Fraction Review

What is a Fraction? A fraction is formed by dividing a whole into a number of parts I’m the NUMERATOR. I tell you the number of parts I’m the DENOMINATOR. I tell you the name of part

Mixed numbers to improper fractions Convert whole numbers to thirds Mixed number Improper fraction

Another Way to change Mixed Numbers to improper fractions In short 5x3+2=17 Since 5/5=1 there are 5 fifths in each whole. So 3 wholes will have 3x5=15 fifths. Plus the 2 fifths already there makes a total of 15+2=17 fifths

Equivalent fractions An equivalent fraction is one that has the same value and position on the number line but has a different denominator Equivalent fractions can be found by multiplying by a special form of 1

Multiplying By a Special Form of One Why does it work? Multiplying any number by 1 does not change the value 4x1=4, 9x1=9 ………. Any number divided by itself =1. Multiplying a fraction by a special form of one changes the numerator and the denominator but DOES NOT CHANGE THE VALUE

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Finding equivalent fractions Convert 5ths to 20ths That’s 4 so I must multiply by What do we multiply 5 by to get a product of 20? Special form of 1

Simplifying Fractions: Cancelling Simplifying means finding an equivalent fraction with the LOWEST denominator by making a special form of 1 equal to 1 1 Another way of doing this

Adding and Subtracting Fractions

Adding Fractions with common denominators

Adding Fractions with different denominators Problem: You can’t add fractions with different denominators without getting them ready first. They will be ready to add when they have common denominators Solution: Turn fractions into equivalent fractions with a common denominator that is find the Lowest Common Multiple (LCM) of the two denominators

Finding the Lowest Common Denominator The lowest common multiple of two numbers is the lowest number in BOTH lists of multiples Multiples of 2 are 2, 4, 6, 8, 10…… Multiples of 3 are 3, 6, 9, 12, ……… What is the lowest common multiple?

You can’t add fractions with different denominators + The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths Special form of 1

Lowest common denominator is 10 so make all fractions tenths

Turn both fractions into twelfths

What is the lowest number BOTH 3 and 7 divide into? Finally the fractions are READY to add. I just have to add the numerators 9+14=23 It is 3/3 So I multiply 3/7 by 3/3 It is 7/7 So I multiply 2/3 by 7/7 What is the lowest number BOTH 3 and 7 divide into? Hmmmmm?????? What special form of 1 will change 7 to 21. Hmmmm? What special form of 1 will change 3 to 21. Hmmmm? It is 21. So that is my common denominator Now 3x3=9 and 2x7=14 Now I know the new numerators

Adding Mixed Numbers Separate the fraction and the whole number sections, add them separately and recombine at the end