By : Neha Uppal
Updated : Oct 19, 2020, 17:58
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.
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.
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:-
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.
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