Algebra
Learning Objectives
- Fractions
- Time and Clock
- Money
Fractions
A fraction is a part of whole. There are two numbers to every fraction, which are called term. A line separates the two terms. Number above the line is called numerator and the number below the line is called denominator. Denominator of a fraction tells us how many parts the whole is divided into and the numerator tells us how many parts are taken out the whole. For example, in the fraction\[\frac{2}{5}\], 5 is denominator. So, the whole unit or one whole has been cut into 5 equal parts.
2 is the numerator. Now, 2 parts out of 5 parts is being talked about or 1 part is going to be shaded or taken out. Here, the number \[\frac{2}{5}\] is known as fractional number and its symbol \[\frac{2}{5}\] is called a fraction.
Types of Fractions
There are several types of fractions. Let us study the fractions and their types.
Unit Fractions
A fraction, whose numerator is 1, is called a unit fraction. For example, \[\frac{1}{5},\frac{1}{3},\frac{1}{9},\frac{1}{10}\]are unit fractions. Here, the denominators of all fractions are different but numerators are 1.
Like and Unlike Fractions
Fractions in which the denominators are same, are called the like fractions and the fractions in which denominators are different, are called unlike fractions. For example, \[\frac{2}{3},\frac{1}{3},\frac{4}{3}\]are like fractions and \[\frac{2}{5},\frac{7}{4},\frac{3}{8}\] are unlike fractions.
Operations with Fractions
Addition of Like Fractions
Suppose two fractions are \[\frac{1}{5}\] and \[\frac{3}{5}\] and we have to add them.
So, we have, \[\frac{1}{5}+\frac{3}{5}=\frac{1+3}{5}=\frac{4}{5}\]
Therefore, the sum of like fractions \[=\frac{Sum\text{ }of\text{ }Numerators}{Common\text{ }Denominator}\]
Word Problems Based on Fractions
A fraction is defined as a portion of the whole. It is made up of two numbers: Numerator and Denominator. Fraction is a small amount of whole quantity. For example, if a piece of wire is divided into three parts, then each part is one-third part or \[\frac{1}{3}\] part of whole. The word problems involving fractions are usually based on real-life. Let us look at the following problems based on fractions.
Time and Clock
Time is important to plan our day. Time is the ongoing sequence of events. We use time to order events in the past, present and future. Time is passing non-stop. We use a clock or watch to measure time. Time is measured in seconds, minutes, hours, days, weeks, months and years with the help of clocks and calendars.
Indian Currency
Currency is a generally accepted form of money, including coins and paper notes. Different countries uses different currencies. Indian currency is know as Rupees. Symbol for Indian rupees is ‘Rs.’ and Symbol for Indian paise is 'p'. We write 78 rupees as Rs.78 and 50 paise as 50 p. There are 100 paise in one rupee. Suppose we have rupees one hundred four and
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