This article provides an overview of decimals and fractions, their definitions, types, operations, and shortcuts to solve related problems quickly. It also covers the importance of mastering decimals and fractions for Quantitative Aptitude in Government Job Exams.
Decimals and fractions are interconnected mathematical concepts involving the division of numbers into equal parts. Mastering decimals and fractions is crucial for solving Quant problems in competitive exams like SSC, Banking, Railways, etc.
Important Details
| Concept | Definition |
|---|---|
| Fraction | A part or portion of a whole number divided into equal parts |
| Decimal | A fraction with denominator as power of 10 |
Fractions can be proper, improper, equivalent based on the relation between numerator and denominator. Operations like addition, subtraction, multiplication, division are performed on fractions after making sure denominators are equal.
Decimal Number System
| Component | Meaning |
|---|---|
| Decimal Point | Separates whole and fractional part |
| Numerical Name | Denotes number and placement of decimal |
Decimals represent fractions with denominators as powers of 10. Decimal operations involve lining up the decimal points and then applying arithmetic rules. Decimals also aid in scientific calculations.
Key Topics in Fractions
| Topic | Concept |
|---|---|
| Equivalent Fractions | Fractions with same numerical value |
| Simplifying Fractions | Reducing to lowest terms using HCF |
When dealing with fractions, equivalent fractions are identified or created to carry out operations like addition, subtraction etc. Simplifying fractions by finding HCF of numerator and denominator is an important technique.
Tips and Tricks
Some useful tips to solve decimals and fractions quickly:
| Tips | Description |
|---|---|
| Convert to fractions | Helps in shifting decimal point |
| Use HCF | To simplify fractions by reducing terms |
Converting decimals to fractions by using powers of 10 allows for flexibly moving the decimal point. Finding HCF of numerator and denominator is key to reducing complex fractions.
Importance for Competitive Exams
Handling decimals and fractions is indispensable for Quantitative Aptitude and numerical calculations across:
| Area | Application |
|---|---|
| Quantitative Aptitude | SSC, Banking, Govt Job exams |
| Academic Subjects | Physics, Chemistry, Mathematics etc. |
Thus, a strong grasp over decimals and fractions can make significant difference in one's performance in competitive exams requiring numerical ability.
Recommended Books
| Book Name | Author |
|---|---|
| Quantitative Aptitude for Competitive Examinations | R.S. Aggarwal |
| Wiley's Quantitative Aptitude | P.A. Anand |
Some good books to study decimals, fractions and other quant topics for competitive exams are by authors R.S. Aggarwal, Sarvesh Verma among others.
Conclusion:
Decimals and fractions form the bedrock of quantitative ability required for government job exams. Understanding their correlation along with tips and tricks can aid faster problem solving involving these concepts. Books by renowned authors also help in mastering decimals, fractions and acing competitive exams.
FAQ:
Q1: How are decimals and fractions related?
A1: Decimals are a special type of fractions where the denominator is a power of 10. So every decimal can also be represented as a fraction, but not vice versa.
Q2: Why simplify fractions in competitive exams?
A2: Simplifying fractions by finding HCF of numerator and denominator reduces complexity allowing faster arithmetic computations involving fractions..
Q3: What are some shortcuts for decimals and fractions?
A3: Useful tips include interconverting decimals and fractions, shifting decimal points by changing bases, using HCF for simplification etc.
Q4: Where are decimals/fractions applied in govt exams?
A4: Quantitative Aptitude section of most competitive exams like SSC, Banking, Railways etc. test decimals and fractions based problem solving.
Q5: Which topics relate to decimals and fractions?
A5: Important interrelated topics are fractions, percentages, ratios, averages etc. covered under Quant section of Govt job exams.
Q6: What are the best books for decimals and fractions?
A6: Some recommended books are Quantitative Aptitude by R.S. Aggarwal, Quantitative Aptitude Quantum CAT by Sarvesh K Verma.
