Lesson 4.1, For use with pages 175-180

2. 75 ÷ 51. 52 ÷ 13

Please do not use a calculator to solve these.

Lesson 4.1, For use with pages 175-180

ANSWER 4 ANSWER 15

2. 75 ÷ 51. 52 ÷ 13

Please do not use a calculator to solve these.

Essential Questions

1. What is the value of studying fractions?

2. What is the relationship between good number sense and working with fractions?

Simplifying Fractions

Section 4.3

P. 187 - 191

Simplest Form

• When the only common factor of the numerator and denominator is 1, the fraction is in simplest form.

34

34÷

11 =

• In this section you will be REVIEWING the concept of simplifying fractions to lowest terms

• You will use the GCF skills to simplify fractions.

• You will also use the GCF skills to simplify algebraic fractions.

• The GCF is the largest number of two or more numbers that is a common factor.

• For example – if we look at the factors for:

12 = 1, 2, 3, 4, 6, 12

20 = 1, 2, 4, 5, 10, 20

Common factors are 1,2,4. The GCF is 4.

A method to find GCF is using the “box” or “division box” method.

84120

Divide out until the numbers at the top are “relatively prime”. Relatively prime means “no common factors besides the number one.” (critical vocabulary word)

•GCF: 12

• Find the GCF for 120 and 84

We can use GCF to simplify fractions.• Using the division box, we found the GCF of 120

and 84 is 12.• Think of 120 and 84 as the fraction 120/84. Use

the division box and divide out common factors until the top two numbers are relatively prime.

• That is your fraction in simplest form. • So 120/ 84 simplifies to 10/7 or 1 3/7.

12 120 84

10 7

• You have also simplified fractions like this before:

• Either method is fine to use.

• Tip: Use your divisibility rules to determine what numbers you can divide by.

120 84

= 107

120 ÷ 12 84 ÷ 12

= = 137

Simplify the fraction 27/96•Hint: What number are both 27 and 96 divisibly by?• 3 because the sum of 2 +7 and 9 + 6 are both divisible by 3.

27 9627

96=

Simplify this fraction

1218

23÷ 6

6 =

Simplify this fraction

921

37÷ 3

3 =

Simplify this fraction

-1220

-35÷ 4

4 =

Simplify this fraction

1216

34÷ 4

4 =

Simplify this fraction

-1016

-58÷ 2

2 =

Vocabulary• Monomial: a number, a variable, or a product of a

number and one or more variables.• Factor a Monomial: write it as a product of prime

numbers and variables with exponents of one.

EXAMPLE 4 Factoring a Monomial

Factor the monomial 12x2y.

Factor 12.

Write x2 as x x.

12x2y =

= 2 2 3 x x y

2 2 3 x2 y

GUIDED PRACTICE for Example 4

10. 3mn

Factor the monomial.

3mn = 3 m n

11. 18t2

Factor 18.18t2 = 2 3 3 t2

= 2 3 3 t t Write t2 as t t.

GUIDED PRACTICE for Example 4

13. 54w3z4

Factor the monomial.

54w3z4 = 2 3 3 3 w3 z4

= 2 3 3 3 w w w z z z z

Factor 54.

Write z4 as z z z z

Write w3 as w w w= 2 3 3 3 w w w z4

Simplifying fractions with monomials

• Factor the numerator and denominator

• Divide out common factors

EXAMPLE 4 use the GCF skills to simplify algebraic fractions

14x7xy

= 2 · 7 · x7 · x · y

Factor numerator and denominator.

Divide out common factor.

Simplify.= 2y

2 ·7 ·x7 ·x ·y

=

1

1

1

1

EXAMPLE 5 use the GCF skills to simplify algebraic fractions

Evaluate powers and simplify.

Factor numerator and denominator.

Simplify.

Simplify and then evaluate the expression when x = 5.–4x3

2x

–4x3

2x

Divide out common factor.

Substitute 5 for x.

= –2x2

= –2(5)2

= –50

–1 ·2 ·2 ·x ·x· x2 ·x

=

1

1

1

1

=–1 · 2 · 2 · x · x · x

2 · x

GUIDED PRACTICEuse the GCF skills to simplify algebraic fractions

Simplify the variable expression. Then evaluate for x = – 2 and y = 3.

Simplify.

Simplify.

12.

4xy6x

Divide out common factor.

Substitute 3 for y.

= 2

Factor numerator and denominator.= 2 · 2 · x · y

2 · 3 · x

=2y3

=2(3)

3

=–1· 2 ·2 ·x ·y

2 ·3 · x

1

1

1

GUIDED PRACTICEuse the GCF skills to simplify algebraic fractions

Simplify the variable expression. Then evaluate for x = – 2 and y = 3.

Simplify.

13.

32x8xy

Divide out common factor.

Substitute 3 for y.

Factor numerator and denominator.

= 4y

= 2 · 2 · 2 · 2 · 2 · x2 · 2 · 2 · x · y

1 1 1 1

1 1 1 1

= 43

= 2 · 2 · 2 · 2 · 2 · x2 · 2 · 2 · x · y

GUIDED PRACTICEuse the GCF skills to simplify algebraic fractions

Simplify the variable expression. Then evaluate for x = – 2 and y = 3.

Simplify.

15.

5x2y10xy

Divide out common factor.

Substitute –2 for x.

Factor numerator and denominator.

= x2

= –2 2

= 5 · x · x · y 2 · 5 · x · y

Simplify.= –1

= 5 · x · x · y 2 · 5 · x · y1 1 1

1 1 1

• Assignment:

• P. 189 #3-12, 26-29

• Put some work/steps on your paper – NOT JUST THE ANSWER!!!

• Make sure you follow directions.