Mental math refers to the ability to solve mathematical problems in one's head without the use of calculators, computers, pen, or paper. It involves the use of various techniques and strategies, such as breaking down complex problems into simpler ones, to perform calculations.
Mental math is often used in everyday life for tasks such as calculating change, estimating costs, and determining distances or time. It helps in improving numerical fluency, problem-solving skills, and overall cognitive abilities.
Example 1 :
40 + 30
Solution :
Both the two digit numbers have zero at one's place. So, add the digits at ten's place and take one zero along with the result.
4 + 3 = 7
Therefore,
40 + 30 = 70
Example 2 :
80 + 50
Solution :
8 + 5 = 13
Therefore,
80 + 50 = 130
Example 3 :
46 + 30
Solution :
= 46 + 30
= 40 + 6 + 30
= (40 + 30) + 6
= 70 + 6
= 76
Example 4 :
52 + 34
Solution :
= 52 + 34
= 50 + 2 + 30 + 4
= (50 + 30) + (2 + 4)
= 80 + 6
= 86
Example 5 :
126 + 78
Solution :
= 126 + 78
= 120 + 6 + 70 + 8
= (120 + 70) + (6 + 8)
= 190 + 14
= 190 + 10 + 4
= 200 + 4
= 204
Example 6 :
208 + 126
Solution :
= 208 + 126
= 200 + 8 + 120 + 6
= (200 + 120) + (8 + 6)
= 320 + 14
= 334
Example 7 :
85 + 49
Solution :
= 85 + 49
Here, 85 is close to the round figure 100. To make 85 as 100, we need to add 15 to 85. Take 15 from 49 and add it to 85 and do the rest of the process.
= 85 + 15 + 24
= 100 + 24
= 124
Example 8 :
291 + 76
Solution :
= 291 + 25
= 291 + 9 + 16
= 300 + 16
= 316
Example 9 :
70 - 30
Solution :
Both the two digit numbers have zero at one's place. So, Subtract the digits at ten's place and take one zero along with the result.
7 - 3 = 4
Therefore,
70 - 30 = 40
Example 10 :
80 - 50
Solution :
8 - 5 = 3
Therefore,
80 - 50 = 30
Example 11 :
56 - 20
Solution :
= 56 - 20
= 50 + 6 - 20
= (50 - 20) + 6
= 30 - 6
= 24
Example 12 :
84 - 55
Solution :
= 84 - 55
= 84 - (50 + 5)
= 84 - 50 - 5
= 34 - 5
= 29
Example 13 :
126 - 78
Solution :
= 126 - 78
= 126 - (70 + 8)
= 126 - 70 - 8
= 56 - 8
= 48
Example 14 :
208 - 126
Solution :
= 208 - 126
= 208 - (100 + 26)
= 208 - 100 - 26
= 108 - 26
= 108 - (20 + 6)
= 108 - 20 - 6
= 88 - 6
= 82
Example 15 :
17 x 5
Solution :
= 17 x 5
= (10 + 7) x 5
It is easier to multiply 10 by any number. Multiplying 10 by 5 results 50. Multiplying 7 by 5 results 35. Adding 50 and 35, we get 75.
= 50 + 35
= 85
Example 16 :
25 x 8
Solution :
= 25 x 8
4 times 25 is equal to 100. So, we can do the above multiplication as shown below.
= 25 x 4 x 2
= 100 x 2
= 200
Example 17 :
25 x 11
Solution :
= 25 x 11
10 times 25 is equal to 250. To get the answer for 11 times 25, take 10 times 25 and add one 25 to the result.
= 250 + 25
= 275
Example 18 :
49 x 7
Solution :
= 49 x 7
Consider the rounded figure near to 49, that is 50. So, we can write 49 as (50 - 1) and multiply it by 7 as shown below.
= (50 - 1) x 7
To multiply 50 by 7, multiply 5 by 7 and take zero along with the result. 5 times 7 is 35. Then, 50 times 7 is 350.
