throughout a child's education. Mental math can also help improve concentration, problem-solving skills and reasoning abilities.

Below are some mental math shortcuts that students can use in certain situations.

To quickly multiply by 5, divide the number being multiplied by 5 in two and then multiply it by 10.

- For example, let's solve for 12 x 5. Take 12 and divide into two so it becomes 6. Next, take 6 and multiply by 10. The product is 60.

To square any two-digits number ending in 5, take the first digit and add 1 to it. Next, take that sum and multiply by the original first digit. Lastly, take that product and put 25 at the end of it.

- For example, let's square the number 25. Take the first digit of the number (2) and add 1, which equals 3. Next, multiply that sum by the first digit of the original number (2 x 3). This gives us 6. Lastly, put 25 at the end of the 6 to get the final answer: 625.

This trick works only when multiplying 6 by even numbers. First, take the number you are multiplying 6 by and half it. This will be the first digit in the answer. Next, take the number you're multiplying 6 by and place it behind the first digit in the answer. That gives you your final answer.

- For example, let's solve for 6 x 2. First, half of 2 is 1. So, 1 is the first digit in the answer. Next, take 2 (the number that you're multiplying 6 by) and place it behind 1. That give you your answer: 12.

This one involves using your hands, but with practice, students will be able to visualize the action in their heads.

To start, hold both hands up in front of you with fingers spread apart and number your fingers 1-10 from left to right. Whichever number is going to be multiplied by 9 is the finger that you will bend. The number of fingers to the left of the bent finger will be the first digit of the answer, and the number of fingers to the right of the bent finger will be the second digit in the answer.

- For example, if 9 is being multiplied by 8, then you would bend down the 8th finger. There are 7 fingers to the left of the bent finger, and 2 fingers to the right. So, the answer of 8 x 9 is 72.

The first digit in the answer is always one less than the number being multiplied by 9. Now, subtract that solution (the first digit in the answer) from 10--this is the second digit in the answer.

- For example, let's solve for 9 x 8. We know the first digit in the answer is 7 (one less than 8, which is the number being multiplied by 9). Now that we have the first digit of the answer, we can find the second. Subtract that first digit (8) from 10 to get 2. Our final answer is 72.

To start, take the two digits being multiplied by 11 and add them. Take that sum and place it between the two original digits that were being multiplied by 11. The new number is your final answer.

- Let's solve for 34 x 11. Add the first and second digits: 3 + 4 = 7. Place that sum between the first and second digits of the original number being multiplied by 11. That gives you your final answer: 374.

Keep in mind that if the result of the addition is greater than 9, you only put the ones-place digit in between and carry the tens-place digit over.

- For example, let's look at 11 x 57. Add the 5 and 7 to get 12. Place the 2 (the ones-place digit) between the first and second digits of the original number being multiplied by 11. Then, carry the tens-place digit over by adding 1 to the number to the left--the 5--making it a 6. You now have your final answer: 627.

For cases like this, always place the larger number first in the equation. Start by taking the first (larger) number and adding it to the second digit of the second (smaller) number. Next, take that sum and put a 0 behind it. Lastly, multiply the second digits from each original number, then add this product with the sum with the 0 at the end.

- Let's solve for 15 x 13. Start by adding 15 (the first number) and 3 (the second digit of the second number) to get 18. Next, place a 0 at the and to get 180. Lastly, multiply the second digit of both original numbers: 3 x 5 = 15. Add this to the previous sum with the 0 at the end (180) to get your answer: 195.

Mental math is when we use nothing but our own brains to solve a math problem. The only way to excel at mental math is to constantly practice these tricks. Being able to perform math tricks quickly and mentally can boost students' self-esteem in and enjoyment of mathematics. Mental math can also help in other aspects of education, such as concentration, problem-solving skills and reasoning abilities.

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Educational Psychology: Tutoring Solution9 chapters | 335 lessons

- Instructional Strategies: Hands-On, Interactive, Expository & Collaborative 6:15
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