Mental Division: 2 Digit by 1 Digit Numbers

We have learned how to multiply 2-digit by 1-digit numbers mentally and in this post, we are going to discuss its corresponding method in division. Division seems to be the most difficult operation in mental calculation, but with the right strategy, it can be done. In the discussion, we will start with easy examples and then proceed to more complicated examples later.

Example 1: 52 ÷ 4


We can separate 52 into 40 and 12. Then, we can divide 40 by 4 which is equal to 10. Next, we can divide 12 by 4 which is equal to 3. So, we have 10 + 3 = 13.

40/4 = 10

12/4 = 3

So, the answer is 10 + 3 = 13.  Continue reading

Cool Multiplication Trick Part 1

We have learned quite a number of multiplication tricks now and in this post, I am going to teach you another multiplication trick which you can use to calculate faster and share with your friends. This multiplication trick is quite similar to squaring a number ending in 5.

The conditions to perform this trick are

(a) the sum of the ones digit is 10.

(b) the other digits (tens, hundreds, and so on) are the same.

Example 1: 23 × 27

This example fits the two conditions above. For (a), 3 + 7 = 10. Then, for (b) the tens digits are the same.

The Math Trick

Step 1:  Add 1 to one of the tens digit, then multiply to the other tens digits.  Continue reading

Why the Addition of Dissimilar Fractions Trick Works

In the pervious post, we have learned a math trick on addition of two dissimilar fraction. This is done by “cross multiplying” the numerators and denominators of the fractions as shown below (read the previous post for more details). In this post, we discuss why this trick works.

Remember: It’s cool to know the math trick, but it’s even cooler, or should I say awesome, to know why the math trick works.

add fractions

Now, why does this trick works? Will it work every time?  Continue reading

How to Add Two Fractions Faster

Fractions whose denominators are the same are called similar fractions, otherwise they are called dissimilar fractions. The fractions 1/9 and 7/9 are similar fractions, while 3/4 and 2/3.

Adding similar fractions is easy. Just copy add the numerator and then copy the denominator. For example,

1/9 + 7/9 = 8/9.

Adding dissimilar fractions is a bit more complicated. You have to get the Least Common Multiple (LCM) of the denominators. For example, if we want to add 3/4 and 2/3, we get the LCM of 4 and 3 which is equal to 12. You then change the given to equivalent fractions. The addition becomes

9/12 + 8/12 = 17/12.

Shortcut: How to Add Two Fractions Faster

We can use a shortcut to add to two add fractions.  We will only discuss dissimilar fractions because similar fractions are too easy to add. Below are the steps for the shortcut 3/4 and 2/3 Continue reading

Mental Math: How to Subtract Numbers Faster

In the previous post, we have learned a faster way to add numbers near multiples of 10. In this post, we are going to learn to subtract numbers faster, but first let’s review some basic terms.

In the subtraction

8 – 6 = 2

8 is the minuend, 6 is the subtrahend and 2 is the difference.

In subtracting numbers, numbers may be added to the minuend and subtrahend in order to simplify calculations. The strategy is to change the subtrahend to multiples of ten, hundred, thousands, etc. Doing this will speed up calculation and with enough practice, may be done mentally. Here are some examples.

Example 1

1.) What is 55 – 18?

In this case, 18 is near 20, so we can add 2. If we add 2 to 20, we should also add 2 to 55. So, the expression becomes

(55 + 2) – (18 + 2).

Simplifying, we have 57 – 20 = 37. And really, 55 – 18 = 37.  Continue reading