= 350 - 7
= 343
Example 19 :
62 x 4
Solution :
= 62 x 4
= (60 + 2) x 4
= 240 + 8
= 248
Example 20 :
99 x 9
Solution :
= 99 x 9
= (100 - 1) x 9
= 900 - 9
= 891
Example 21 :
125 x 4
Solution :
= 125 x 4
Consider the rounded figure near to 125, that is 100. So, we can write 125 as (100 + 25) and multiply it by 4 as shown below.
= (100 + 25) x 4
= 400 + 100
= 500
Example 22 :
102 x 8
Solution :
= 102 x 8
= (100 + 2) x 8
= 800 x 16
= 816
Example 23 :
250 x 8
Solution :
= 250 x 8
= 250 x 4 x 2
To multiply 250 by 4, multiply 25 by 4 and take one zero along with the result. 25 times 4 is 100. Then, 250 times 4 is 1000.
= 1000 x 2
= 2000
Example 24 :
298 x 7
Solution :
= 298 x 7
= (300 - 2) x 7
To multiply 300 by 7, multiply 3 by 7 and take two zeros along with the result. 3 times 7 is 21. Then, 300 times 7 is 2100.
= 2100 - 14
= 2086
Multiplying a Two Digit Number by Another Two digit Number
Beware !
The method explained in the examples below will work only when you have 1 at the ten's place of both the two digit numbers (Times Table).
Example 25 :
13 x 17
Solution :
= 13 x 17
Step 1 :
Choose one of the two numbers, larger one is preferred, that is 17. Add the digit in one's place in the other number.
= 17 + 3
= 20
Step 2 :
Multiply 20 by 10. And also, multiply the digits in one's place of both the numbers.
20 x 10 = 200 |
3 x 7 = 21 |
Step 3 :
Add the results of the above two multiplications.
= 200 + 21
= 221
Therefore,
13 x 17 = 221
Example 26 :
14 x 16
Solution :
Step 1 :
= 16 + 4
= 20
Step 2 :
20 x 10 = 200 |
4 x 6 = 224 |
Step 3 :
= 200 + 224
= 224
Therefore,
14 x 16 = 224
Example 27 :
17 x 15
Solution :
Step 1 :
= 17 + 5
= 22
Step 2 :
22 x 10 = 220 |
7 x 5 = 35 |
Step 3 :
= 220 + 35
= 255
Therefore,
17 x 15 = 255
Example 28 :
11 x 12
Solution :
Step 1 :
= 12 + 1
= 13
Step 2 :
13 x 10 = 130 |
1 x 2 = 2 |
Step 3 :
= 130 + 2
= 132
Therefore,
11 x 12 = 132
Example 29 :
18 x 19
Solution :
Step 1 :
= 19 + 8
= 27
Step 2 :
27 x 10 = 270 |
8 x 9 = 72 |
Step 3 :
= 272 + 72
= 342
Therefore,
18 x 19 = 342
Trick 1 :
To calculate 10% of a number, move the decimal point one digit to the left.
Trick 2 :
To calculate 1% of a number, move the decimal point two digits to the left.
Example 30 :
10% of 48.5
Solution :
To calculate 10% of 48.5, move the decimal point in 48.5 one digit to the left.
10% of 48.5 = 4.85
Example 31 :
10% of 670
Solution :
In 670, there is no decimal point. So, we have to assume there is decimal point at the and.
= 10% of 670.
To calculate 10% of 670., move the decimal point in 670. one digit to the left
= 67.0
= 67
Example 32 :
30% of 600
Solution :
= 30% of 600
= 3 x 10% of 600
= 3 x 60.0
= 3 x 60
= 180
Example 33 :
45% of 800
Solution :
= 40% of 800 + 5% of 800
= 40% of 800 = 4 x 10% of 800 = 4 x 80 = 320 |
= 5% of 800 = ½ x 10% of 800 = ½ x 80 = 40 |
Add the above two results.
= 320 + 40
= 360
Therefore,
45% of 800 = 360
Example 34 :
5% of 250
Solution :
= 5% of 250
= ½ x 10% of 250
= ½ x 25
= 12.5
Example 35 :
4% of 300
Solution :
= 4% of 300
= 4 x 1% of 300.
