1. Why Calculation Shortcuts Matter
Competitive-exam simplification is not only about getting the correct answer; it is also about reaching that answer quickly and safely. Many apparently long calculations can be reduced to only a few steps by recognising factors, convenient bases, identities and cancellation opportunities.
Key Principle:
Before starting a long multiplication or division, ask:
• Can anything be cancelled?
• Is there a common factor?
• Are the numbers close to 10, 100 or 1000?
• Can a standard identity simplify the calculation?
• Can the terms be rearranged into easier pairs?
Exam Tip:
A shortcut is useful only when it preserves the exact mathematical value. Never change the order of operations merely to make the calculation look easier.
2. Cancellation Means Cancelling Factors, Not Terms
Cancellation is one of the fastest tools in simplification, but it works only between common factors in multiplication or division.
Example:
Simplify:
18/35 × 14/27
Cancel:
18/27 = 2/3
14/35 = 2/5
Therefore:
2/3 × 2/5 = 4/15.
Common Mistake:
You cannot cancel across addition or subtraction.
For example:
(12+6)/6 ≠ 12+1.
Correctly:
(12+6)/6 = 18/6 = 3.
3. Extracting a Common Factor
If several terms contain a common factor, extracting it can convert a long calculation into a very short one.
Key Rule:
ab + ac = a(b+c)
ab − ac = a(b−c)
Example:
37×48 + 37×52
Take 37 common:
= 37(48+52)
= 37×100
= 3700.
Shortcut:
Whenever the same number appears as a multiplier in two or more terms, check whether taking it common creates 10, 100, 1000 or another convenient value.
4. Difference of Squares
The identity for the difference of two squares is extremely useful in numerical simplification.
Important Identity:
a2 − b2 = (a−b)(a+b)
Example:
Evaluate:
582 − 422
= (58−42)(58+42)
= 16×100
= 1600.
Exam Shortcut:
If two squares are being subtracted, do not calculate both squares separately. Check the difference-of-squares identity first.
5. Product of Numbers Equally Spaced from a Base
If two numbers are equally above and below the same convenient number, their product can be found using the difference-of-squares identity.
Key Pattern:
(a−b)(a+b) = a2−b2
Example:
103×97
= (100+3)(100−3)
= 1002−32
= 10000−9
= 9991.
Example:
48×52
= (50−2)(50+2)
= 502−22
= 2500−4
= 2496.
Shortcut:
Look for pairs such as 98×102, 47×53, 995×1005 and 198×202. Their average often gives the convenient base immediately.
6. Multiplication by 5, 25 and 125
These numbers are closely connected with powers of 10 and can often be handled without ordinary multiplication.
Useful Conversions:
×5 = ×10 ÷2
×25 = ×100 ÷4
×125 = ×1000 ÷8
Example:
48×25
= 48×100÷4
= 4800÷4
= 1200.
Example:
64×125
= 64×1000÷8
= 8000.
Exam Shortcut:
For ×25, divide by 4 and append two zeros when convenient.
For ×125, divide by 8 and multiply by 1000.
7. Division by 5, 25 and 125
The reverse conversions are equally useful.
Useful Conversions:
÷5 = ×2 ÷10
÷25 = ×4 ÷100
÷125 = ×8 ÷1000
Example:
875÷25
= 875×4÷100
= 3500÷100
= 35.
Example:
3750÷125
= 3750×8÷1000
= 30000÷1000
= 30.
8. Multiplication by 9, 99 and 999
Numbers consisting mainly of 9s can be rewritten as a power of 10 minus 1.
Key Patterns:
9 = 10−1
99 = 100−1
999 = 1000−1
Example:
47×99
=47(100−1)
=4700−47
=4653.
Example:
83×999
=83(1000−1)
=83000−83
=82917.
Shortcut:
For multiplication by 99, multiply by 100 and subtract the original number. For multiplication by 999, multiply by 1000 and subtract the original number.
