Practice maths tricks questions and check your answers with the solutions given. These maths tricks will help a lot for quick mental calculations. Following are few tricks for quick addition, subtraction and multiplication:
Addition of numbers by doubling them: When we have to add two numbers which are close to each other, we double the smaller number and then add the difference between both numbers. Let us take an example, 17 + 19
Now 2 × 17 = 34 and 19 – 17 = 2
∴ 17 + 19 = 34 + 2 = 36.
Also, go through:
Addition with 9: It is very easy to add any number with 9, just add 10 with the given number and take away one. For example, 23 + 9, then 23 + 10 = 33 and 33 – 1 = 32
∴ 23 + 9 = 32
Addition by compensation: If any of the given numbers for addition is nearer to any tens, hundreds or thousands, round it off, then take away that much from the answer. For example, 295 + 187
295 can be rounded off to 300, then 300 + 187 = 487
Now, 295 + 187 = 487 – 5 = 482.
Subtraction with smaller numbers: For example, 57 – 48. First, we have to find 7 – 8, which needs regrouping; instead, exchange the numbers and find 8 – 7 = 1. Now find a number which is added with 1 to get 10; that number is the answer for the ones place. Now, just add 1 to the number in the next place and subtract.
Subtracting a teen number by single-digit number: For example, 16 – 4
Step I: 10 – 4 = 6
Step II: Add 6 and 6 = 12
∴ 16 – 4 = 12.
Maths Tricks Questions with Solutions
Let us solve the given questions quickly with easy maths tricks.
Question 1:
Add the following:
(i) 198 + 2 + 45 + 87
(ii) 207 + 193
(iii) 2067 + 506
(iv) 845 + 67
Solution:
(i) 198 + 2 + 45 + 87
= (198 + 2) + 42 + (3 + 87)
= 200 + 42 + 90 = 332.
(ii) 207 + 193
= 200 + (7 + 193)
= 200 + 200 = 400.
(iii) 2067 + 506
= (2000 + 500) + 60 + (7 + 6)
= 2573
(iv) 845 + 67
= 842 + (3 + 67)
= 842 + 70 = 912.
Question 2:
Add by using the method of adding by doubling:
(i) 13 + 14
(ii) 81 + 82
(iii) 34 + 33
(iv) 12 + 15
Solution:
(i) 13 + 14
= (2 × 13) + 1 = 26 + 1 = 27
(ii) 81 + 82
= (2 × 81) + 1 = 162 + 1 = 163
(iii) 34 + 33
= (2 × 33) + 1
= 66 + 1 = 67
(iv) 12 + 15
= (2 × 12) + 3
= 24 + 3 = 27
Question 3:
Subtract:
(i) 23 from 41
(ii) 34 from 61
(iii) 672 from722
Solution:
(i) 23 from 41
41 – 23
Step I: 3 – 1 = 2 and 2 + 8 = 10
Step II: 4 – (2 + 1) = 1
∴ 41 – 23 = 18.
(ii) 34 from 61
61 – 34
Step I: 4 – 1 = 3 and 3 + 7 = 10
Step II: 6 – (3 + 1) = 2
∴ 61 – 34 = 27.
(iii) 672 from 722
722 – 672
Step I: 2 – 2 = 0
Step II: 7 – 2 = 5 and 5 + 5 = 10
Step III: 7 – ( 6 + 1) = 0
∴ 722 – 672 = 50.
Question 3:
Subtract by rounding to the nearest tens, hundreds or thousands.
(i) 45 – 23
(ii) 302 – 33
(iii) 569 – 190
Solution:
(i) 45 – 23
45 can be made 50 by adding 5, then,
50 – 20 – 3 = 27
∴ 45 – 23 = 27 – 5 = 22.
(ii) 302 – 33
302 can be made 300 by taking away 2
300 – 30 – 3 = 267
∴ 302 – 33 = 267 + 2 = 269.
(iii) 569 – 190
190 can be made to 200 by adding 10
569 – 200 = 369
∴ 569 – 190 = 369 + 10 = 379.
|
Trick for multiplication by 5: (i) If any even number is multiplied by 5, then half the given number and add zero at the end. For example: 64 × 5 64 ÷ 2 = 32 and 64 × 5 = 320 (ii) If any odd number is multiplied by 5, then half one less than the given number and add five at the end. For example: 23 × 5 Then, 22 ÷ 2 = 11 and 23 × 5 = 115. Trick for multiplication by 6: When any even number is multiplied by 6 the ones digit of the product is same as the number. For example, 6 × 2 = 12 6 × 8 = 48 6 × 4 = 24 6 × 6 = 36 Now for tens and hundreds digits, half the given number and add first digit of the number to the halved number. For example 32 × 6 = __2 32 ÷ 2 = 16 16 + 3 = 19 ∴ 32 × 6 = 192. |
Question 4:
Evaluate:
(i) 34 × 5
(ii) 123 × 5
(iii) 76 × 5
(iv) 19 × 5
Solution:
(i) 34 × 5
Step I: 34 ÷ 2 = 17
Step II: 34 × 5 = 170
(ii) 123 × 5
Step I: 122 ÷ 2 = 61
Step II: 123 × 5 = 615
(iii) 76 × 5
Step I: 76 ÷ 2 = 38
Step II: 76 × 5 = 380.
