Unit 1; Part 2: Using Factors for Fractions and Solving Problems You need to be able to find the GCF, LCM and solve problems using them.

Advanced Homework Answers pp is not prime · · · 3 · 5 · ft · 3 2 · · 3 · Composite46. 2 by 3 or 2 by · 2 · 5 · p · q x3’s or 12 2x5’s · 7 · y · y48. Prime if n = 1; ·2 ·2 ·2 ·3 ·a ·a ·b ·b Composite if n > 1 since 2 is a factor of each.

Unit 1, Lesson 9 Advanced – GCF and Simplify Fractions Assignment – pp ; #9-19 odd, 27, 32, 33, 38, & 40. p. 209; #9-19 odd, #26-28, 30, 32 & 33.

1. GCF is the largest factor that will divide evenly into all the original numbers. 2. Use the ladder to find the GCF. 3. Divide by the primes, IN ORDER, that go into BOTH numbers.

 Follow the same procedure as before, but look for primes that go into both numbers.  You are through when you run out of common factors.  The numbers down the side are multiplied to make the GCF.

 Two numbers with nothing in common have a GCF of 1.  A simplified fraction has a numerator and a denominator with a GCF of 1.  So, the numbers on the bottom of the ladder make the simplified fraction.

) ) 2 ) 3 GCF= 2x2x3=12

) ) 3 GCF=2x3=6

) GCF=5

 The GCF works the same way with 3 numbers.  You are done when there are no common factors for ALL 3 numbers.

) ) 3 GCF=2x3=6

) ) 7 GCF=2x7=14

) ) 2 ) 5 GCF=2x2x5=20

) GCF=2

) ) 2 ) 2 GCF=2 4 =16 ) 2

Example 2-1a Find the GCF of 28 and 42. So, the GCF is 14.

Simplify Fractions Simplify. You also can use the old way to simplify. Answer:

Example 2-1b Find the GCF of 18 and 45. Answer: 9

Example 3-1a Write in simplest form. Answer: written in simplest form is

Example 2-2a Find the GCF of 20 and 32. Answer: 4

Example 3-1b Write in simplest form. Answer:

Example 3-2b Write in simplest form. Answer:

Example 2-2b Find the GCF of 24 and 36. Answer: 12

Example 3-2a Write in simplest form. Answer: written in simplest form is

Example 3-3b MARBLES In a bag of 96 marbles, 18 of the marbles are black. Write the fraction of black marbles in simplest form. Answer:

Example 2-4b ALGEBRA Find the GCF of Answer: 7mn

Example 2-4a ALGEBRA Find the GCF of 12p 2 and 30p 3. Answer: The GCF is 2 Find the GCF of the numbers, then take the highest exponent they have in common.

Example 2-3a Find the GCF of 21, 42, and 63. Answer: The GCF is 3  7, or 21.

Example 2-3b Find the GCF of 24, 48, and 60. Answer: 12

Example 2-5a ART Searra wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. What is the length of the side of the squares she should use? The largest length of side possible is the GCF of the dimensions of the tag board. The GCF of 15 and 25 is 5. Answer: Searra should use squares with sides measuring 5 centimeters.

Example 2-5b TABLE TENNIS: Rebecca has 20 table tennis balls and 16 paddles. She wants to sell packages of balls and paddles bundled together. What is the greatest number of packages she can sell with no leftover balls or paddles? How many balls and how many paddles will be in each package? Answer: 4 packages; 5 balls and 4 paddles

Example 2-5b TABLE TENNIS: Rebecca (from the last problem) is going to tie the packages with string. If she has 2 yards of string, how many inches of string will she use for each package? Answer: 18 inches

Note Cards for Unit 1-Lesson Fraction to Decimal Top divided by bottom. 1-2.Terminating Decimal Divides evenly with no remainder. 1-3.Repeating Decimal Decimal places repeat over and over. 1-4.Bar Notation A line over decimals to show that they repeat.

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End of Lesson 2

Advanced Homework Answers pp & D26. 1/ s27. 3/ /728. 2/ /1030. A / / · 3 2 · 5 · b inches19. 5/6 33. No only 16 4” pieces–need 18