Get papers sit down get out homework &quietly work on bellringer Solve Using ladder to find GCF LCM and simplify fraction 72 and 56

Ch 2-3 Simplifying Fractions c2

Identify the fraction below. Number of parts shaded total parts available Numerator Denominator

Equivalent Fractions Fractions

Models of Equivalent Fractions Check out don’t write

Halves Check out don’t write

The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1.

Use multiples to write Equivalent Fractions Multiply the numerator and the denominator by the same number. Multiply the numerator and the denominator by the same number x = Write under Use multiples to write equivalent fractions

Use multiples to write Equivalent Fractions Multiply the numerator and the denominator by the same number. Multiply the numerator and the denominator by the same number x = Write under Use multiples to write equivalent fractions

Equivalent Fractions therefore are: Equivalent Fractions therefore are: = = Write under Use multiples to write equivalent fractions

Use Common Factors to write Equivalent Fractions Divide the numerator and the denominator by the same number. Divide the numerator and the denominator by the same number ÷ = Write under Use common Factors to write equivalent fractions

Use Common Factors to write Equivalent Fractions Divide the numerator and the denominator by the same number. Divide the numerator and the denominator by the same number ÷ = Write under Use common Factors to write equivalent fractions

Equivalent Fractions therefore are: Equivalent Fractions therefore are: = = Write under Use common Factors to write equivalent fractions

Determining if fractions are equivalent 1. Cross multiply. 2. Compare the products ‐ 1. If the cross product are equal, the fractions are equivalent. If the cross products are not equal, the fractions are not equivalent. If the cross products are not equal, the fractions are not equivalent.

Equivalent or not?

Simplest form When the only common factor of the numerator and denominator is 1, the fraction is in simplest form ÷ 1 1 = Yes it’s in the simplest form No it’s not in the simplest form

How to Find the Simplest Form of a Fraction Find the greatest common factor of the numerator and the denominator and divide both the numerator and the denominator by that number ÷ 3 3 =

You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3 which is the greatest common factor. 12 of the 15 boxes are shaded. 4 of the 5 boxes are shaded. The same total area is shaded =

Simplify or Reduce This Fraction ÷ 12 = GCF is 12

Use the Ladder for Simplifying Fractions  WRITE the two numbers on one line.  DRAW THE L SHAPE  DIVIDE out common prime numbers starting with the smallest = 3 2 Simplified fraction is on the bottom

Homework Pg. 84 # 2-32 evens only (show your work) Pg. 84 # 2-32 evens only (show your work) 8-14 use multiples which means the denominators should be larger than the original fraction 8-14 use multiples which means the denominators should be larger than the original fraction use common factors which means the denominators should be smaller than the original fraction use common factors which means the denominators should be smaller than the original fraction simplify using ladder or GCF simplify using ladder or GCF

Simplifying Fractions Example a.Write 63 / 105 in simplest form. 63 = The GCF of 63 and 105 is 3*7 or 21 1.Divide the numerator and the denominator by Since the GCF of 3 and 5 is 1, the fraction is in simplest form.

Example 1 You are working on a 60- problem math assignment. You have completed 35 problems so far. Write a fraction in simplest form for the number of problems that are NOT yet completed. You are working on a 60- problem math assignment. You have completed 35 problems so far. Write a fraction in simplest form for the number of problems that are NOT yet completed.

Example 2 A bag of 24 balloons contains 15 blue balloons. A larger bag of 60 balloons has 38 blue balloons. For each bag of balloons, write a fraction in simplest form comparing the number of blue balloons to the TOTAL number of balloons. A bag of 24 balloons contains 15 blue balloons. A larger bag of 60 balloons has 38 blue balloons. For each bag of balloons, write a fraction in simplest form comparing the number of blue balloons to the TOTAL number of balloons. Are the fractions equivalent? Are the fractions equivalent?

Example 3 At a pet store, there are 18 rabbits. 3 of the rabbits are purple. What fraction of the rabbits are NOT purple? (REDUCE!) At a pet store, there are 18 rabbits. 3 of the rabbits are purple. What fraction of the rabbits are NOT purple? (REDUCE!)