FRACTIONS

Fractions have numerators and denominators Fractions represent the division of the numerator by the denominator or it ’ s the same as 4 divided by 5 The numerator is the top number or tells us how many such pieces are being considered. The denominator is the bottom number or tells us how many congruent (equal) pieces the whole is divided into. numerator denominator

What is a fraction? Fractions are one or more parts of a whole that is divided into equal parts. Fractions can represent numbers less than 1, equal to 1, or greater than 1. The whole can be broken up into regions, sets, or segments.

How does the denominator control a fraction? If you share a cake evenly among two people, you will get If you share a cake evenly among three people, you will get If you share a cake evenly among four people, you will get Conclusion: The larger the denominator the smaller the pieces, and if the numerator is kept fixed, the larger the denominator the smaller the fraction!!!

Equivalent fractions: are fractions that represent the same amount but they have different numerators and denominators. You can multiply or divide the numerator and denominator by the same number to get an equivalent fraction. In the following picture we have ½ of a cake because the whole cake is divided into two equal parts and we have only one of those parts. =X

Find the Equivalent Fraction Multiply the numerator and the denominator by the same number x= or you can also divide the numerator and the denominator by the same number ÷ 4 4 = 1 3

Equivalent Fractions 1 2 = What number was multiplied by the numerator and the dominator to get the new equivalent fraction?

Make An Equivalent Fraction Find the Missing Numerator! Given the new denominator, can you find the missing numerator? x 4

Make An Equivalent Fraction Find the Missing Numerator! Given the new denominator, can you find the missing numerator? x 9

Given the new denominator, can you find the missing numerator? Make An Equivalent Fraction Find the Missing Numerator! x 4

Make Equivalent Fractions Find the Missing Numerators!

Find a new Equivalent fraction by multiplying the numerator and dominator by the same number 1/3 = 2/7= 5/6= 5/10= 9/18= 12/24= 30/40 3/8 =

Putting Fractions in Simplest Form A fraction is in its lowest terms is reduced or simplified if we cannot find a whole number that can divide into both its numerator and denominator. Reducing a fraction in lowest terms gives you its equivalent fraction with the lowest possible numerator and denominator. Steps to Reducing Fractions or putting fractions into Simplest Forms: 1.Find the GCF of the numerator and the denominator. 2.Divide the GCF into both the numerator and the denominator to get the fraction in simplest form. 6= 1, 2, 3, 6 10= 1, 2, 5, 10 2 is the GCF so divide 2 into the numerator and the dominator to get the fraction in simplest forms. = 3 5

Simplify Fractions Divide both numerator and denominator by the Greatest Common Factor Factors are 1, 2, 4, 7, 14, 28 Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48, 72 Greatest Common Factor is ÷ ÷ 4 4 = = 7 18 So = 7 18

10= 1, 2, 5, 10 60= 1, 2, 3, 4, 6,10, 30, is the GCF and can be divided into both 10 and = 1,11 23= 1, 23 1 is the GCF and so this fraction is already in simplest form. Fractions in Simplest Forms: Remember to first find the GCF, then divide. 35= 1, 5, 7, 35 40= 1,2, 4,10, 20, 40 5 is the GCF and divides into both 35 and 40.

Simplification - Let ’ s Try It! = = = = 21 7 = 15 6 =

Simplify/Reduce the Fractions 8/32 = 7/56 = 24/36 32/48 =

Comparing Fractions with Like Denominators > Susan walks a greater distance That makes sense because 7 of something is more than 5 of something > 5so Comparing fractions with like denominators is a lot like comparing whole numbers EXAMPLE: EXAMPLE: George walks mile to school. Susan walks mile. Who walks the greater distance? When fractions have the same denominator, compare the numerator.

The fractions 1414 and 3434 have the same denominator. Fractions with the same denominators are Fractions with Like Denominators like fractions.

Compare. Write, or =. 4 6 __ < From the model, <. 4 6 __ 6 5

Compare. Write, or =. 6 7 __ > From the model, >. 6 7 __ 7 4

Sometimes you can compare fractions just by looking at them 1212 > 1414 I’ll take 1212