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Mathematics Class 7 - Fractions And-Decimals Notes

Comprehensive study notes for Class 7 - Fractions And-Decimals olympiad preparation

Fractions and Decimals

Welcome to the chapter on Fractions and Decimals for Class 7. In this chapter, you will learn how to work with fractions and decimals, convert between them, and solve problems using these concepts. By the end of this chapter, you will be able to add, subtract, multiply, and divide fractions and decimals confidently!

Introduction

Fractions and decimals are ways to represent parts of a whole. Fractions use numbers like 1/2 or 3/4, while decimals use numbers like 0.5 or 0.75. Both are important in mathematics and daily life.

Fractions

A fraction shows how many parts of a whole you have. It has a numerator (top number) and a denominator (bottom number).

  • Example: In 3/5, 3 is the numerator and 5 is the denominator.
  • Proper fractions: Numerator is less than denominator (e.g., 2/7).
  • Improper fractions: Numerator is greater than or equal to denominator (e.g., 7/4).
  • Mixed numbers: A whole number and a fraction together (e.g., 2 1/3).

Operations with Fractions

  • Addition and subtraction: Use common denominators.
  • Multiplication: Multiply numerators and denominators.
  • Division: Multiply by the reciprocal of the second fraction.

Example: 1/2 + 1/4 = 2/4 + 1/4 = 3/4

Decimals

Decimals are another way to show parts of a whole. They use a dot called a decimal point.

  • Example: 0.5, 2.75, 3.04
  • Tenths, hundredths, thousandths, etc.

Operations with Decimals

  • Addition and subtraction: Line up the decimal points.
  • Multiplication: Multiply as whole numbers, then place the decimal point.
  • Division: Move the decimal point as needed and divide as whole numbers.

Example: 0.6 + 0.25 = 0.85

Converting Fractions and Decimals

  • To convert a fraction to a decimal, divide the numerator by the denominator.
  • To convert a decimal to a fraction, write the decimal as a fraction and simplify.

Example: 3/4 = 0.75; 0.2 = 2/10 = 1/5

Word Problems

Use fractions and decimals to solve real-life problems. Read the question, choose the correct operation, and solve.

  • Example: If you eat 0.5 of a pizza and your friend eats 0.25, how much did you eat together? (0.5 + 0.25 = 0.75)

Fun Activity: Fraction and Decimal Hunt!

Look for fractions and decimals in your home—on measuring cups, clocks, money, and more. Write down what you find!

Summary

  • Fractions and decimals show parts of a whole.
  • You can add, subtract, multiply, and divide fractions and decimals.
  • Convert between fractions and decimals by dividing or simplifying.

Practice Questions

  1. Add: 2/5 + 1/5
  2. Subtract: 0.8 - 0.3
  3. Multiply: 3/4 × 2
  4. Divide: 0.6 ÷ 0.2
  5. Convert 1/2 to a decimal.

Challenge Yourself

  • Make your own word problem using fractions and decimals.
  • Convert 0.75 to a fraction and simplify.

Did You Know?

  • Decimals are used in money, measurements, and science!
  • Fractions are used in cooking, sharing, and dividing things.

Glossary

  • Fraction: A part of a whole, written as a/b.
  • Decimal: A number with a decimal point, showing parts of a whole.
  • Numerator: The top number in a fraction.
  • Denominator: The bottom number in a fraction.
  • Convert: To change from one form to another.

Answers to Practice Questions

  1. 3/5
  2. 0.5
  3. 1.5
  4. 3
  5. 0.5

Practice fractions and decimals every day to become a math expert!

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