9. Multiplication by 11
For a two-digit number, multiplication by 11 can often be performed mentally.
Example:
43×11
Write the outer digits 4 and 3 and place their sum between them:
4 (4+3) 3
= 473.
Example with Carry:
78×11
7+8=15.
Write 8 at the end, 5 in the middle and carry 1 to 7:
= 858.
Exam Tip:
The mental shortcut is especially convenient for two-digit numbers. For larger numbers, use place-wise addition carefully rather than blindly inserting digit sums.
10. Squaring Numbers Ending in 5
Any integer ending in 5 can be squared very quickly.
Shortcut:
For a number ending in 5:
Take the part before 5, say n.
Multiply n by n+1.
Append 25.
Example:
752
7×8 = 56
Append 25
= 5625.
Example:
1152
11×12 = 132
Append 25
= 13225.
Why It Works:
(10n+5)2 = 100n(n+1)+25.
11. Squares Near a Convenient Base
Squares of numbers close to 10, 50, 100, 1000 or another convenient base can often be obtained by expansion.
Useful Identity:
(a+b)2 = a2+2ab+b2
(a−b)2 = a2−2ab+b2
Example:
982
=(100−2)2
=10000−400+4
=9604.
Example:
1032
=(100+3)2
=10000+600+9
=10609.
Scope Note:
The identities are used here only as calculation shortcuts. Their detailed algebraic treatment belongs to Chapter 22 : Algebra.
12. Splitting a Number for Easy Multiplication
A difficult multiplier can often be split into convenient parts using the distributive property.
Example:
48×37
=48×(40−3)
=1920−144
=1776.
Example:
124×16
=124×(8×2)
=992×2
=1984.
Exam Tip:
Choose a split that creates easy multiples such as 10, 20, 25, 50, 100 or powers of 2.
13. Doubling and Halving Technique
In multiplication, one factor can sometimes be doubled while the other is halved without changing the product.
Key Property:
a×b = (2a)×(b/2), whenever the halving is convenient.
Example:
25×48
=50×24
=100×12
=1200.
Shortcut:
This method is especially useful when one factor contains 25, 125, 2.5, 12.5 or another value that can be transformed into a power of 10.
14. Smart Regrouping in Addition and Subtraction
After all higher-priority operations have been completed, numbers may be grouped into convenient pairs.
Example:
398 + 247 + 602 − 147
Group conveniently:
398+602 = 1000
247−147 = 100
Total = 1100.
Shortcut:
Search for complements that make 10, 100, 1000 or another round number.
Exam Trap:
Do not regroup terms across unresolved brackets, multiplication or division. Regrouping is safest only after the relevant BODMAS operations have been completed.
15. Telescoping Products
Some products are deliberately designed so that most factors cancel with neighbouring factors. These are called telescoping products.
Example:
(1−1/2)(1−1/3)(1−1/4)...(1−1/10)
=1/2 × 2/3 × 3/4 × ... × 9/10
Almost everything cancels.
Result = 1/10.
Exam Shortcut:
Before multiplying a long sequence of fractions, rewrite each factor in its simplest fractional form and look for a cancellation chain.
16. Using Factorisation Before Division
If the numerator contains an expression that can be factorised against the denominator, factorise before performing numerical calculation.
Example:
(582−422) ÷ (58+42)
Factorise the numerator:
=(58−42)(58+42)/(58+42)
Cancel (58+42):
=58−42
=16.
Shortcut:
Expressions of the form:
(a2−b2)/(a+b)
directly simplify to a−b, provided a+b ≠ 0.
17. Choosing the Best Shortcut
One expression may sometimes be solvable by more than one shortcut. The best method is the one that reduces both the number of steps and the risk of error.
Decision Guide:
• Same repeated multiplier → take common factor.
• Two squares being subtracted → difference of squares.
• Numbers equally spaced around a base → (a−b)(a+b).
• Multiplier 25 or 125 → convert using 100 or 1000.
