Fraction Basics Richard Dunton University of Phoenix Online EDTC 560 Janet Wright August 25, 2004

We will learn to… Identify and write proper fractions Identify and write improper fractions and mixed numbers Create equivalent fractions Reduce fractions to lowest terms Raise fractions to higher terms

What is a proper fraction? A proper fraction stands for part of a whole or of a group The smaller number, the part, is on top and the larger number, the whole, is on the bottom The top number is called the numerator The bottom number is called the denominator

The whole maybe a single object… Count the number of equal parts in the circle. This number is the denominator and is equal to 4. Count the number of shaded parts. This is the numerator and is equal to 3 What fractional part of the circle is shaded?

That’s right… 3 parts of the circle are shaded… The circle is divided into 4 equal parts Read 3/4 as three-fourths Numerator → 3/4 ← denominator

Or it maybe a group of objects… What fraction of the group of circles is shaded?

Four out of five circles are shaded Numerator → 4/5 ← denominator Read as four-fifths

Writing improper fractions and mixed numbers In an improper fraction the numerator is equal to or larger than the denominator A mixed number has a whole number and a fraction part You may need to change an improper fraction to a whole or mixed number

Writing improper fractions The top number (numerator) stands for the number of shaded pieces The bottom number (denominator) stands for number of pieces in 1 whole…in this case four Therefore here we have 4/4 or 1 whole pizza pie

Writing improper fractions In an improper fraction there are more pieces then are defined by 1 whole Here each pie is divided into 5 equal parts What fraction do these two pies represent?

Writing improper fractions In the last example we have 9 parts The 2 pies divided into 5 equal portions There are 4 pieces more than 1 whole Therefore, we write it as 9/5, read as nine- tenths

Writing mixed numbers A mixed number is a whole number together with a fraction You can rewrite an improper fraction as a mixed number by dividing the denominator into the numerator and writing the remainder over the denominator Notice that 9/5 and 1 4/5 represents the same amount

Changing a mixed number to an improper fraction Using 1 4/5 as an example: Multiply the whole number by the denominator Add the numerator to it, and Put the total over the denominator 5 x / 5 = 9/5

Equivalent fractions Each of the circles represents 1 whole pizza pie In the first pie 1 of 2 equal parts is shaded; in the second 4 of 8 are shaded Both represent 1/2 of a pizza pie, as the same area is shaded in each circle Equivalent fractions are different fractions that represent the same amount

Renaming fractions to lowest terms Fractions are reduced to lowest terms by dividing both the numerator and denominator by the same number A fraction is in lowest terms when 1 is the only number that can divide evenly into both the numerator and the denominator

Reduce fractions to lowest terms In the equivalent fraction example 1/2 is the same as 2/4 We reduce the second fraction (2/4) by diving the numerator and denominator by 2 Therefore 2/4 = 2÷ 2/ 4÷ 2 = 1/2

Raising fractions to higher terms When you change a fraction to an equivalent fraction with a higher denominator, you raise it to higher terms To raise a fraction to higher terms, multiply both the numerator and denominator by the same number

Examples Multiply the numerator and denominator by 2 to raise each fraction to higher terms: 2/3 = 2 x 2 ∕ 2 x 3 = 4/6 3/5 = 3 x 2 ∕ 2 x 5 = 6/10 4/7 = 4 x 2 ∕ 7 x 2 = 8/14

We have learned to… Identify proper fractions Write improper fractions and mixed numbers Create equivalent fractions Reduce fractions to lowest terms Raise fractions to higher terms

Congratulations!!! We are now ready to learn how to add subtract, multiply an divide fractions