(iv) 19 × 5
Step I: 18 ÷ 2 = 9
Step II: 19 × 5 = 95.
Question 5:
Evaluate:
(i) 24 × 6
(ii) 38 × 6
(iii) 34 × 60
Solution:
(i) 24 × 6
Step I: 24 × 6 = __4
Step II: 24 ÷ 2 = 12 + 2 = 14
∴ 24 × 6 = 144
(ii) 38 × 6
Step I: 38 × 6 = __8
Step II: 38 ÷ 2 = 19 + 3 = 22
∴ 38 × 6 = 228.
(iii) 34 × 60
Step I: 34 × 60 = __40
Step II: 34 ÷ 2 = 17 + 3 = 20
∴ 34 × 60 = 2040.
Also Read:
Question 6:
Evaluate:
(i) 34 × 11
(ii) 26 × 11
(iii) 73 × 11
Solution:
(i) 34 × 11
34 × 11 = 3 (3 + 4) 4 = 374.
(ii) 26 × 11
26 × 11 = 2 (2 + 6) 6 = 286
(iii) 73 × 11
73 × 11 = 7 (7 + 3)3 = 803
As 7 + 3 = 10, 1 is carried over to 7.
|
Trick to find Square Root: First, we have to remember squares upto 10, specially the unit digit of each square number. For example, we have to find the square root of 841 Similarly, we can find square root of a 4 and 5-digit numbers. |
Question 7:
Find the square root of 23104 mentally.
Solution:
By looking at the last ones digit which is 4
Then the one’s digit could be 2 or 8
Now, take 231
152 < 231 < 162
Also, 231 < 15 × 16, therefore we choose 2 instead of 8
∴ √23104 = 152.
Question 8:
Find the square root of 7921 without actual calculation.
Solution:
By looking at the last one’s digit, which is 1
Then the one’s digit could be 1 or 9.
Now, take 79
82 < 79 < 92.
Also, 79 > 8 × 9; therefore we choose 9 instead of 1
∴ √7921 = 89.
Question 9:
Find the square root of 5929 without actual calculation.
Solution:
By looking at the last one’s digit, which is 29
Then the one’s digit could be 3 or 7.
Now, take 59
72 < 59 < 82.
Also, 59 > 7 × 8, therefore, we choose 7 instead of 3
∴ √5929 = 77.
|
Multiplication trick This trick is to calculate the product of any two-digit numbers quickly. Let us understand this with an example, 23 × 18. Step I: Multiply 2 by 1 and 3 by 8; the unit digits will make the first and the last digit. 2 × 1 = 2 and 3 × 8 = 24 ∴ 23 × 18 = 2 __24 Step II: Now multiply 2 by 8 and 3 by 1 and find their sum, this will make the middle digit of the product. 2 × 8 = 16 3 × 1 = 3 16 + 3 = 19 ∴ 23 × 18 = 2 19 + 24 ⇒ 23 × 18 = 2 + 214 ⇒ 23 × 18 = 414 |
Question 10:
Evaluate:
(i) 67 × 18
(ii) 56 × 15
(iii) 32 × 15
Solution:
(i) 67 × 18
For first and last part of the product:
6 × 1 = 6
7 × 8 = 56
5 is carried to the middle part
For the middle part:
6 × 8 = 48
7 × 1 = 7
48 + 7 = 55
55 + 5 = 60
6 is carried to the last part.
Now, 67 × 18 = 6 + 606 = 1206.
(ii) 56 × 15
For first and last part of the product:
5 × 1 = 5
6 × 5 = 30
3 is carried to the middle part
For the middle part:
5 × 5 = 25
6 × 1 = 6
25 + 6 = 31
31 + 3 = 34
3 is carried to the last part.
Now, 56 × 15 = 5 + 340 = 840.
(iii) 32 × 15
For first and last part of the product:
3 × 1 = 3
2 × 5 = 10
1 is carried to the middle part
For the middle part:
3 × 5 = 15
2 × 1 = 2
15 + 2 = 17
17 + 1 = 18
1 is carried to the last part.
Now, 32 × 15 = 3 + 180 = 480.
Related Articles |
|
Practice Questions on Maths Tricks
1. Evaluate:
(i) 23 × 67
(ii) 39 × 16
(iii) 97 × 18
2. Find the square root of the following:
(i) 10609
(ii) 2304
(iii) 10404
3. Evaluate:
(i) 56 × 11
(ii) 89 × 110
(iii) 56 × 6
Keep visiting BYJU’S to get more such study materials explained in an easy and concise way. Also, register now and get access to 1000+ hours of video lessons on different topics.
