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MATHEMATICS Chapter 2: Fractions and Decimals
(1) FRACTIONS AND DECIMALS 02 Fractions and Decimals Introduction: Fractions The word fraction derives from the Latin word “Fractus” meaning broken. It represents a part of a whole, consisting of a number of equal parts out of a whole. E.g. : slices of a pizza. 10, 39, 389 To know more about Fractions, visit here. Fractions play an important part in our daily lives. There are many examples of fractions you will come across in real life. We have to willingly or unwillingly share that yummy pizza amongst our friends and families. Three people, four slices. If you learn and visualize fractions in an easy way, it will be more fun and exciting. For example, slice an apple into two parts, then each part of the sliced apple will represent a fraction (equal to 1/2). Parts of Fractions The fractions include two parts, numerator and denominator.
(2) FRACTIONS AND DECIMALS 02 • Numerator: It is the upper part of the fraction, that represents the sections of the fraction • Denominator: It is the lower or bottom part that represents the total parts in which the fraction is divided. Example: If 3 4 is a fraction, then 3 is the numerator and 4 is the denominator. Properties of Fractions Similar to real numbers and whole numbers, a fractional number also holds some of the important properties. They are: • Commutative and associative properties hold true for fractional addition and multiplication • The identity element of fractional addition is 0, and fractional multiplication is 1 • The multiplicative inverse of a/b is b/a, where a and b should be non zero elements • Fractional numbers obey the distributive property of multiplication over addition Types of Fractions Based on the properties of numerator and denominator, fractions are sub-divided into different types. They are: • Proper fractions • Improper fractions • Mixed fractions • Like fractions • Unlike fractions • Equivalent fractions Proper Fractions The proper fractions are those where the numerator is less than the denominator. For example, 8 9 will be a proper fraction since “numerator < denominator”. Improper Fractions
(3) FRACTIONS AND DECIMALS 02 The improper fraction is a fraction where the numerator happens to be greater than the denominator. For example, 9 8 will be an improper fraction since “numerator > denominator”. Mixed Fractions A mixed fraction is a combination of the integer part and a proper fraction. These are also called mixed numbers or mixed numerals. For example: 3 2 3 = [(3 × 3) + 2] 3 = 11 3 Like Fractions Like fractions are those fractions, as the name suggests, that are alike or same. For example, take 1 2 and 2 4 ; they are alike since if you simplify it mathematically, you will get the same fraction. Unlike Fractions Unlike fractions, are those that are dissimilar. For example, 1 2 and 1 3 are unlike fractions. Equivalent Fractions Two fractions are equivalent to each other if after simplification either of two fractions is equal to the other one. For example, 2 3 and 4 6 are equivalent fractions. Since, 4 6 = (2×2) (2×3) = 2 3 Unit Fractions A fraction is known as a unit fraction when the numerator is equal to 1. One half of whole = 1 2 One-third of whole = 1 3 One-fourth of whole = 1 4