CBSE Notes Class 7 Maths Chapter 2 Fractions and Decimals

Chapter 2 of the CBSE Class 7 Maths syllabus, Fractions and Decimals, delves into fundamental concepts that play a crucial role in understanding arithmetic and algebra. This chapter helps students build a strong foundation in working with fractions and decimals, which are crucial for carrying out addition, subtraction, multiplication, and division accurately and effectively.

Fractions express portions of a whole, while decimals express values in a different format using place value. The chapter provides an in-depth understanding of both, focusing on their applications, comparison, and conversion. Additionally, students will learn various operations on fractions and decimals, including complex ones like multiplying and dividing them.

1.0Fractions 

A fraction is a number that is a part of a group. Fractions are expressed as $\frac{a}{b}$, where a and b are whole numbers, with b ≠ 0.

Here “a” is Numerator and “b” is Denominator.

2.0Types of Fractions 

Proper Fractions:

Fractions having numerator less than the denominator are called proper fractions. For e.g. $\frac{3}{45},\frac{6}{68},\frac{67}{987}$, etc. 

Improper Fractions:

Fractions having numerator greater than the denominator are called improper fractions. 

For example: $\frac{46}{9},\frac{3664}{200}$, etc. 

Mixed Fractions:

Numbers having a whole number part, and a fractional part are called mixed fractions. We denote a mixed fraction in the form of $a\frac{b}{c}$ e.g. $4\frac{1}{3},19\frac{31}{60}$, etc.

Decimal Fractions:

Fractions having denominators as 10,100 or 1000 or any other higher power of 10 are called decimal fractions. 

For example: $\frac{6}{100},\frac{765}{1000},\frac{6454}{10000}$, etc.

Vulgar Fractions:

Fractions having a denominator as a whole number other than any power of 10 are called vulgar fractions. 

For example: $\frac{5}{31},\frac{546}{8700},\frac{376}{9000}$ etc.

Unit Fractions:

The fractions having 1 as a numerator are called unit fractions. 

For example: $\frac{1}{2},\frac{1}{3},\frac{1}{6}$, etc.

Simple Fractions:

Fractions having both numerator and denominator as whole numbers are called simple fractions. 

For example: $\frac{7}{98},\frac{45}{876},\frac{98}{90},\frac{77}{1000}$, etc. 

Complex Fractions:

Fractions having either or both the numerator and denominator as fraction or mixed fractions are called complex fractions. 

For example: $\frac{1}{\frac{1}{3}},\frac{\frac{2}{5}}{\frac{6}{7}}$, etc.

Equivalent Fractions:

Fractions representing the same value are called equivalent fractions. A few equivalent fractions for $\frac{2}{3}are\frac{4}{6},\frac{6}{9},\frac{8}{12}$, etc.

Like and unlike Fractions:

Fractions having the same denominator are called like fractions, whereas fractions having different denominators are called unlike fractions. 

For e.g. $\frac{3}{77},\frac{66}{77},\frac{45}{77}$ are like fractions. 

For e.g. $\frac{7}{6},\frac{8}{5},\frac{4}{7}$ are unlike fractions.

3.0Addition and Subtraction of Fractions

To add or subtract two like fractions, we add or subtract the numerator, and denominator remaining the same.

To add or subtract two unlike fractions, we may convert them into equivalent like fractions and then add or subtract.

4.0Multiplication of Fractions 

Multiplication of a Fraction by a Whole Number

To multiply a fraction by a whole number, you should multiply the whole number with the numerator of the fraction while keeping the denominator unchanged. 

For example, $3\times \frac{2}{5}=\frac{6}{5}$ . 

If the result is an improper fraction, it can be converted to a mixed number. 

Multiplication of a Fraction by a Fraction 

To multiply two fractions, multiply their numerators together and their denominators together. For example:  

$\frac{a}{b}\times \frac{c}{d}=\frac{a\times c}{b\times d}$

5.0Reciprocal of Fractions 

The reciprocal of a given fraction can be obtained by swapping the numerator and denominator  of the fraction. 

Reciprocal of any non-zero fraction

$\frac{a}{b};[a\ne 0andb\ne 0]=\frac{b}{a}$

The product of a number and its reciprocal is always 1.

6.0Division of Two Fractions 

If $\frac{a}{b}$ and $\frac{c}{d}$ are two fractions, where $(\frac{c}{d})\ne 0,then(\frac{a}{b})\times (\frac{d}{c})$ i.e. the dividend is multiplied by the reciprocal of divisor. 

Divide a Fraction by a Whole Number 

The rule for the division of a fractional number by a whole number is fraction. 

$\frac{Fraction}{WholeNumber}=Fraction\times Reciprocalofwholenumber$

Division of Whole Number by Fractions 

To divide a whole number by a fraction, follow the steps mentioned below. 

1. Find the reciprocal of the given fraction. 
2. Multiply the reciprocal with the given whole number. The product will be required answer. 

The rule of the division of a whole number by a fraction number is 

$\frac{WholeNumber}{Fraction}=Wholenumber\times ReciprocalofFraction$

7.0Mind Map for Fractions 

8.0Decimals

A decimal consists of two components: the whole number part and the decimal part, which are separated by a dot known as the decimal point.

Like and Unlike Decimals 

Decimals that have the same number of decimal places are referred to as Like Decimals. 

Examples: 65.87, 873.33, 0.98 etc. 

Decimals having different number of decimal places are known as Unlike Decimals. 

Examples: 9.8733, 93.33, 0.383333 etc…

9.0Decimal Place Value 

The decimal place value chart shows the place value of the digits in a decimal number. Place value is the numerical value represented by a digit in a number. Therefore, decimal place value charts are utilized to determine the appropriate position of each digit in a decimal number.

10.0Operations on Decimals 

1. Addition and Subtraction of Decimal Numbers 

• Write the provided numbers one below the other with decimal points in a vertical line (same column). 
• Equal the number of decimal places in all the numbers by adding the required number of zeroes to the right end, whenever needed. 
• Now add and subtract as for whole numbers placing the decimal point in the result directly under the other decimal points

2. Multiplication of Decimal Numbers 

• To multiply a decimal number by 10 or any power of 10: Move the decimal point as many places to the right as there are zeros in the multiplier. Multiplying a decimal number by 10ⁿ, moves the decimal point n places to the right.
• Multiplication of a decimal number by a whole number or a decimal number: Multiply as if there were no decimal points then adjust the position of the decimal by ensuring that the product contains the same total number of decimal places as the combined decimal places of the multiplier and multiplicand.

3. Division of Decimal Numbers

• Dividing a whole number or decimal number by 10 or any higher power of 10: Dividing a whole number or decimal number by 10ⁿ, moves the decimal point n places to the left.
• To divide a decimal number by a whole number: To divide a decimal number by a whole number, follow the same procedure as with whole numbers. However, position the decimal point in the quotient directly aligned with the decimal point in the dividend.
• To divide a decimal number by a decimal number: Move the decimal point of the divisor to the right until it becomes a whole number (that is, multiply it by 10 or a power of 10). Next move the decimal point of the dividend the same number of places to the right, add zero if necessary.

11.0Conversion of Units 

A unit conversion simply means expressing the same quantity using a different unit of measurement. For example, instead of hours, we can express time in minutes. Similarly, when it comes to distance, we can switch from miles to kilometers, feet, or any other measurement of length.

• 1 km = 10 hm = 100 dam = 1000 m 
• 1 hm = 10 dam = 100 m 
• 1 dam = 10 m 
• 1 m = 10 dm = 100 cm = 1000 mm 
• 1 dm = 10 cm = 100 mm 
• 1 cm = 10 mm

12.0Mind Map for Decimals

13.0Sample Questions on Fractions and Decimals

1. What are equivalent fractions?

Ans: Equivalent fractions are different fractions that represent the same value. For example, $\frac{1}{2}and\frac{2}{4}$ are equivalent.

2. What is a mixed number?

Ans: A mixed number consists of a whole number and a proper fraction, such as $2\frac{1}{2}.$

3. How do you convert a decimal to a fraction?

Ans: To convert a decimal to a fraction, write the decimal over its place value (for example, 0.75 = $\frac{75}{100}$ and simplify if possible.

4. Can a fraction be greater than one?

Ans: Yes, a fraction can be greater than one if the numerator is larger than the denominator $(e.g.,\frac{5}{4})$.