August 9, 2024

# Simplification Questions for Navodaya Exam

Are you preparing for the Navodaya Exam and looking for practice  “Simplification Questions for Navodaya Exam” to improve your simplification skills? Look no further! This post is designed to provide you with a set of comprehensive simplification questions specifically  for the Navodaya Exam.

Simplification is a crucial topic in any competitive exam, including the Navodaya Exam. It tests your ability to solve complex mathematical expressions by simplifying them into their most concise and manageable forms. Mastering simplification not only enhances your problem-solving skills but also saves valuable time during the exam.

In this post, you’ll find a diverse range of simplification Questions for Navodaya Exam that cover various concepts, including arithmetic operations,  fractions, percentages, decimals, and more.  Each question is accompanied by detailed explanations and step-by-step solutions, making it easier for you to understand the underlying concepts.

## Simplification Questions for Navodaya Exam ( Navodaya Practice Questions )

In order to simplify an arithmetic expression we must follow the rule of  VBODMAS.
VBODMAS Rule
The operation have to be carried out in the order in which they appear in the word ‘VBODMAS’, where
V → Vinculum (a horizontal line drawn over a group of term or bar ‘−’)
B → Bracket [], {},()
O → Of (×)   (‘Of ’ means multiplication but is operated even before division)
D → Division ( ) ÷
M → Multiplication (×)
A → Addition ( ) +
S → Subtraction ( ) −

Note : If there is no sign between a number and bracket, it indicates multiplication.

Question :1 Simplify 10+4÷2-3×2+4+2×2-4
Solution:
10+4÷2-3×2+4+2×2-4 = 10+2-3×2+4+2×2-4             (solving division)
= 10+2-6+4+4-4                                      (solving multiplication)
= 10                                                               (solving subtraction)

2)  $\frac{3}{8}\div&space;(\frac{5}{3}-\frac{1}{6})+\frac{5}{8}$

Solution : $\frac{3}{8}\div&space;(\frac{5}{3}-\frac{1}{6})+\frac{5}{8}$

= $\frac{3}{8}\div&space;(\frac{10-1}{6})+\frac{5}{8}$

$=\frac{3}{8}\div&space;(\frac{9}{6})+\frac{5}{8}$

$=\frac{3}{8}\div&space;(\frac{3}{2})+\frac{5}{8}$

$=\frac{3}{8}\times&space;\frac{2}{3}+\frac{5}{8}$

=$\frac{1}{4}+\frac{5}{8}$

$=\frac{7}{8}$ .

3) What is the result of simplification of the expression 25÷0.5×0.1-0.05 ?
Solution :
25÷0.5×0.1-0.05 =25÷0.5×0.1-0.05
=50×0.1-0.05
=5-0.05
= 4.95

4) The simplification of 10+ 4 ÷ 2 − 3 × 2+ 4 ÷2 × 2− 4    gives (1) 0      (2) 1        (3) 6       (4) 8
Solution:
10+ 4 ÷ 2 − 3 × 2+ 4 ÷2 × 2− 4  = 10+ 2 − 3 × 2+ 2 × 2− 4
= 10+ 2 − 6+ 4− 4
= 10+ 2 − 6+ 4− 4
=16-6-4
=6

5) The simplification of 24+ [ 6- {5 − 2 (4 −  3 )}] gives the result  (1) 22     (2) 23      (3) 24     (4) 27
Solution:  24+ [ 6- {5 − 2 (4 −  3 )}] = 24+ [ 6- {5 − 2 x 1}]     (Solving expression in innermost bracket)
= 24+ [ 6- 3]
= 24+ 3
=27

6) Simplify  $25-[12-\{5+18\div&space;(4-\overline{5-3})\}]$
Solution:
Simplifying bar first
$25-[12-\{5+18\div&space;(4-\overline{5-3})\}]$ =$25-[12-\{5+18\div&space;(4-2)\}]$
=$25-[12-\{5+18\div&space;2\}]$            (simplifying small bracket  )
=25[12{5+9}]                                 (simplifying curly bracket )
=25[1214]
=25+2                       (simplifying square bracket i,e., [ ] )
=27                             (  Evaluating sum)

7) The simplification of 98− [ 65 +{32 −( 12  +5 )}] gives the result   (1) 8      (2) 18     (3) 178      (4) 212
Solution :
98− [ 65 +{32 −( 12  +5 )}] =98− [ 65 +{32 −17}]
= 98− [ 65 +15]
=98-  80
=18

8)Which of the following is equal to $\frac{3}{2}\div&space;\frac{3}{2}\times&space;2+\frac{3}{2}$       1)2      2) 6        3) $\frac{7}{2}$         4)$\frac{2}{7}$

Solution :  $\frac{3}{2}\div&space;\frac{3}{2}\times&space;2+\frac{3}{2}$ = $\frac{3}{2}\times&space;\frac{2}{3}\times&space;2+\frac{3}{2}$

