Fractions – Definition, Parts, & Examples

Key Concepts

• Expressing fractions in tenths as decimals.
• Expressing fractions in hundredths as decimals.
• Comparing and ordering decimals.
• Number patterns.

Introduction: 

• In this chapter, we will learn to express fractions as equivalent fractions with a denominator 10. 
• Simplifying fractions with a denominator of 10. 
• Rounding numbers to the nearest ten. 
• Knowing fractions and mixed numbers. 

Fractions:  

Fractions are represented as numerical values and can be defined as the parts of a whole.  

Parts of Fraction:  

All fractions consist of a numerator and a denominator. 

• The denominator indicates how many parts the whole has been divided into. It is placed in the lower part of the fraction. 
• The numerator indicates how many sections of the fraction are represented. It is placed in the upper part of the whole. 

Example: 

Example: 

Understanding Tenths: 

Decimals:  A decimal number can be defined as a number whose whole number part and the decimal point separates the fractional part. The dot in a decimal number is called a decimal point. 

Read and write tenths in decimal and fractional forms. 

Tenths: The first digit to the right of the decimal point is one out of 10 equal parts of a whole. 

Example: 

Example:  0.6 means six-tenths or  

Decimal form: A decimal is a fraction written in a particular form. 

Example: 

E.g., Instead of writing   

You can express the fraction as 0.5. 

Decimal point: A point used to separate the whole number part from the fractional part of the decimal number. 

Example: 

Example: 34.9 

Here, 34 = Whole number part 

9 = Fractional part 

. = Decimal 

Expanded form: The expanded notation, also called expanded form, for decimals is the same as the integer expanded form. A decimal can be written as the sum of all the place values. 

E.g., (a) Write 317.29 in an expanded form. 

Sol: 

Place value chart: 

Example: Write the place value of the digits 2 and 4 in the number 326.471 

Sol: 

Place value of 2 = Tens = 20  

Place value of 4 = Tenths = 0.4 

Understanding Hundredths: 

Hundredths: Divide one whole into 100 equal parts or one-hundredth. In the decimal form, each part has a value equal to 0.01. 

Example: Express the fraction in decimal? 

Place holder zero: The zero is called a place holder. It is not worth anything on its own, but it changes the value of other digits.  

Look at the number 502. 

Sol:  52 = five tens and two units 

The zero place-holder is keeping the 5 and 2 in their correct places: 

Examples:  

(a) Express as a decimal. 

       Sol:  = 0.05 

(b) Express 15 hundredths as decimal. 

       Sol:  = 0.15  

(c) Express 1  as decimal 

       Sol:  

  1 = 1 one and 2 tenths 5 hundredths  

= 1 one and 25 hundredths 

                = 1.25 

Comparing Decimals: 

Compare and order decimals. 

Comparing Decimals: Comparing means examining the differences between numbers, quantities, or values to decide if it is greater than, smaller than, or equal to other quantities. 

Example: Compare 4.27 and 4.65 using a number line. 

Sol: 

Example:  

(a) Compare 0.6 and 0.8 

       Sol: 0.6 = 6 tenths 

               0.8 = 8 tenths 

               Because 8 tenths > 6 tenths 

    0.8 > 0.6 

(b) Compare 0.317 and 0.341 

        Sol: 0.317 = 0.3 + 0.01 + 0.007 

                            = 3 tenths + 1 hundredths + 7 thousandths 

                0.341 = 0.3 + 0.04 + 0.001 

                            = 3 tenths + 4 hundredths + 1 thousandths 

           3 tenths = 3 tenths 

         Now, compare the next digit 

         1 hundredths < 4 hundredths 

         Thus, 0.317 < 0.341 

Ordering: Arranging things in relation to each other according to a particular sequence or a pattern. 

Example: 

 (a) Order 9.34, 83.9, 21.4, 0.96 from smallest to largest. 

         Sol: 0.96, 9.34, 21.4, 83.9 

(b) Order 7.93, 5.94, 0.93, 28.7 from largest to smallest. 

        Sol: 28.7, 7.93, 5.94, 0.93 

Complete number patterns 

Number pattern is a pattern or sequence in a series of numbers by using a specific rule or pattern. 

Example: (a) Complete the pattern 1.5, 1.9, 2.3, 2.7, 3.1, 3.5, 3.9,  ____,  ____ 

Sol: 

(b) Find the next two numbers in the pattern 6.8, 6.4, 6, 5.6, 5.2, 4.8, 4.4. 

       Sol: 

What have we learnt:

• Introduction of decimals.
• How the place value of a digit changes when we multiply or divide by ten.
• How to read, write, and model fractions with 10 and 100 in the denominator.
• How to compare decimals from the least to greatest and from the greatest to least.
• Ordering of decimals.