CHAPTER 02 Typed notes Q&A included

Fractions and Decimals

Overview

Fractions and Decimals is a key chapter in Class 7 Maths that builds on earlier knowledge of fractions and introduces operations like multiplication and division on both fractions and decimals. Students learn to multiply fractions by whole numbers and other fractions, divide fractions, and perform all four operations on decimals. Real-life applications such as money, measurement, and data make these concepts practical and easy to understand.

Typed Notes

Multiplication of Fractions

Multiplying a fraction by a whole number means repeated addition. For example, 3 × (2/5) = 6/5. To multiply two fractions, multiply the numerators and the denominators separately. For example, (3/4) × (2/5) = 6/20 = 3/10 after simplification. A fraction multiplied by its reciprocal always gives 1. Mixed numbers must first be converted to improper fractions before multiplying. Always simplify the result to its lowest terms by dividing numerator and denominator by their HCF.

Division of Fractions

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a/b is b/a. For example, (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 = 1 and 7/8. To divide a whole number by a fraction, write the whole number as a fraction with denominator 1, then multiply by the reciprocal. Mixed numbers must be converted to improper fractions before dividing. Always check if the final answer can be simplified or written as a mixed number.

Multiplication of Decimals

To multiply two decimals, ignore the decimal points and multiply as whole numbers. Then count the total number of decimal places in both numbers and place the decimal point that many places from the right in the product. For example, 2.3 × 1.2: multiply 23 × 12 = 276, total decimal places = 2, so answer = 2.76. Multiplying a decimal by 10 shifts the decimal one place right, by 100 shifts two places right, and by 1000 shifts three places right.

Division of Decimals

To divide a decimal by a whole number, divide normally and place the decimal point in the quotient directly above its position in the dividend. For example, 6.4 ÷ 4 = 1.6. To divide a decimal by another decimal, convert the divisor to a whole number by multiplying both numbers by 10, 100, or 1000 as needed, then divide. Dividing by 10 shifts the decimal one place left, by 100 shifts two places left, and by 1000 shifts three places left. Always verify the answer by multiplying back.

Key Concepts

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01A fraction p/q means p parts out of q equal parts; proper fractions have numerator less than denominator, improper fractions have numerator greater than or equal to denominator.
02To multiply two fractions, multiply numerators together and denominators together, then simplify: (a/b) × (c/d) = ac/bd.
03To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second: (a/b) ÷ (c/d) = (a/b) × (d/c).
04When multiplying decimals, multiply as whole numbers first, then place the decimal point so the total decimal places equal the sum of decimal places in both numbers.
05To divide a decimal by 10, 100, or 1000, shift the decimal point 1, 2, or 3 places to the left respectively.

Important Formulas

(a/b) × (c/d) = (a × c) / (b × d)

(a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc

Reciprocal of a/b = b/a; (a/b) × (b/a) = 1

Decimal × 10 → shift decimal 1 place right; Decimal ÷ 10 → shift decimal 1 place left

To multiply decimals: multiply as integers, then place decimal point = sum of decimal places of both numbers

Mixed number to improper fraction: a(b/c) = (a×c + b)/c

Questions & Solutions

Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.

Multiply: (3/7) × (14/9)

Divide: (5/8) ÷ (15/16)

Multiply: 2.35 × 1.4

Divide: 48.6 ÷ 0.6

A ribbon is 7.5 m long. It is cut into pieces each 0.25 m long. How many pieces are obtained?

Summary

In this chapter, students mastered multiplication and division of fractions including mixed numbers by converting them to improper fractions and using reciprocals for division. For decimals, they learned to multiply by counting decimal places and to divide by converting the divisor to a whole number. Multiplying or dividing by powers of 10 simply shifts the decimal point left or right.

Handwritten notes

Chapter-end quiz

4 MCQs

Option tap karo — turant pata chalega sahi ya galat, explanation ke saath.

Q1.What is the reciprocal of 4/7?
Q2.What is 0.5 × 0.5?
Q3.Which of the following is an improper fraction?
Q4.What is 3.6 ÷ 10?

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