The word Fraction is etymologically traced back to Latin ‘fractus’ which translates to ‘broken’, as in, broken down into equal parts. Fractions refer to a mathematical concept, wherein a ‘fraction’ is defined as a number that represents a ‘part’ or ‘portion’ of a (whole) number. (For eg. if an integer ‘2’, is divided into 8 equal parts, i.e. 28= 14 = 0.25). A fraction is a division of an integer into a specific number of parts. Fractions have a numerator that is displayed above the ‘fraction bar’ (a line that divides them), and a non-zero denominator that is written below. Denominator refers to the number that needs to be divided (dividend), and numerator displays the number that refers to the number of divisions to be performed on the dividend (divisor). Fractions can be categorised as proper and improper fractions, wherein, if the absolute value of a fraction is less than 1 and more than -1, i.e. ab= x, where x is a number that lies between (-1>x>1).
Decimals are a form of fractions that have a number that has the power of 10 (10, 100, 1000) in the place of the denominator, regardless of the number in its numerator. Thus, decimals represented as:
a10n where, a is any integer, and n is any non-zero number.
The definition of a decimal fraction, in short, refers to ‘fractions that are restricted to a base of 10’. So, the fraction 1/10 can be represented with the help of a decimal point as “0.1”. Thus, every decimal is essentially a fraction, but every fraction might not be able to be represented decimally.
Important Decimals and Fractions Topics for SSC Exams
Sub-topics (for Decimals)
Explanation (with Formulas)
Nomenclature and placement of the decimal
The numerical name that any decimal number holds is important, as well as closely related to the place of the decimal. (e.g. 54.02 is named as Fifty four and two hundredths.)
The relation between Decimals and fractions, and their visualization.
Decimals are a simpler way of writing fractions with the base of 10. Being able to comprehend and visualise how the number is broken down into parts is needed. (0.4 = 4/10 or 400/1000)
Addition and Subtraction of decimals
For addition and subtraction of decimals, the numbers need to have their decimal points lined up to match one-another. (45.5 +0.12 = 45.62)
Multiplying and dividing decimals
For multiplication and division, we have to calculate the arithmetic value first, while ignoring the decimal, and then add the decimal point, based on the place of the decimal point.
Word problems based on decimals
Most of the word problems of decimals are related to monetary transactions and scientific values.
Topic (For fractions)
They are fractions that have numerically the same value/output. For eg. ⅔ = 1/1.5 = 4/6
Reducing essentially means reducing the values of numerator and denominator to their Least Common Multiple (LCM). (Eg, reduce 15/45 to ⅓)
Adding & Subtracting Fractions
For addition and subtraction of fractions, the denominator must be the same, and then numerators are added/subtracted.
Converting Between Mixed Numbers & Improper Fractions. ...
Mixed numbers can be turned into improper fractions by multiplying the whole number to the denominator, and adding it to the numerator. (313= 103)
Adding & Subtracting Mixed Numbers. ...
By turning the fractional part of a number into having a common denominator, and then adding the whole numbers, it is used to add or subtract mixed numbers.
Multiplying Fractions & Mixed Numbers
Multiply the numerators and the denominators, and then calculate HCF.
Take the reciprocal of the 2nd fraction, and then multiply with first, to perform division on fractions.
Tips to Prepare Decimals and Fractions Questions (Short Tricks)
Decimals and Fractions have a few tips and tricks for solving, that can help the students to speedily complete these sections of Quants effectively. Some of them are:-
- To simplify the arithmetic operation to be performed on decimals, the decimal point needs to be shifted at times. To do so, we can convert the decimal into fraction form and then multiply both the numerator and denominator with the same order of magnitude of 10. (Eg. 0.005 = 5 x 10-3 = 5/1000)
- If the exponent of 10 is a positive integer, then the decimal point needs to be shifted to the right side of its current placement. And, if the exponent of 10 is a negative number, then the decimal point shifts to left. (Eg 5100.00 = 5.1 x 103)
- HCF (highest common factor) is calculated to simplify fractions, as the HCF thus obtained is then multiplied to both numerator and denominator, in order to reduce the fractions down to their lowest common fraction. (eg 75/100 = 3x25/4x25 = ¾)
- Dividing two fractions is to be simplified by multiplying the reciprocal of the divisor to the dividend. (Eg, ¾ divided by ½ = ¾ x 2/1 = 1.5)
Importance of Decimals and Fractions in Quantitative Section of Competitive Banking & Government Exams
Decimal and fraction questions are a very crucial concept, for the preparation of almost every competitive examination hosted in our country. Almost all science-based exams, commerce-based exams, and all others, such as SSC, CHSL, etc. essentially require the knowledge of decimals and fractions & its conversions. Physics, chemistry, mathematics, applied sciences, etc. and their mathematical calculations, applies this concept in almost every stage and level of their application. This makes the topic of Decimal Fractions an absolute necessity for everyone, who is preparing for any kind of examination that involves numerical calculations.
