Mental math concepts for everyday math- Part 1

Turn your brain into calculator with the mental math concepts discussed in this blog series. Mental math stimulates both sides of brain and is strongly associated with better memory skills. It helps to reduce mistakes in problem solving and improves your self-confidence. It also stimulates your interest in math and ability to concentrate.

The first step is to learn the concepts and then the second and most important step is to develop speed by doing it again and again.

Let’s start..

1. Dividing a number by 5

• To divide any numbery by 5, we can simply double it and divide by 10

Suppose, we have to divide 630 by 5. Our answer is 5 times bigger than 630 and doubling it would make it 10 times bigger.

• Step 1: Double 630 -> 1260
• Step 2: Divide by 10 -> 126
• And, that’s our answer
• Practice this concept for these numbers: 235 by 5, 1140 by 5

2. Multiplying a number by 5

• Same way, to multiple any number by 5, we can multiple it by 10 and halve it (divide by 2).
• If it is even number, you can first halve it and then multiple by 10 for faster calculation.
• Use case: To find 5% of something, say, to find 5% of 120,
• Step 1: find 10% of 120, which is 12
• Step 2: halve it -> answer is 6. 5% of 120 is 6.

3. Doubling and halving in multiplication

• Say you have to multiple 16 and 35, it is much easier to halve 16 (to 8) and double 35 (to 70) and then multiple 8 and 70 which you can do in your head.
• This method of doubling and halving is useful when one of the factors end in 5 or an odd multiple of 50 and the other number is even.
• Some practice problems:
• 260 * 15 = 130 * 30 = 390
• 56 * 25 = 28 * 50 = 14 * 100 = 1400
• 24 * 75 = 12 * 150 = 6 * 300 = 1800

4. Squaring shortcuts

• Any number ending 5 is half-way between two multiples of 10. 45 is half-way between 40 and 50 and thus its square value would be between 1600 and 2500 (assuming, you can find square of multiples of 10s easily).
• Next, you need to know all squares of 5 ends in 25
• 4 * 4 =16 and 5 * 5 =25 and our remaining number (last two digits are 25!) is between 16 and 25
• As the lower limit is (4 * 4 ) and upper limit is ( 5 * 5), we can find the half-way by 4 * 5 which is 20
• Thus, 45 * 45 = 2025

To summarize the last concept,

To find square of any number ending in 5,

1. Remove the 5, leaving the remaining digits: e.g. 75 -> 7
2. Add one to that remaining digit, 7+1=8
3. Find the product of these 2 numbers, 7*8=56
4. Put this in-front of 25, thus 75² is 5625

When we know the squares of multiples of 10 and 5, it is easy to approximately estimate square of any number in-between these.

Conclusion:

I have started this series with 4 easy but very useful and immediately applicable mental math concepts in this blog. Hope you find this helpful. Happy Mathing!