• Multiplier 99 or 999 → use 100−1 or 1000−1.
• Number ends in 5 and is squared → ending-in-5 shortcut.
• Long fractional product → look for telescoping cancellation.
• Addition/subtraction terms near round numbers → smart regrouping.
18. Common Exam Traps
Trap 1:
Cancelling terms instead of factors.
Trap 2:
Using a2−b2=(a−b)2. This is false.
Correct: a2−b2=(a−b)(a+b).
Trap 3:
Using a numerical shortcut without checking BODMAS first.
Trap 4:
Forgetting the carry while multiplying a number by 11 mentally.
Trap 5:
Applying the “ending in 5” square shortcut to a number that does not actually end in 5.
Trap 6:
Multiplying every factor of a telescoping product separately instead of looking for cancellation.
19. Quick Revision
Remember:
• Cancel factors, not terms.
• Take common factors before performing long multiplication.
• a²−b²=(a−b)(a+b).
• (a−b)(a+b)=a²−b².
• ×5 = ×10÷2.
• ×25 = ×100÷4.
• ×125 = ×1000÷8.
• ×99 = ×100−original number.
• ×999 = ×1000−original number.
• For a number ending in 5, multiply the preceding part by its successor and append 25.
• Use doubling and halving when it creates easier numbers.
• Look for complements such as 100 or 1000.
• In long fraction products, search for telescoping cancellation before multiplying.
20. Verified Previous-Year Questions
SSC CGL PYQ
Cancellation & Simplification
18 August 2021 · Tier-I · Shift III
Q1. Simplify: 441 ÷ [270 ÷ (3/7) + (17 ÷ 1/3) − (8 1/2 − 5/2)]
A. 29/75
B. 49/75
C. 39/75
D. 19/75
Correct Answer: B. 49/75
17÷1/3 = 51.
8 1/2−5/2
=17/2−5/2
=6.
Also:
270÷3/7
=270×7/3
=630.
Therefore the bracket becomes:
630+51−6 = 675.
Hence:
441/675.
Cancel the common factor 9:
=49/75.
SSC CGL PYQ
Telescoping Cancellation
2010
Q2. Evaluate the product: (2−1/3)(2−3/5)(2−5/7)...(2−997/999)
A. 1001/999
B. 999/1001
C. 1001/3
D. 5/1001
Correct Answer: C. 1001/3
Rewrite the factors:
2−1/3 = 5/3
2−3/5 = 7/5
2−5/7 = 9/7
...
2−997/999 = 1001/999.
Therefore the product becomes:
5/3 × 7/5 × 9/7 × ... × 1001/999.
All intermediate factors cancel, leaving:
1001/3.
CG PSC PYQ
Telescoping Product
2013
Q3. Find the value of: (1+1/2)(1+1/3)(1+1/4)...(1+1/150)
A. 65.5
B. 50.5
C. 105
D. 75.5
Correct Answer: D. 75.5
Rewrite each factor:
1+1/2 = 3/2
1+1/3 = 4/3
1+1/4 = 5/4
...
1+1/150 = 151/150.
Thus:
3/2 × 4/3 × 5/4 × ... × 151/150.
All intermediate factors cancel:
=151/2
=75.5.
21. Practice MCQs
Practice MCQ
Q1. Find the value of 48×25.
A. 1000
B. 1100
C. 1200
D. 1250
Correct Answer: C. 1200
×25 = ×100÷4. Therefore 48×25=4800÷4=1200.
Practice MCQ
Q2. Find the value of 103×97.
A. 9991
B. 9997
C. 10009
D. 10091
Correct Answer: A. 9991
(100+3)(100−3)=10000−9=9991.
Practice MCQ
Q3. Find the value of 752.
A. 5525
B. 5625
C. 5725
D. 5825
Correct Answer: B. 5625
7×8=56 and append 25. Therefore 75²=5625.