To calculate 1% of 300., move the decimal point in 300. two digits to the left
= 4 x 3.00
= 4 x 3
= 12
Example 36 :
8% of 750
Solution :
= 8% of 750
= 8 x 1% of 750.
To calculate 1% of 750., move the decimal point in 750. two digits to the left
= 8 x 7.50
= 8 x 7.5
We know that 2 times 7.5 is 15 and 4 times 7.5 is 30.
= 2 x 4 x 7.5
= 2 x 30
= 60
Example 37 :
7% of 80
Solution :
= 7% of 80
= 7 x 1% of 80.
To calculate 1% of 80., move the decimal point in 80. two digits to the left
= 7 x 0.80
= 7 x 0.8
To multiply 7 and 0.8, multiply 7 and 8, that is 56. Since there is one digit after the decimal in 0.8, take decimal point in 56 such that there is one digit to the right of the decimal point.
= 5.6
Example 38 :
Calculate simple ineterest on $800 for 3 years at the rate of 5% per year.
Solution :
Simple interest for one year :
= 5% of 800
= ½ x 10% x 800
= ½ x 80.0
= ½ x 80
= $40
Since we have to calculate simple interest for 3 years, multiply the above result by 3.
= 3 x $40
= $120
Example 39 :
Calculate simple ineterest on $400 for 2 years at the rate of 4.5% per year.
Solution :
Simple interest for one year :
= 4.5% of 400
= 4.5 x 1% x 400
= 4.5 x 4.00
= 4.5 x 4
= (4 + 0.5) x 4
= 16 + 2
= $18
Since we have to calculate simple interest for 2 years, multiply the above result by 2.
= 2 x $18
= $36
Example 40 :
Calculate simple ineterest on $1000 for 9 months at the rate of 10% per year.
Solution :
Simple interest for one year :
= 10% of 1000
= 100.0
= $100
Simple interest for 3 months :
= $100 ÷ 4
= $25
Simple interest for 9 months :
= 3x $25
= $75
Example 41 :
In simple interest, a sum of money doubles itself in 10 years. In how many years will it triple itself?
Solution :
If I invest $100, it will become $200 in 10 years.
So, interest earned in the first ten years :
= 200 - 100
= $100
In simple interest, interest earned for the same principal and same time period will always be same. Since $100 is the interest earned in the first ten years, the interest earned earned in the next ten years also (from year 11 to year 20) will be $100.
Principal = $100
Interest (year 1 to 10) = $100
Interest (year 11 to 20) = $100
Add the above amounts,
= 100 + 100 + 100
= $300
Therefore, the sum of money will triple itself in 20 years.
Compound Interest
Example 42 :
Calculate compound ineterest on $1000 for 2 years at the rate of 10% per year, if interest is compounded annually.
Solution :
Interest for the first year :
= 10% of 1000
= 100.0
=$100
Principal for the second year :
= 1000 + 100
= $1100
Interest for the second year :
= 10% of 1100
= 110.0
=$110
Total interest earned in 2 years :
= 100 + 110
= $220
Example 43 :
Calculate compound ineterest on $1000 for 1 year at the rate of 10% per year, if interest is compounded semi- annually.
Solution :
Interest for the first six months :
= ½ x (interest for one year)
= ½ x 10% of 1000
= ½ x 100
= $50
Principal for the next six months :
= 1000 + 50
= $1050
Interest for the next six months :
= ½ x 10% of 1050
= ½ x 105
= $52.5
Total interest earned in 2 years :
= 50 + 52.5
= $102.5
Example 44 :
In compound interest, a sum of money doubles itself in 10 years. In how many years will it become 4 times of itself?
Solution :
If I invest $100, it will become $200 in 10 years.
For the next ten years (from year 11 to year 20), the principal is $200 and it will double itself at the end of year 20. That is, it will become $400 at the end of 20 years.
Therefore, the sum of money will become 4 times of itself in 20 years.
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