LESSON 2 FRACTIONS

Learning Outcomes By the end of this lesson, students should be able to: ◦ Understand types of fractions. ◦ Convert improper fractions into mixed numbers. ◦ Write a fraction in lowest terms. ◦ Add, subtract, multiply and divide fractions. ◦ Convert decimals to fractions. ◦ Convert fractions to decimals.

Topics Understanding the types of fractions. ◦ Improper fractions and mixed numbers. ◦ Writing a fraction in lowest terms. ◦ Adding, subtracting, multiplying and dividing fractions. ◦ Converting decimals to fractions. ◦ Converting fractions to decimals.

Understanding the types of fractions A fraction represents part of a whole. Fractions are written in the form of one number over another, with a line between two numbers. The line, or bar between the top number and the bottom number means “divided by”. The top number is called the numerator, and the bottom number is called the denominator.

Types of fractions Proper fraction: Numerator smaller than denominator e.g. 2/3, ¾, 8/15 and 9/10 Improper fraction Numerator equal or greater than denominator e.g. 5/5, 11/5, 3/2 and 9/4  Mixed fraction  Whole number and proper fraction e.g.

Contd…

Converting fractions Mixed numbers to improper fractions A mixed number can be changed to an improper fraction as follows: Multiply the whole number by the denominator of the fraction. Add the numerator to that product. The resulting sum becomes the new fraction’s numerator. Put that sum (the new numerator) over the original fraction’s denominator.

Example

Contd… Improper fractions to mixed numbers To convert an improper fraction to a mixed number, divide the numerator of the improper fraction by the denominator, and place the remainder (if any) over the original denominator (the divisor). Example Convert 29/5 to mixed numbers

Contd… Writing a fraction in lowest terms If both the numerator and denominator of a fraction cannot be divided without remainder by any number other than 1, then the fraction is in lowest terms The lowest terms for 2/4 is ½

Contd… Adding and subtracting fractions Fractions with the same denominator are called like fractions. Such fractions have a common denominator. Addition and subtraction of fractions which have a common denominator can be done by applying the operation on both numerators. Example Add 3/5 and 1/5

3/5 + 1/5 = 4/5 Fraction with different denominators, are called unlike fractions. To add or subtract unlike fractions, a common denominator should be found or generated. Once a common denominator exists, apply the operation on both numerators.

Subtraction ½ - 2/3

Multiplying and dividing fractions  Multiplying proper or improper fractions Three steps are involved when multiplying proper and improper fractions: Multiply the numerators. Multiply the denominators. Reduce to lowest terms if necessary.

Multiplying mixed numbers To multiply mixed numbers, first convert them into improper fractions. Then proceed as with multiplication of proper fractions.

Dividing proper or improper fractions To divide proper or improper fractions, the followings steps should be observed: Invert the divisor or divisors (turned upside down). The divisor is the number by which we are dividing. The inverse of a number is referred to as its reciprocal. Proceed with multiplication.

Dividing mixed numbers Steps to divide mixed numbers are as follows: Convert all mixed numbers to improper fractions. Invert the divisor or divisors and change signs from division to multiplication. Proceed as in multiplication

Converting decimals to fractions Decimals can be converted to fractions. For example, 0.32 is properly read as “thirty-two hundredths”, which is the same as 32/100. Rules to convert decimals to fractions: Count the digits to the right of the decimal point. Place that many zeros in the denominator of the common fraction. Remove the decimal point from the number in the numerator position. Place a 1 in front of the zeros in the denominator position. Convert to a mixed number and/or reduce to lowest terms if necessary.

Converting fractions to decimals To convert a fraction to a decimal, divide the numerator of the fraction by the denominator

Lesson Summary This lesson explains the types of fractions and the calculations involving fractions. Calculation using fractions will be easier if you know how to simplify and convert fractions to decimals, and vice versa