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Until now, we have studied all about the integers, the positive and negative integers, representing integers on the number line, and their properties. Now in NCERT Class 7 Maths Chapter 2, we will study fractions and decimals in detail. We will also study properties like multiplication and division on fractions and decimals. Let us continue to read the NCERT Class 7 Maths Chapter 2 Fractions and Decimals Notes and Solutions (PDF) below.
Download NCERT Class 7 Maths Chapter 2 Fraction and Decimals Notes and Solutions PDF
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NCERT Class 7 Maths Chapter 2 Notes – PDF Available
Check the topic-wise notes for NCERT Maths Class 7 – Chapter 2 below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the exam hall.
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Topic 1: Multiplication of Fractions
Let us see the different cases of multiplication of fractions.
- Multiplication of a Fraction by a Whole Number: to multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator the same.
Note:- To multiply a mixed fraction to a whole number, first convert the mixed fraction to an improper fraction and then multiply. For example,
- Fraction as an operator ‘of’: ‘of’ represents multiplication. For example,
- Multiplication of a Fraction by a Fraction: We multiply two fractions as: (Product of Numerators/Product of Denominators).
- Value of the Products: There are 2 cases of the product of improper and proper fractions. Let us see each one by one.
- When two proper fractions are multiplied, the product is less than each of the fractions. Or, we say the value of the product of two proper fractions is smaller than each of the two fractions.
- The product of two improper fractions is greater than each of the two fractions. Or, the value of the product of two improper fractions is more than each of the two fractions.
So, as a result, we can say that The product obtained is less than the improper fraction and greater than the proper fraction involved in the multiplication.
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Topic 2: Division of Fractions
Let us see each case of the division of fractions below.
- Division of Whole Number by a Fraction: To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.
Note:- While dividing a whole number by a mixed fraction, first convert the mixed fraction into an improper fraction and then solve it as above.
- Division of a Fraction by a Whole Number: Based on our earlier observations we have:
- Division of a Fraction by Another Fraction: Just like the above case, the division of a fraction by a fraction can be calculated by –
Topic 3: Multiplication of Decimal Numbers
Let us see the different cases here.
- Multiplication of Decimal Numbers by 10, 100 and 1000: when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are the same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Topic 4: Division of Decimal Numbers
- Division by 10, 100 and 1000: while dividing a number by 10, 100 or 1000, the digits of the number and the quotient are the same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
- Division of a Decimal Number by a Whole Number: To divide a decimal number by a whole number, we first divide them as whole numbers. Then place the decimal point in the quotient as in the decimal number.
For example, 8.4 ÷ 4 = 2.1
- Division of a Decimal Number by another Decimal Number: While dividing two decimal numbers, first shift the decimal point to the right by an equal number of places in both, to convert the divisor to a whole number. Then divide. Thus, 2.4 ÷ 0.2 = 24 ÷ 2 = 12.
Download NCERT Class 7 Maths Chapter 2 Fraction and Decimals Notes and Solutions PDF
Explore all the Chapters of Class Mathematics:-
| Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 5 |
| Chapter 6 | Chapter 7 | Chapter 8 | Chapter 9 | Chapter 10 |
| Chapter 11 | Chapter 12 | Chapter 13 |
NCERT Solutions of Class 7 Maths Chapter 2: Fractions and Decimals- Free PDF Download
Below we have provided solutions for NCERT Class 7 Maths Chapter 2, Fractions and Decimals. Go through for answers to some important questions.
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Exercise 2.1 Solutions
Q 1. Multiply (7 × ⅗) and reduce to the lowest form and convert into a mixed fraction.
Solutions. The answer is given below.
Q 2. Find 1/2 of
- 24
- 46
Solutions. The answers are given below.
- ½ of 24 = ½ × 24 = 12
- ½ of 46 = ½ × 46 = 23
Exercise 2.2 Solutions
Q 1. Find ¼ of the following.
- ¼
- ⅗
- 4/3
Solutions. The answers are given below.
- ¼ of ¼ = ¼ × ¼ = 1/16
- ¼ of ⅗ = ¼ × ⅗ = 3/20
- ¼ of 4/3 = ¼ × 4/3 = ⅓
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Q 2. Which is greater: (2/7 of ¾) or (⅗ of ⅝)?
Solutions. The answers are given below.
2/7 of ¾ = 2/7 × ¾ = 6/28 = 3/14; and
⅗ of ⅝ = ⅗ × ⅝ = ⅜
Now, taking LCM, the LCM of 8 and 14 is 56.
So, making their denominators the same: 3/14 × 4/4 = 12/56 and ⅜ × 7/7 = 21/56
So, clearly 12/56 < 21/56
∴ (2/7 of ¾) [<] (⅗ of ⅝)
Exercise 2.3 Solutions
Q 1. Find 12 ÷ ¾.
Solutions. To find 12 ÷ ¾, we multiply 12 with the reciprocal of the fraction.
12 ÷ ¾ = 12 × 4/3 = 16
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Q 2. Find ⅖ ÷ ½.
Solution: To find ⅖ ÷ ½, we multiply ⅖ with the reciprocal of the fraction ½.
⅖ ÷ ½ = ⅖ × 2/1 = ⅘
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Explore Notes of All subjects of CBSE Class 7:-
| CBSE NCERT Notes Class 7 English | CBSE NCERT Notes Class 7 History | CBSE NCERT Notes Class 7 Geography |
| CBSE NCERT Notes Class 7 Civics | CBSE NCERT Notes Class 7 Mathematics | CBSE NCERT Notes Class 7 Science |
Check out Maths Class 6 Notes and Exercise Solutions for other chapters below.
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FAQs
Ans: To multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator the same.
Note:- To multiply a mixed fraction to a whole number, first convert the mixed fraction to an improper fraction and then multiply.
Ans: To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.
Ans: To divide a decimal number by a whole number, we first divide them as whole numbers. Then place the decimal point in the quotient as in the decimal number.
For example, 8.4 ÷ 4 = 2.1
This was all about NCERT Class 7 Maths Chapter 2, Fractions and Decimals in which we studied the different properties of integers. Download the NCERT Class 7 Maths Chapter 2 Notes and Solutions PDF to ace your exam preparations. Follow the CBSE Class 7 Maths Solutions and Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 7 Maths.