Practice MCQ
Q4. Find the value of 47×999.
A. 46953
B. 46963
C. 47047
D. 47953
Correct Answer: A. 46953
47×999=47×(1000−1)=47000−47=46953.
Practice MCQ
Q5. Find the value of 64×125.
A. 6000
B. 7000
C. 8000
D. 9000
Correct Answer: C. 8000
×125 = ×1000÷8. Therefore 64×125=64000÷8=8000.
Practice MCQ
Q6. Find the value of 875÷25.
A. 25
B. 30
C. 35
D. 40
Correct Answer: C. 35
÷25 = ×4÷100. Hence 875×4÷100=3500÷100=35.
Practice MCQ
Q7. Simplify: (582−422)/(58+42)
A. 14
B. 16
C. 18
D. 20
Correct Answer: B. 16
a²−b²=(a−b)(a+b). The denominator cancels with (58+42), leaving 58−42=16.
Practice MCQ
Q8. Find the value of (1−1/2)(1−1/3)(1−1/4)...(1−1/10).
A. 1/5
B. 1/8
C. 1/9
D. 1/10
Correct Answer: D. 1/10
The product becomes 1/2×2/3×3/4×...×9/10. All intermediate factors cancel, leaving 1/10.
Practice MCQ
Q9. Find the value of 198×202.
A. 39904
B. 39996
C. 40004
D. 40096
Correct Answer: B. 39996
(200−2)(200+2)=200²−2²=40000−4=39996.
Practice MCQ
Q10. Find the value of 48×52.
A. 2396
B. 2446
C. 2496
D. 2546
Correct Answer: C. 2496
(50−2)(50+2)=50²−2²=2500−4=2496.
1. Calculation Shortcuts क्यों महत्वपूर्ण हैं?
Competitive-exam simplification में केवल सही answer निकालना ही पर्याप्त नहीं है; सही answer को कम समय में और कम error के साथ निकालना भी महत्वपूर्ण है। Factors, convenient bases, identities तथा cancellation पहचानने पर कई लंबी calculations केवल कुछ steps में solve हो जाती हैं।
मुख्य विचार:
Long calculation शुरू करने से पहले देखें:
• क्या कोई cancellation संभव है?
• क्या common factor लिया जा सकता है?
• क्या numbers 10, 100 या 1000 के आसपास हैं?
• क्या कोई identity calculation को छोटा कर सकती है?
• क्या terms को convenient pairs में regroup किया जा सकता है?
Exam Tip:
Shortcut वही सही है जो expression का exact mathematical value बनाए रखे। Calculation आसान करने के लिए BODMAS का order न बदलें।
2. Cancellation Factors की होती है, Terms की नहीं
Cancellation multiplication या division में मौजूद common factors के बीच होती है। Addition या subtraction से जुड़े individual terms को सीधे cancel नहीं किया जा सकता।
उदाहरण:
18/35 × 14/27
18/27 = 2/3
14/35 = 2/5
अतः:
2/3 × 2/5 = 4/15।
सामान्य गलती:
Addition या subtraction के across cancellation न करें।
(12+6)/6 को 12+1 नहीं लिखा जा सकता।
सही calculation:
18/6 = 3।
3. Common Factor निकालना
मुख्य नियम:
ab+ac = a(b+c)
ab−ac = a(b−c)
उदाहरण:
37×48 + 37×52
37 common लें:
=37(48+52)
=37×100
=3700।
Shortcut:
यदि same multiplier कई terms में दिखाई दे रहा हो, तो देखें कि common लेने के बाद 10, 100 या1000 जैसा convenient value बन रहा है या नहीं।
4. Difference of Squares
महत्वपूर्ण Identity:
a2−b2=(a−b)(a+b)
उदाहरण:
582−422
=(58−42)(58+42)
=16×100
=1600।
Exam Shortcut:
दो squares subtract हो रहे हों तो दोनों squares separately calculate करने से पहले difference-of-squares identity देखें।