Most Recommended Books for Decimals and Fractions
The Pearson Guide To Quantitative Aptitude For Competitive Examination
Quantitative Aptitude for Competitive Examinations
Quantitative Aptitude Quantum CAT
Sarvesh K Verma
Wiley’s Quantitative Aptitude
Teach yourself quantitative aptitude
Why prepare Decimals and Fractions from BYJU'S Exam Prep
BYJU'S Exam Prep is India’s largest platform for online education, in-depth study material and resources, along with Decimals and Fractions practice questions, quizzes and study guides. Students preparing for almost all major competitive examinations can find academic guidance relevant to their respective fields. BYJU'S Exam Prep hosts frequently updated quizzes, solved/unsolved questions, test series, mock series, detailed solutions and performance analysis, free video lectures, and real-time exam-prep community, that is dedicated to bringing out our best potential and helps us achieve our academic goals. BYJU'S Exam Prep also hosts exam-related notifications, to keep the students updated about all the latest news regarding their individual examinations.
- What is the difference between decimals and fractions?
In fraction, when the denominator divides the numerator with remainder and points a decimal on quotient and remainder is multiplied by 10 and then further divide the quotient will be in decimal format.
E.g. 5/4 is a fraction that can also be displayed as 1.25 in decimal form.
- How do I convert between percentages, decimals and fractions?
All three are linked. Fractions are ratios or comparisons between two integers. To find its decimal equivalent, we just divide the denominator into the numerator. We call these numbers the set of Rational Numbers, denoted by Q. For example, if we have 7/8, we divide 7 by 8. This gives 0.875.
To find the percentage, just take the decimal, and then multiply it by 100. To get it back to a fraction, what is helpful to us is if we remember that a percentage is a part of a whole, which is 100. If we have something like 65%, then we can just put it over a 100 (because percent means per 100, cent = 100). So then we have 65/100, which reduces down to 13/20.
- Are all fractions also decimals?
All fractions can be made into decimals. For example, the fraction 3/5 is made into a decimal by dividing 3.00 by 5. as the divisor (the number put outside of the box (so to speak) is the divisor. You need to try a few “the long way” actual pen and pencil ways to understand how the conversion of fractions to decimals works. With a calculator. With a calculator press 3/5= for your answer.
- What is the use of fractions and decimals?
Both fractions and decimals are used to describe parts smaller than 1. For instance, both 1/2 and .5 are used to show the same number, half of 1. But when do you use a fraction and when do you use a decimal? Fractions are used more in word problems and “real life” scenarios than decimals; for instance, a farmer would look out his window and say, “I have 32 cows, and half are white” instead of saying, “I have 32 cows, and .5 are white”. Decimals are used for exact measurements, like in recipes or experiments. Fractions can also be used in math where the decimal form is repeating and/or infinitely long. Example: 1/3 = .3333333… on and on.
- What are some examples of decimal fractions?
A decimal fraction is a fraction whose base is a power of 10.
Some of the examples are
7/10 = 7/10^1 = 0.7
56/100 = 56/10^2 = 0.56
333/1000 = 333/10^3 = 0.33333
4/10000 = 0.0004
- What are equivalent fractions?
The word equivalent means equal in value, so equivalent fractions are fractions that, although written in different forms (numerators and denominators are different), the value or ratio between the top and bottom remains the same.
For example, 1/2 = 2/4 = 3/6 = 4/8
You can say you ate 1/2 of a pizza if you cut it into two parts, or 4 parts or 6 parts etc. As long as you ate half of the total number, the value, or ratio, remains the same - 1/2.
One way to find equivalent fractions is to multiply the numerator and denominator by the same number.
- What fraction is between 2/3 and 3/4?
There is an infinite number of factions between any two rational numbers. 2/3 is approximately 0.667, and 3/4 is exactly 0.75. You can pick any of the decimal values between those two values and convert it into a fraction that satisfies the requirements.
0.668 = 668/1000
0.66801 = 66801/100000