Lessons Grade 7

Chapter 2

Chapter 2: Fractions

2.1 Introduction to Fractions

A fraction represents a part of a whole. It consists of two numbers: the numerator (the number on top) and the denominator (the number on the bottom). The fraction is written as:

numeratordenominatorfrac{numerator}{denominator}denominatornumerator​

Example: 34frac{3}{4}43​ means 3 out of 4 equal parts.

Fractions can be proper (numerator is less than the denominator), improper (numerator is greater than or equal to the denominator), or mixed (a whole number combined with a fraction).

2.2 Types of Fractions

Proper Fractions: The numerator is smaller than the denominator.

Example: 25frac{2}{5}52​

Improper Fractions: The numerator is greater than or equal to the denominator.

Example: 74frac{7}{4}47​

Mixed Numbers: A whole number combined with a proper fraction.

Example: 2132frac{1}{3}231​

2.3 Converting Between Improper Fractions and Mixed Numbers

To convert an improper fraction to a mixed number:

Divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the numerator of the fraction.

Example: 74frac{7}{4}47​ becomes 1341frac{3}{4}143​.

To convert a mixed number to an improper fraction:

Multiply the whole number by the denominator and then add the numerator.

Example: 2132frac{1}{3}231​ becomes 73frac{7}{3}37​.

2.4 Adding and Subtracting Fractions

To add or subtract fractions, the denominators must be the same (called a common denominator).

Steps to Add/Subtract Fractions:

Find a common denominator (LCM of the denominators).

Adjust the fractions so they have the same denominator.

Add or subtract the numerators.

Simplify the result, if necessary.

Example (Addition): 14+24=34frac{1}{4} + frac{2}{4} = frac{3}{4}41​+42​=43​

Example (Subtraction): 56−16=46=23frac{5}{6} - frac{1}{6} = frac{4}{6} = frac{2}{3}65​−61​=64​=32​ (simplified)

2.5 Multiplying and Dividing Fractions

Multiplication: Multiply the numerators and the denominators.

Example: 23×45=815frac{2}{3} times frac{4}{5} = frac{8}{15}32​×54​=158​

Division: Multiply by the reciprocal of the second fraction.

Example: 23÷45=23×54=1012=56frac{2}{3} ÷ frac{4}{5} = frac{2}{3} times frac{5}{4} = frac{10}{12} = frac{5}{6}32​÷54​=32​×45​=1210​=65​

Exercises

**Exercise 1: Compare the following fractions using >, Example: 68frac{6}{8}86​ can be simplified by dividing both the numerator and denominator by 2, which gives 34frac{3}{4}43​.

Exercises

Exercise 2: Simplify the following fractions:

812frac{8}{12}128​

1525frac{15}{25}2515​

1824frac{18}{24}2418​

927frac{9}{27}279​

610frac{6}{10}106​