5. Common Base से समान दूरी वाले Numbers का Product
मुख्य Pattern:
(a−b)(a+b)=a2−b2
उदाहरण:
103×97
=(100+3)(100−3)
=10000−9
=9991।
उदाहरण:
48×52
=(50−2)(50+2)
=2500−4
=2496।
Shortcut:
98×102, 47×53, 995×1005 तथा198×202 जैसे pairs में दोनों numbers का average convenient base देता है।
6. 5, 25 और 125 से Multiplication
महत्वपूर्ण Conversions:
×5 = ×10 ÷2
×25 = ×100 ÷4
×125 = ×1000 ÷8
उदाहरण:
48×25
=48×100÷4
=4800÷4
=1200।
उदाहरण:
64×125
=64×1000÷8
=8000।
Exam Shortcut:
×25 के लिए ×100÷4 तथा ×125 के लिए ×1000÷8 का प्रयोग अक्सर ordinary multiplication से तेज होता है।
7. 5, 25 और 125 से Division
महत्वपूर्ण Conversions:
÷5 = ×2 ÷10
÷25 = ×4 ÷100
÷125 = ×8 ÷1000
उदाहरण:
875÷25
=875×4÷100
=3500÷100
=35।
उदाहरण:
3750÷125
=3750×8÷1000
=30।
8. 9, 99 और 999 से Multiplication
मुख्य Patterns:
9=10−1
99=100−1
999=1000−1
उदाहरण:
47×99
=47(100−1)
=4700−47
=4653।
उदाहरण:
83×999
=83000−83
=82917।
Shortcut:
×99 → पहले ×100 और फिर original number subtract करें।
×999 → पहले ×1000 और फिर original number subtract करें।
9. 11 से Multiplication
उदाहरण:
43×11
Outer digits 4 और3 रखें तथा बीच में उनका sum रखें:
4 (4+3) 3
=473।
Carry वाला उदाहरण:
78×11
7+8=15।
8 अंतिम digit, 5 middle digit तथा 1 carry होगा:
=858।
Exam Tip:
Two-digit numbers के लिए यह method बहुत useful है। Larger numbers में carry और place value को carefully handle करें।
10. 5 पर समाप्त होने वाली Number का Square
Shortcut:
Number के अंतिम 5 से पहले वाले part को n मानें।
n को n+1 से multiply करें।
Result के अंत में 25 लिखें।
उदाहरण:
752
7×8=56
अंत में25 लगाएँ:
=5625।
उदाहरण:
1152
11×12=132
अंत में25:
=13225।
यह क्यों काम करता है?
(10n+5)2=100n(n+1)+25।
11. Convenient Base के पास Squares
Useful Identities:
(a+b)2=a2+2ab+b2
(a−b)2=a2−2ab+b2
उदाहरण:
982
=(100−2)2
=10000−400+4
=9604।
उदाहरण:
1032
=(100+3)2
=10000+600+9
=10609।
Scope Note:
इन identities का यहाँ उपयोग केवल calculation shortcuts के रूप में किया जा रहा है। इनकी detailed algebraic theory Chapter 22 : Algebra में पढ़ी जाएगी।
12. Easy Multiplication के लिए Number को Split करना
उदाहरण:
48×37
=48×(40−3)
=1920−144
=1776।
उदाहरण:
124×16
=124×8×2
=992×2
=1984।
Exam Tip:
Number को इस प्रकार split करें कि 10, 20, 25, 50, 100 या powers of 2 जैसे आसान multipliers प्राप्त हों।
13. Doubling और Halving Technique
मुख्य Property:
a×b=(2a)×(b/2), जब halving convenient हो।
उदाहरण:
25×48
=50×24
=100×12
=1200।
Shortcut:
25, 125, 2.5 और12.5 जैसे factors के साथ doubling-halving method बहुत useful हो सकती है।
14. Addition और Subtraction में Smart Regrouping
उदाहरण:
398 + 247 + 602 − 147
398+602 = 1000
247−147 = 100
Total = 1100।
Shortcut:
ऐसे pairs खोजें जो 10, 100, 1000 या कोई अन्य round number बनाएँ।
Exam Trap:
Unresolved bracket, multiplication या division के across terms को regroup न करें। पहले BODMAS के relevant operations complete करें।
15. Telescoping Products
कुछ long products इस प्रकार बनाए जाते हैं कि neighbouring fractions के अधिकांश factors एक-दूसरे से cancel हो जाएँ। इन्हें telescoping products कहा जाता है।
उदाहरण:
(1−1/2)(1−1/3)(1−1/4)...(1−1/10)
=1/2 × 2/3 × 3/4 × ... × 9/10
Intermediate factors cancel हो जाते हैं।
Answer = 1/10।
Exam Shortcut:
Long fractional product को multiply करने से पहले प्रत्येक factor को simplest fraction में लिखें और cancellation chain देखें।
16. Division से पहले Factorisation
उदाहरण:
(582−422) ÷ (58+42)
=(58−42)(58+42)/(58+42)
(58+42) cancel होगा।
=58−42
=16।
Shortcut:
(a2−b2)/(a+b)=a−b,
बशर्ते a+b ≠ 0।
17. सही Shortcut कैसे चुनें?
Decision Guide:
• Same multiplier बार-बार हो → common factor लें।
• दो squares subtract हों → difference of squares देखें।
• दो numbers common base से समान दूरी पर हों → (a−b)(a+b) उपयोग करें।
• Multiplier 25 या125 हो → 100 या1000 conversion देखें।
• Multiplier 99 या999 हो → 100−1 या1000−1 लिखें।
• Square होने वाली number 5 पर समाप्त हो → ending-in-5 shortcut।
• Long fractional product हो → telescoping cancellation देखें।
• Addition/subtraction में round-number pairs हों → smart regrouping करें।
18. Common Exam Traps
Trap 1:
Factors के बजाय terms को cancel करना।
Trap 2:
a²−b²=(a−b)² मान लेना। यह गलत है।
सही identity: a²−b²=(a−b)(a+b)।
Trap 3:
BODMAS check किए बिना shortcut लगाना।
Trap 4:
11 से mental multiplication में carry भूल जाना।
Trap 5:
Ending-in-5 square shortcut ऐसी number पर लगा देना जो 5 पर समाप्त नहीं होती।
Trap 6:
Telescoping product में cancellation देखने के बजाय सभी factors separately multiply करना।
19. Quick Revision
एक नज़र में:
• Factors cancel करें, terms नहीं।
• Long multiplication से पहले common factor देखें।
• a²−b²=(a−b)(a+b)।
• (a−b)(a+b)=a²−b²।
• ×5 = ×10÷2।
• ×25 = ×100÷4।
• ×125 = ×1000÷8।
• ×99 = ×100−original number।
• ×999 = ×1000−original number।
• 5 पर समाप्त number का square: preceding part × successor, फिर25 append करें।
• Doubling-halving से convenient values बनाएँ।
• 100 या1000 बनाने वाले complements पहचानें।
• Long fraction products में telescoping cancellation देखें।
20. Verified Previous-Year Questions
SSC CGL PYQ
Cancellation & Simplification
18 अगस्त 2021 · Tier-I · Shift III
प्रश्न 1. सरल कीजिए: 441 ÷ [270 ÷ (3/7) + (17 ÷ 1/3) − (8 1/2 − 5/2)]
A. 29/75
B. 49/75
C. 39/75
D. 19/75
सही उत्तर: B. 49/75
17÷1/3 = 51।
8 1/2−5/2
=17/2−5/2
=6।
270÷3/7
=270×7/3
=630।
Bracket:
630+51−6 = 675।
अतः:
441/675।
9 से cancel करें:
=49/75।
SSC CGL PYQ
Telescoping Cancellation
2010
प्रश्न 2. (2−1/3)(2−3/5)(2−5/7)...(2−997/999) का मान ज्ञात करें।
A. 1001/999
B. 999/1001
C. 1001/3
D. 5/1001
सही उत्तर: C. 1001/3
Factors को rewrite करें:
2−1/3 = 5/3
2−3/5 = 7/5
2−5/7 = 9/7
...
2−997/999 = 1001/999।
Product:
5/3 × 7/5 × 9/7 × ... × 1001/999।
सभी intermediate factors cancel हो जाते हैं।
अतः answer = 1001/3।
CG PSC PYQ
Telescoping Product
2013
प्रश्न 3. (1+1/2)(1+1/3)(1+1/4)...(1+1/150) का मान ज्ञात करें।
A. 65.5
B. 50.5
C. 105
D. 75.5
सही उत्तर: D. 75.5
प्रत्येक factor को rewrite करें:
1+1/2=3/2
1+1/3=4/3
1+1/4=5/4
...
1+1/150=151/150।
अब:
3/2 × 4/3 × 5/4 × ... × 151/150।
Intermediate factors cancel होने के बाद:
=151/2
=75.5।
21. Practice MCQs
Practice MCQ
प्रश्न 1. 48×25 का मान ज्ञात करें।
A. 1000
B. 1100
C. 1200
D. 1250
सही उत्तर: C. 1200
×25=×100÷4। इसलिए 48×25=4800÷4=1200।
Practice MCQ
प्रश्न 2. 103×97 का मान ज्ञात करें।
A. 9991
B. 9997
C. 10009
D. 10091
सही उत्तर: A. 9991
(100+3)(100−3)=10000−9=9991।
Practice MCQ
प्रश्न 3. 752 का मान ज्ञात करें।
A. 5525
B. 5625
C. 5725
D. 5825
सही उत्तर: B. 5625
7×8=56 और अंत में25 लगाएँ। अतः 75²=5625।
Practice MCQ
प्रश्न 4. 47×999 का मान ज्ञात करें।
A. 46953
B. 46963
C. 47047
D. 47953
सही उत्तर: A. 46953
47×999=47×(1000−1)=47000−47=46953।
Practice MCQ
प्रश्न 5. 64×125 का मान ज्ञात करें।
A. 6000
B. 7000
C. 8000
D. 9000
सही उत्तर: C. 8000
×125=×1000÷8। इसलिए 64×125=64000÷8=8000।
Practice MCQ
प्रश्न 6. 875÷25 का मान ज्ञात करें।
A. 25
B. 30
C. 35
D. 40
सही उत्तर: C. 35
÷25=×4÷100। अतः 875×4÷100=3500÷100=35।
Practice MCQ
प्रश्न 7. सरल कीजिए: (582−422)/(58+42)
A. 14
B. 16
C. 18
D. 20
सही उत्तर: B. 16
a²−b²=(a−b)(a+b)। Denominator में (58+42) cancel होगा और 58−42=16 बचेगा।
Practice MCQ
प्रश्न 8. (1−1/2)(1−1/3)(1−1/4)...(1−1/10) का मान ज्ञात करें।
A. 1/5
B. 1/8
C. 1/9
D. 1/10
सही उत्तर: D. 1/10
Product =1/2×2/3×3/4×...×9/10। Intermediate factors cancel होकर 1/10 बचता है।
Practice MCQ
प्रश्न 9. 198×202 का मान ज्ञात करें।
A. 39904
B. 39996
C. 40004
D. 40096
सही उत्तर: B. 39996
(200−2)(200+2)=200²−2²=40000−4=39996।
Practice MCQ
प्रश्न 10. 48×52 का मान ज्ञात करें।
A. 2396
B. 2446
C. 2496
D. 2546
सही उत्तर: C. 2496
(50−2)(50+2)=50²−2²=2500−4=2496।