NCERT Class 7 Maths Chapter 8
Working with Fractions
This chapter from Ganita Prakash Part 1 strengthens CBSE Class 7 students' understanding of fractions, including proper, improper, and mixed fractions, and develops skills in performing all four operations with fractions. Students learn to add, subtract, multiply, and divide fractions and mixed numbers in real-life contexts. The chapter also covers comparison of fractions and simplification to lowest terms.
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Key Terms
- Proper Fraction
- A fraction in which the numerator is smaller than the denominator. Its value is less than 1. Examples include 2/3, 5/8, and 1/4.
- Improper Fraction
- A fraction in which the numerator is greater than or equal to the denominator. Its value is equal to or greater than 1. Examples include 7/3, 5/5, and 9/4.
- Mixed Number
- A number consisting of a whole number and a proper fraction, such as 3½ or 2¾. It can be converted to an improper fraction.
- Equivalent Fraction
- Fractions that represent the same value despite having different numerators and denominators. For example, 1/2, 2/4, and 3/6 are all equivalent fractions.
- Lowest Terms
- A fraction is in its lowest (simplest) terms when the numerator and denominator have no common factors other than 1. For example, 4/6 simplified to lowest terms is 2/3.
- Reciprocal
- The reciprocal of a fraction is obtained by swapping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3. Division of fractions is performed by multiplying by the reciprocal.
Frequently Asked Questions
What is the difference between proper, improper, and mixed fractions?▾
A proper fraction has a numerator smaller than the denominator (e.g., 3/7). An improper fraction has a numerator equal to or larger than the denominator (e.g., 9/4). A mixed number combines a whole number and a proper fraction (e.g., 2¼), which is the same as an improper fraction.
How do you add fractions with different denominators?▾
To add fractions with different denominators, first find the LCM of the denominators (the common denominator). Convert each fraction to an equivalent fraction with the common denominator, then add the numerators. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
How do you multiply two fractions?▾
To multiply two fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Then simplify if possible. For example, 2/3 × 3/5 = (2×3)/(3×5) = 6/15 = 2/5.
How do you divide one fraction by another?▾
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For example, 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, which as a mixed number is 1⅞.
How do you simplify a fraction to its lowest terms?▾
Find the HCF (Highest Common Factor) of the numerator and denominator, then divide both by the HCF. For example, to simplify 18/24: HCF of 18 and 24 is 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4 in lowest terms.
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