Easy Method for Memorizing the Multiplication Table
When beginning to memorize the multiplication table, it is advisable to start with the simpler tables, such as those for the numbers (0, 1, 2, 10). The product of any number multiplied by zero is zero, for example, 7 × 0 = 0. Similarly, the product of any number multiplied by one is the number itself, such as 8 × 1 = 8. After mastering these, one can move on to more challenging multiplication tables. Additionally, knowing certain tricks can significantly ease the process of memorizing the multiplication table. Here are some of those tricks:
Multiplication Table of 2
To multiply by the number 2, simply double the number. For instance, 2 × 9 = (9 + 9) = 18.
Multiplication Table of 4
The product of any number multiplied by 4 is essentially the number doubled twice, or added to itself four times.
Multiplication Table of 5
It’s important to remember that the units digit of the result when multiplying 5 by an odd number will always be 5, while the units digit for an even number will be 0. A helpful trick to remember the multiplication table of 5 is that the product of any number multiplied by 5 is essentially half of the result of that number multiplied by 10. For example, 5 × 8 = 40 (which is half of 80, where 10 × 8 = 80), and 5 × 5 = 25 (which is half of 50, where 10 × 5 = 50).
Multiplication Table of 6
For the multiplication table of 6, an effective trick is that when multiplying six by an even number, write the multiplied number in the units place and half of it in the tens place. For example, for 6 × 8 = 48 and 6 × 6 = 36.
Multiplication Table of 8
The result of multiplying by 8 can be achieved by doubling the multiplied number three times. For instance, to calculate 8 × 6, first double the number 6 to get 12, double 12 to get 24, and then double 24 to arrive at 48.
Multiplication Table of 9
The product of any number multiplied by 9 can be found by multiplying that number by 10 and then subtracting the original number from the result. For example, 6 × 9 = 54, which comes from 6 × 10 = 60, and then 60 – 6 = 54.
Another method to determine the results of the 9 multiplication table is to observe that the sum of the digits in the product will always equal 9. For example, with 9 × 6 = 54, the sum 5 + 4 = 9. Furthermore, the tens digit of the result will always be one less than the number being multiplied by 9: (tens place = number being multiplied by 9 – 1). Therefore, if you want to compute 9 × 7, subtract 1 from 7 to find the tens place: 7 – 1 = 6, then subtract 6 from 9 for the units place: 9 – 6 = 3, resulting in the final answer of 63.
Another approach for finding the product involving the number 9 employs the use of fingers. You can extend your fingers on both hands, and number them sequentially from the pinky (representing 6) to the thumb (10). For example, to find 9 × 3, count three fingers from the left and fold the third finger, then count the fingers on both sides to find the tens and units digits of your answer.
Multiplication Table of 10
The multiplication table of 10 is the easiest, as any number multiplied by 10 is simply the number followed by a zero. For instance, 10 × 5 = 50, achieved by writing 5 in the tens place and adding a zero in the units place.
Multiplication Table of 11
For products of any number from 1 to 9 with 11, the result is the same number repeated twice, such as 11 × 9 = 99 and 11 × 5 = 55. For products involving numbers 10 and above, you can place the units and tens digits of the multiplied number in the result, separating them with a space for clarity, then summing the two to place in the middle. For example, 11 × 43 = 3_4, and 4 + 3 = 7, which means 11 × 43 = 473. If you have a scenario like 11 × 68 = 8_6, where the sum exceeds 9 (6 + 8 = 14), the approach changes by placing the units digit of the sum in the units place, while the tens digit is combined with the left digit: 11 × 68 = 748.
Multiplication Table of 12
To simplify learning the multiplication table of 12, break down the process. The calculation involves multiplying the number by 10 and then by 2, adding the two results together for the final product. For instance, with 5 × 12, knowing that 10 × 5 = 50 and 2 × 5 = 10 results in: 50 + 10 = 60, so 5 × 12 = 60.
Multiplication Table of 15
To find the product of numbers multiplied by 15, first multiply the number by 10, then add half of that result. For example, 15 × 4 first calculates as 40 (4 × 10), then add half of that, resulting in 40 + 20 = 60, which is the proper result.
General Multiplication Trick for Numbers with a Difference of 2
A useful trick applies to numbers that have a difference of 2, such as: 5,7 / 6,8 / 4,2. The product of such numbers can be calculated as the square of the number in between, minus one. Thus, for 5 × 7 = 35, equivalent to 6^2 (36) minus 1. Similarly, for 4 × 2 = 8, based on 3^2 (9) minus 1.
Using Fingers for Multiplication Results
The finger method is a valuable technique for memorizing the multiplication tables, applicable for tables 6-9 as follows:
- Extend both hands in front of you with palms facing you, ensuring the fingers are in alignment.
- Assign a number to each finger; the pinky represents 6, the ring finger represents 7, the middle finger represents 8, the index finger represents 9, and the thumb represents 10, mirroring this on the other hand.
- For finding 6 × 8, connect the finger representing 6 on the right hand with the finger for 8 on the left hand.
- Count the fingers below the connected ones to define the tens place or left digit (in this case, 4).
- Count the fingers above the connected ones on both hands separately and multiply the two results to form the units place or right digit of the answer (e.g., with 4 on the right hand and 2 on the left, the result is 8).
- This organizes the answer as 48.
In special cases, if the upper fingers’ product results in two digits and the connected fingers don’t correctly indicate the tens place, the computation requires adjustment. For example, when multiplying 7 × 6, the total in connected fingers may be 3, which isn’t accurate since the tens place should be 4. In this instance, use the units digit from multiplying both hand’s fingers in the answer’s unit place (2), adjusting the tens digit by adding 1 to the sum of fingers connected for the correct result of 42 for 7 × 6.
Additional Strategies for Remembering the Multiplication Table
Other effective techniques for memorizing the multiplication table include:
- Listening to multiplication songs available online for easy memorization.
- Downloading apps or watching videos designed to assist in learning the multiplication table on your phone.
- Collaborating with a friend for practice, spending 5-10 minutes, twice daily. Start with ordered questions like 2 × 1, then 2 × 2, continuing sequentially to reinforce learning.
- Once comfortable, shift to random questions, such as 2 × 3 or 4 × 5, to enhance retention.
- To optimize memorization, rephrase questions creatively. Instead of asking for the result of 2 × 3, ask what number, when multiplied by 2, yields 6.
- Write down the multiplication table in a large grid consisting of ten rows and ten columns, placing it in a visible area.
- Understand that multiplication is commutative; thus, memorizing half of the table is sufficient since 7 × 8 = 8 × 7 and 5 × 6 = 6 × 5.
Video: The Easiest Way to Memorize the Multiplication Table
Watch the video to learn the most effective method for memorizing the multiplication table: