Fractions and Decimals Class 7 Notes CBSE Maths Chapter 2 [Free PDF Download]

• In the previous session, we learned about fractions and decimals, as well as the operations of addition and subtraction on them.

• Multiplication and division operations on fractions and decimals are now being studied.

• We've learnt the art of multiplying fractions. When two fractions are multiplied, the numerators and denominators are multiplied separately, and the product is written as the product of numerators by product of denominators. For example, $\dfrac{1}{2}\times \dfrac{3}{2}=\dfrac{3}{4}$

• A fraction serves as a ‘of' operator, like,$\dfrac{3}{4}$of $2=\dfrac{3}{2}$.

1. The product of two correct fractions is less than the product of the multiplied fractions.

2. A proper and an improper fraction's product is smaller than the improper fraction and bigger than the appropriate fraction.

3. The sum of two improper fractions is larger than the sum of the two fractions.

• By inverting a fraction upside down, you can get its reciprocal. We've already looked at how to divide two fractions.

1. When dividing a whole number by a fraction, the reciprocal of the fraction is multiplied by the whole number. For example, $3\div \dfrac{1}{2}=3\times 2=6$

2. When dividing a fraction by a whole number, the reciprocal of the whole number is multiplied by the fraction. For example,$\dfrac{3}{4}\div5=\dfrac{3}{4}\times \dfrac{1}{5}=\dfrac{3}{20}$.

3. We multiply the first fraction by the reciprocal of the other while dividing one fraction by another fraction. As a result,  $\dfrac{3}{4}\div \dfrac{5}{2}=\dfrac{3}{4}\times \dfrac{2}{5}=\dfrac{3}{10}$.

• We learned how to multiply two decimal values as well. Multiply two decimal numbers as whole numbers first before multiplying them as decimal numbers. In both the decimal figures, count the number of digits to the right of the decimal point. Add the total number of digits you've counted. Count the digits from the rightmost spot in the product to get the decimal point. The total acquired before should be used as the count. For example,$0.3\times 0.4=0.12$.

• To multiply a decimal value by $10,100$ or $1000$we move the decimal point to the right by as many places as the number of zeros over one. For example, $0.24\times 10=2.4,$

$0.24\times 100=24,$

$0.24\times 1000=240.$

• We've already looked at how to divide the decimal numbers.

1. To divide a decimal number by a whole number, we must first divide the two values into whole numbers. Then, as with the decimal number, place the decimal point in the quotient. For example,$1.2\div 2=0.6$.

It's worth noting that we're only looking at divisions with a zero remainder.

2. To determine the quotient when dividing a decimal number by $10,100$ or $1000$, shift the digits in the decimal number to the left by as many places as there are zeros over $1$. For example, 

$12.8\div 10=1.28$,

$12.8\div 100=0.128,$

$12.8\div 1000=0.0128$

3. To convert the divisor to a whole number when dividing two decimal values, shift the decimal point to the right by an equal number of places in both. After that, split. Thus, $3.6\div 0.3=12$

Revision Notes for CBSE Class 7 Maths Chapter 2 - Free PDF Download

Fraction word is taken from the Latin word “ Fractus” which means broke. Which mainly represent a part of a whole, consisting of a number of equal parts out of a whole. For example, we have a pizza of four equal slices and now we are left with only two slices of pizza. So we can write it in fractional form as 2/4 or ½. Here 2 or 1 is a numerator and 4 or 2 is a denominator. The numerator tells us about the left pizza slices and the denominator tells us about the total number of pizza slices. So in general fraction form is written as a numerator/denominator, Where, denominator ≠ 0. In case the numerator is equal to the denominator then the fraction becomes a whole i.e. 1. This is termed as a unity of fraction.

Types of Fraction

Mainly there are six types of fractions. All these types of fraction are discussed below:

1. Proper Fraction: In this fraction, the numerator is always less than the denominator. It shows the part of a whole.

2. Improper Fraction: In this fraction numerator is always more than the denominator and it shows the mixture of whole and a proper fraction.

3. Mixed Fraction: In this type of fraction we write mixed form as it is the mixture of whole numbers and a fraction.

4. Like Fraction: In this type, there are fractions with the same denominator. 

5. Unlike Fraction: In this fraction, there are fractions with different denominators. 

6. Equivalent Fraction: The fraction which is proportional to each other is termed as an equivalent fraction. 

Decimals

Numbers that are generally used to represent numbers that are smaller than the unit 1 are termed as decimal. It is also known as the base 10 system since each place value is denoted by a power of 10.

When we multiply a decimal number with the whole number then we get the same number of digits after the decimal point as that of the decimal number.

E.g : 22.2×4 = 88.8

When we multiply decimal with power of 10, then in that case the decimal point shifts to the right by the number of zeros in its power.

Example: 22.22 × 100 = 2222

When we multiply the decimal with decimal, then they will give decimal points in the answer as many places are the same as the total number of places right to the decimal points in both numbers.

Example: 22.22 × 2.2 = 48.884

Key Features of Class 7 Maths Chapter 2 Fractions and Decimals

• Available in PDF format

• Covers all important topics and subtopics of Fractions and Decimals

• A step-by-step explanation for sums

• Prepared by Maths experts

• Can be downloaded for free of cost

• These notes are as per the updated CBSE syllabus for Class 7 Maths

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Chapter wise Revision Notes for Class 7 Maths

• Chapter 1 - Integers Notes

• Chapter 3 - Data Handling Notes

• Chapter 4 - Simple Equations Notes

• Chapter 5 - Lines and Angles Notes

• Chapter 6 - The Triangle and Its Properties Notes

• Chapter 7 - Congruence of Triangles Notes

• Chapter 8 - Comparing Quantities Notes

• Chapter 9 - Rational Numbers Notes

• Chapter 10 - Practical Geometry Notes

• Chapter 11 - Perimeter and Area Notes

• Chapter 12 - Algebraic Expressions Notes

• Chapter 13 - Exponents and Powers Notes

• Chapter 14 - Symmetry Notes

• Chapter 15 - Visualising Solid Shapes Notes