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NCERT Class 7 Maths Chapter 2 Fractions and Decimals: Introduction
Fractions and decimals are two ways to represent part of a whole. A fraction is a way to show a part of a whole as a ratio of two numbers. A decimal is a way to show a part of a whole as a number with a point.
Fractions
Definition
A fraction is a way to show a part of a whole as a ratio of two numbers.
Types of Fractions
1. Proper Fraction: A fraction where the numerator is less than the denominator. Example: 3/4
2. Improper Fraction: A fraction where the numerator is greater than or equal to the denominator. Example: 5/3
3. Mixed Fraction: A fraction that is a combination of a whole number and a proper fraction. Example: 2 1/3
NCERT Class 7 Maths Chapter 2 Fractions and Decimals: Operations on Fractions
1. Addition: To add fractions, we need to have the same denominator. Example: 1/4 + 1/4 = 2/4
2. Subtraction: To subtract fractions, we need to have the same denominator. Example: 2/3 - 1/3 = 1/3
3. Multiplication: To multiply fractions, we multiply the numerators and denominators separately. Example: 1/2 × 3/4 = 3/8
4. Division: To divide fractions, we invert the second fraction and multiply. Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3
Decimals
Definition
A decimal is a way to show a part of a whole as a number with a point.
Types of Decimals
1. Terminating Decimal: A decimal that ends. Example: 0.5
2. Non-Terminating Decimal: A decimal that does not end. Example: 0.33333... (where the dots represent the repeating pattern)
3. Recurring Decimal: A decimal that has a repeating pattern. Example: 0.66666... (where the dots represent the repeating pattern)
Operations on Decimals
1. Addition: To add decimals, we need to line up the decimal points. Example: 2.5 + 1.8 = 4.3
2. Subtraction: To subtract decimals, we need to line up the decimal points. Example: 4.5 - 2.2 = 2.3
3. Multiplication: To multiply decimals, we multiply the numbers as if they were whole numbers, and then place the decimal point accordingly. Example: 2.5 × 3.2 = 8.0
4. Division: To divide decimals, we divide the numbers as if they were whole numbers, and then place the decimal point accordingly. Example: 4.5 ÷ 2.5 = 1.8
NCERT Class 7 Maths Chapter 2 Fractions and Decimals: Conversion between Fractions and Decimals
1. Fraction to Decimal: To convert a fraction to a decimal, we divide the numerator by the denominator. Example: 3/4 = 0.75
2. Decimal to Fraction: To convert a decimal to a fraction, we write the decimal as a fraction with the decimal part as the numerator and the place value as the denominator. Example: 0.75 = 75/100 = 3/4
Multiple Choice Questions
1. What is the simplest form of the fraction 6/8?
a) 3/4
b) 1/2
c) 2/3
d) 3/2
2. What is the decimal equivalent of the fraction 3/4?
a) 0.5
b) 0.75
c) 0.25
d) 0.33
3. What is the result of multiplying 2/3 by 3/4?
a) 1/2
b) 1/3
c) 2/3
d) 1/4
Section B: Short Answer Questions
1. Convert the fraction 2/5 to a decimal.
2. Simplify the fraction 8/12.
3. Multiply 3/4 by 2/3.
Section C: Long Answer Questions
1. Convert the decimal 0.45 to a fraction.
2. Divide 2/3 by 3/4.
3. Add 1/2 and 1/4.
Test Paper for Fractions and Decimals Class 7 -
Here is a link for test paper
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