= $2+\frac{3}{2}$

= $\frac{4+3}{2}$

=$\frac{7}{2}$

9) 10 + 4 ÷ 2 – 3 × 2 + 4 + 2 × 2 – 4
Solution :
10 + 4 ÷ 2 – 3 × 2 + 4 + 2 × 2 – 4 = 10 + 2 – 3 × 2 + 4 + 2 × 2 – 4
= 10 + 2 – 6 + 4 + 4 – 4
= 20 – 6  – 4
=10

10) 12 + 3 × 4 – 6 ÷ 2 + 5 × 2 – 7
Solution:
12 + 3 × 4 – 6 ÷ 2 + 5 × 2 – 7 =12 + 3 × 4 – 3 + 5 × 2 – 7
=12 + 12 – 3 + 10 – 7
=34 – 3  – 7
= 24

11)   20×5+30÷6-3+8
Solution: 20×5+30÷6-3+8
= 20×5+5-3+8
=100+5-3+8
=113-3
=110

12)   9-4+18÷6+3-2+1
Solution:
9-4+18÷6+3-2+1= 9-4+3+3-2+1
= 9+3+3+1-4-2
=16-6
= 10

13) 14 + 5 ÷ 5 – 2 × 3 + 9 – 4 ÷ 2
Solution :
14 + 5 ÷ 5 – 2 × 3 + 9 – 4 ÷ 2 = 14 + 1 – 2 × 3 + 9 – 2
= 14 + 1 – 6 + 9 – 2
= 24 -6-2
=16

14) 0.5×0.5÷0.5-0.5+0.5
Solution:
0.5×0.5÷0.5-0.5+0.5 = 0.5×1-0.5+0.5
= 0.5+0.5-0.5
= 1.0-0.5
= 0.5

15)  2+2+2÷2×2+2-2
Solution:
2+2+2÷2×2+2-2 = 2+2+1×2+2-2
= 2+2+2+2-2
= 8-2
= 6

16) 36 – {18 – {14 – (15 – 4 ÷ 2 × 2)}}
Solution : 36 – {18 – {14 – (15 – 4 ÷ 2 × 2)}}
= 36 – {18 – {14 – (15 – 4 ÷ 2 × 2)}}
= 36 – {18 – {14 – (15 – 2 ×2)}}            (by performing division)
= 36 – {18 – {14 – (15 – 4)}}                  (by performing multiplication)
= 36 – {18 – {14 – 11}}                             (by removing braces)
= 36 – {18 – 3}
= 36 – 15
= 21

17)  30- [ 40-{ 56-(25-13-12)}]
Solution:
30- [ 40-{ 56-(25-13-12)}]  =30- [ 40-{ 56-0}]
=30- [ 40- 56]
= 30- (-16 )
=30+16
=46

18) $4(10+15\div&space;5&space;\times&space;4-2&space;\times&space;2)$
Solution:
$4(10+15\div&space;5&space;\times&space;4-2&space;\times&space;2)$=$4(10+3&space;\times&space;4-2&space;\times&space;2)$
= $4(10+12-&space;4)$
= 4(22-4)
=4 x 18
=72

19)   5 x 50 +57 -57 ÷ 57
Solution :
5 x 50 +57 -57 ÷ 57 =  5 x 50 +57 -1
= 250 +57-1
= 307-1
=306

20) 18 ÷ (4 – 2) x 5 – 3
Solution:
18 ÷ (4 – 2) x 5 – 3 =18 ÷ 2 x 5 – 3
=9 x 5 – 3
=45-3
= 42

21) 12-[6÷3+{8÷2(8-6)}]
Solution :
12-[6÷3+{8÷2(8-6)}] =12-[6÷3+{8÷2 x 2}]
=12-[6÷3+{4 x 2}]
=12-[6÷3+ 8]
=12-[2 + 8]
= 12- 10
= 2

22) 34 ÷ 1.7 + 45 × 2
Solution:  0.34 ÷ 1.7 + 45 × 2 = 0.34 ÷ 1.7 + 45 × 2
= 0.2 +45 × 2
= 0.2+ 90
=90.2

23) 2 [2 + 2 {39 -2 (17 + 2)}]
Solution: 2 [2 + 2 {39 -2 (17 + 2)}]
=2 [2 + 2 {39 -2 x 19}]
=2 [2 + 2 {39 – 38}]
=2 [2 + 2 x 1]
= 2 x 4
= 8

24) (3 + 3) x (3 ÷ 3) x (3 x 3)
Solution: (3 + 3) x (3 ÷ 3) x (3×3)
=6 x 1 x 9
=54

25)[90 – 77 ÷ 11 – 9 ]+ ( 18 – 6) ÷ 4
Solution: [90 – 77÷ 11 – 9 ]+ ( 18 – 6) ÷ 4
=[90 – 7 – 9 ]+ 12 ÷ 4
=74+ 12 ÷ 4
= 74+ 3
=77

Simplification questions for navodaya exam pdf

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