Multiplication Algorithm Using Squares with Diagonals


Aside from the standard multiplication algorithm (algorithm really means steps or methods) that we already know, there is another method to do multiplication. That is, to place the numbers in squares. This method can be used for multiplying 2-digit numbers. We will call this method the Square Diagonal Multiplication Algorithm

Steps in Multiplication Algorithm

1. Create a 2 by 2 square and place the numbers on top and on the right side. Each digit should be assigned to one row and one column. The example is shown below for 63 × 17.

multiplication algorithm 0

2. In each square, draw a diagonal slanting to the right.  Continue reading

The Whole Number Mixed Fraction Multiplication Secret

In the previous post, we have learned a strategy on multiplying whole numbers by mixed fractions. We have learned that instead of converting the mixed fraction part to improper fractions, we split the numbers and the fraction and then multiplied them separately.

One example for this is 8 ¾ × 2. Instead of converting 8 ¾ to the improper fraction 35/4, we then split it to 8 and ¾ and then multiply each by 2. Therefore, 8 × 2 = 16 and ¾ × 2 = 3/2 which means equals to 17 ½.

Now, why does this math trick work?

First we know that 8 ¾ really means 8 and ¾ which is equal to 8 + ¾. Now, if we multiply 8 + ¾ by 2, we have

2(8 + ¾) = 2(8) + 2(¾) = 16 + 6/4 = 16 + 3/2.

Are the expressions and equations familiar?  Continue reading

A Tip on Multiplying Mixed Fractions by Whole Numbers

One of the common mistakes in multiplying mixed fractions by whole numbers is converting the mixed fraction into improper fractions immediately. What is more difficult is that if the teacher requires the answer to be in mixed fraction. This means that you have to convert it back to mixed fraction. Below is a common scenario of this mistake.

Question:  Multiply  8 ¼ × 3 the and show your answer in mixed form.

Common Steps

Step 1: Convert the mixed fraction to improper fraction.

\displaystyle \frac {4 \times 8 + 1}{4} = \frac{33}{4}

Step 2: Multiply the impproper fraction to the whole number.

\displaystyle \frac {33}{4} \times 3 = \frac{99}{4}

Step 3: Convert the product back to mixed fraction.

By manual division, the answer is 24 ¾ .   Continue reading

Why The Sum Prediction Math Trick Works

In the previous post, we have learned the sum prediction math trick, a cool math trick that let’s you predict the sum of five numbers. In this post, we are going to learn why this math trick works. Needless to say, you need to read the previous post in order to understand the explanation below.

The steps in the previous post of this trick requires a friend to write a 3-digit number. The number 2 is then subtracted from this number. The number 2 is then appended at the first digit of the number. For example, if the number written is 893, we subtract 2, to get 891 and then append 2 to get 2891.  Continue reading

Amaze Your Friends with The Sum Prediction Math Trick

If you want to impress your friends by reading their mind in advance, I bet that you want to learn this trick. This allows you to predict the sum in advance of the 5 numbers that you and your friend will write on a piece of paper. Note that the time your friend wrote the first number, you will already know the sum.

Below are the steps of the sum prediction math trick.

Step 1

Ask your friend to write a 3-digit number. For example, he wrote, 428.

During this step, even if you haven’t written the additional four numbers yet, you will already know the answer. The answer is 2426.

How to get 2426? Subtract 2 from the first 428 (becomes 426) and then place 2 as the first digit. Note that the first of the sum or total will always be 2!  Continue reading