2015 Year in Review – Second Quarter

Starting today aside from the monthly reviews, we will also be having reviews at the end of every quarter. This is to go back to all the posts for the last three months.

First, learn the 1089 Magic trick and learn how it works.

Secondly, learn how to square 2 digit numbers mentally from 1 to 100.

Next, amaze your friends with the sum prediction trick and teach the close ones how it works.  Continue reading

Month in Review – June 2015

Starting last month, at the end of the month, or the first week of the month, I will be reviewing the posts for the whole month. In this post, we review what we have learned so far last month, June 2015.

June 2015 in Review – Summary of Posts

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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