unit 1; part 2: using factors for fractions and solving problems

Unit 1; Part 2:Using Factors for

Fractions and Solving Problems

You need to be able to findthe GCF, LCM and solveproblems using them.

Advanced Homework Answerspp. 199-200

3. 9 is not prime. 39. 721. 22 · 32 40. 32

23. 32 · 11 41. 52

25. 2 · 3 · 5 · 7 44. 120 ft2

27. 2 · 32 · 7 45. 23 · 3 · 529. Composite 46. 2 by 3 or 2 by 531. 2 · 2 · 5 · p · q 47. 20 2x3’s or 12 2x5’s33. 7 · 7 · y · y 48. Prime if n = 1; 35. 2 ·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 FractionsAssignment – pp. 205-206;

#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.

GCF & Simplified Fractions

GCF & Simplified Fractions

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.

GCF & Simplified Fractions

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.

GCF

24 6012 30 6 15

2 5

2))2)3

GCF= 2x2x3=12

24 260 5

GCF

300 18150 9 50 3

2))3

GCF=2x3=6

GCF

625 30125 6

5)

GCF=5

GCF of 3 Numbers

The GCF works the same way with 3 numbers.

You are done when there are no common factors for ALL 3 numbers.

GCF of 3 Numbers

18 42 60 9 21 30 3 7 10

2))3

GCF=2x3=6

GCF of 3 Numbers

56 14 7028 7 35 4 1 5

2))7

GCF=2x7=14

GCF of 3 Numbers

200 120 180100 60 90 50 30 45

10 6 15

2))2)5

GCF=2x2x5=20

GCF of 3 Numbers

12 18 28 6 9 14

2)

GCF=2

GCF of 3 Numbers

32 80 96 16 40 48

8 20 24 4 10 12 2 5 6

2))2)2

GCF=24=16

)2

Find the GCF of 28 and 42.

So, the GCF is 14.

Simplify Fractions• Simplify .

You also can use the old way to simplify.

3075

Answer: 23

Find the GCF of 18 and 45.

Answer: 9

Write in simplest form.

Answer: written in simplest form is

Find the GCF of 20 and 32.

Answer: 4

Write in simplest form.

Answer:

Write in simplest form.

Answer:

Find the GCF of 24 and 36.

Answer: 12

Write in simplest form.

Answer: written in simplest form is

MARBLES In a bag of 96 marbles, 18 of the marbles are black. Write the fraction of black marbles in simplest form.

Answer:

ALGEBRA Find the GCF of

Answer: 7mn

ALGEBRA Find the GCF of 12p2 and 30p3.

Answer: The GCF is 2

Find the GCF of the numbers, then take the highest exponent they have in common.

Find the GCF of 21, 42, and 63.

Answer: The GCF is 3 7, or 21.

Find the GCF of 24, 48, and 60.

Answer: 12

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.

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

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 1

1-1. Fraction to DecimalTop divided by bottom.

1-2. Terminating DecimalDivides evenly with no remainder.

1-3. Repeating DecimalDecimal places repeat over and

over.1-4. Bar Notation

A line over decimals to show that they repeat.

Advanced Homework Answerspp. 205-206 & 209

9. 6 38. D 26. 1/411. 5 40. 10s 27. 3/413. 24 9. 5/7 28. 2/1515. 8 11. 7/10 30. A17. 6 13. 4/7 32. 2319. 7 15. 6/7 33. 2 · 32 · 5 · 727. 9b 17. 132. 4 inches 19. 5/633. No only 16 4” pieces–need 18