4-3 Equivalent Expressions

Warm Up Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

4-3 Equivalent Expressions

Warm UpFind the GCF of each set of numbers.

1. 12 and 50 3. 30, 45 and 30

2. 18 and 30 4. 16, 24 and 30

5. 72, 80 and 96

2 15

6 2

8

4-3 Equivalent Expressions

Problem of the DayErin takes half of the cherries from a bowl. Then her brother takes half of the remaining cherries. Finally, Diego takes 3 of the remaining cherries. This leaves 4 cherries in the bowl. How many cherries were in the bowl to start?

28 cherries

4-3 Equivalent Expressions

I can factor numerical and algebraic expressions and write equivalent numerical and algebraic expression.

4-3 Equivalent Expressions

Vocabulary

term

coefficient

equivalent expressions

4-3 Equivalent Expressions

The terms of an expression are the parts of the expression that are added or subtracted. The terms of the expressions 140+4x are 140 and 4x.

You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

In the term 4x, 4 is called the coefficient. A coefficient is the number that is multiplied by a variable in a algebraic expression.

4-3 Equivalent Expressions

Equivalent expressions are expressions that have the same value for all the values of the variables. The expressions 15x+18 and 3(5x+6) are equivalent expressions since 15x+18=3(5x+6) for every value of x.

4-3 Equivalent Expressions

The greatest common factor (GCF) is the largestcommon factor of two or more given numbers.

Remember!

4-3 Equivalent Expressions

Additional Example 1: Factoring Numerical Expressions

Factor the sum of terms as a product of the GCF and a sum.

3.3.3+3.13

27+39

27+39

3(9+13)

The terms are 27 and 39

The GCF of the terms is 3

Rewrite each term as a product with GCF

3.9+3.13

Apply the distributive law

4-3 Equivalent Expressions

Check It Out: Example 1

Factor the sum of terms as a product of the GCF and a sum.

3.5+3.3.5

15+45

27+39

15(1+3)

The terms are 15 and 45

The GCF of the terms is 15

Rewrite each term as a product with GCF

1.15+3.15

Apply the Distributive property

4-3 Equivalent Expressions

Additional Example 2: Factoring Algebraic Expressions

Factor the sum of terms as a product of the GCF and a sum.

12b + 28

12b + 28

2.2.3.b+2.2.7

4.3b + 4.7

4(3b+7)

The terms are 12b and 28

The GCF of the terms is 2.2

Rewrite each term as a product with GCF

Apply the Distributive law

4-3 Equivalent Expressions

Check It Out: Example 2

Factor the sum of terms as a product of the GCF and a sum.

2.2.2.2.b+2.2.2.2.2

16b+32

16b+32

16(b+2)

The terms are 16b and 32

The GCF of the terms is 2.2.2.2

Rewrite each term as a product with GCF

16.b+16.2

Apply the distributive property

4-3 Equivalent Expressions

There are many other ways to write equivalent expressions for each of the expressions in Example 3.

Helpful Hint

4-3 Equivalent Expressions

Additional Example 3: Writing Equivalent Expressions

Write four equivalent expressions for each given expression.

A. 9+15

9+15

3(3+5)

3.3+3.5

3(5+3)

3(8)

The terms are 9 and 15Rewrite each term as a product with GCF

Apply the Commutative property

Apply the Distributive property

Add

4-3 Equivalent Expressions

Continued: Example 3

B. 25m-5m

25m-5m

(5-1)5m

5.5m-1.5m

4.5m

20m

The terms are 25m and 1m

Rewrite each term as a product with common factor 5m

Subtract

Apply the Distributive property

Multiply

4-3 Equivalent Expressions

C. 2(4p+2)

2(4p+2)

8p+4

2.4p+2.2

4+8p

4+23p

Apply the Distributive property

Apply the Commutative property

Multiply

Write the coefficient of 8 as 23

Continued: Example 3

4-3 Equivalent Expressions

Check It Out: Example 3

Write four equivalent expressions for each given expression.

3(9p+3)

3(9p+3)

27p+9

3.9p+3.3

9+27p

9+33p

Apply the Distributive property

Apply the Commutative property

Multiply

Write the coefficient of 27 as 33

4-3 Equivalent Expressions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

4-3 Equivalent Expressions

Lesson Quiz

Factor the sum of terms as a product of the GCF and a sum

15(3+1)1. 45 + 15

2. 24 + 40 8(3+5)

4(4y+9)

30(3+2s)

3. 16y + 36

4. 90 + 60s

4-3 Equivalent Expressions

Continued: Lesson Quiz

5. 20 - 8

6. 9z + 12

2(10-4); 4(5-2); 4.3; 12

3(3z+4); 3(4+3z); 32z+12; 12+9z

Write four equivalent expressions for each given expression.

4-3 Equivalent Expressions

Lesson Quiz for Student Response Systems

1. Factor the sum of terms as a product of the GCF and a sum

60+30

A. 60(1+2)

B. 90

C. 30(2)

D. 30(2+1)

Lesson Quizzes

4-3 Equivalent Expressions

Continued: Lesson Quiz for Student Response Systems

2. Factor the sum of terms as a product of the GCF and a sum

13+39r

A. 13(1+3r)

B. 13(1+3)

C. 13(3r)

D. 42r

4-3 Equivalent Expressions

Continued: Lesson Quiz for Student Response Systems

3. Which expression is not equivalent to 12-3?

A. 3(4-1)

B. 3(22-1)

C. 3.4-3

D. 3(1-3)

4-3 Equivalent Expressions

Continued: Lesson Quiz for Student Response Systems

4. Which expression is not equivalent to 8z+12?

A. 8z+4.3

B. 4(2z+3)

C. 4(2z+12)

D. 4(3+2z)