Exercise 1-
Expressions

Exercise 2-
Expressions
Ratios
The Distributive Property
New LESSON
Lesson 1-1 (p12)
Number Properties
100

#2, page 5

Sumin bought a pen and a book for $x. The pen cost $5. 

(a) Express the cost of the book in terms of x.

x - $5 = cost of book

The total cost - cost of pen = cost of book

OR

cost of pen + cost of book = total cost

$5  + cost of book = total cost or 

$5 + cost if book (x) = total 

100

#1a, page 8

1. Peter bought 6 mangoes at $x each. He also bought a papaya for $5.

(a) Express the total cost of the fruits in terms of x.


6x + 5

100

Express the following ratio is a fraction:

12 feet out of 30 feet

12/30 or 2/5

100

Indicate which property should be done first:

(3 * 4) + (3 * 6)

multiplication

100

There are certain rules of properties of math that are always true. The commutative properties of addition and multiplication stat that the order in which numbers are added or multiplied does not change the result.

For example:  a + b = b + a     and a * b = b * a

If a is 2 and b is 3, what is the result for addition and multiplication?

2 + 3 = 3 + 2; 5

2 * 3 = 3 * 2; 6


200

#2, page 5

Sumin bought a pen and a book for $x. The pen cost $5. 

(b) If x = 11, find the cost of the book.

$11 - $5 = $6 

cost of pen + cost of book = total cost

$5 + x = $11

200

1b, page 8

1b. Peter bought 6 mangoes at $x each. He also bought a papaya for $5.

(b) If x = 2, find the total cost of the fruits

6x + 5=

6(2) + 5=

12 + 5=

17

200

Express the ratio is a fraction then reduce:

3 dimes out of 18 dimes

3/18= 1/6

200

Indicate which operation should be done first: 

8 * (5 + 2)

addition

200

The associative properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

Associative Property of(+): (a + b) + c = a + (b + c)   

Associative Property of (*):  (a * b) * c = a * (b * c)

Example: What is the result for the associative property of addition and the associative property of multiplication if a = 3, b = 2, c = 1

Associative Property of Addition: 

(a + b) + c = a + (b + c)

(3 + 2) + 1 = 3 + (2 + 1)

5 + 1 = 3 + 3

6 = 6

Associative Property of Multiplication:

(a * b) * c = a * (b * c)

(3 * 2) * 1 = 3 * (2 * 1)

6 * 1 = 3 * 2

6 = 6

The addition and multiplication results being the same is just a coincidence

300

#2, page 5

Sumin bought a pen and a book for $x. The pen cost $5. 

(b) If x = 15, find the cost of the book

cost of pen + cost of book = total cost

$5   + $x =  $15

-$5               -$5

$x= $10

300

#1c, page 8

1. Peter bought 6 mangoes at $x each. He also bought a papaya for $5. 

(c) If x = 3, find the total cost of the fruits

6x + 5=

6(3) +5=

18 + 5=

=23

300

Express the ratio as a fraction. Then reduce:

There are 48 meters out of 80 meters

48/80 = 3/5 

(dividing 16 in both the numerator and denominator)


48/80 = 6/10= 3/5 

(first dividing by 8, then reducing more by dividing by 2)

300
Rewrite each expression using the distributive property:


5 * (3 + 5)

(3 * 4) + (3 * 3)

(5 * 3) + (5 * 5)


3 * (4 + 3)

300

The Identity Property of Addition states that the sum of an addend and 0 is the addend. 

For example 8 + 0 = 8

The Identity Property of Multiplication states that the product of a factor and 1 is that factor.

For example: 4 * 1 = 4

Which property is the following: 33 * 1

The Identity Property of Multiplication

400

#5h, page 7

5. Find the value of each of the following expressions when n = 15.

(h) 5n =

5(15) = 75

400

#3d, page 9

Find the value of each of the following expressions when k = 6

(d) 10 - (2k)/3

12/3

4

400

Express the ratio as a fraction and then a colon:

There are 16 dogs and 21 cats in the adoption fair. Write the ratio of dogs to cats.

16/21,  16:21

400

Write the missing number:

(8 * 2) + (n * 3) = 8 * (2 + 3)

n=?

n = 8

400

The Properties of Zero state that the product of a factor and 0 is 0 and that quotient(the answer) of zero and any non-zero divisor(the number dividing into the dividend) is 0.

For example: 3 * 0 = 0  and 0 / 5 = 0

What is the quotient of 0 / 18

0

500

#5j, page 7

5j. Find the value of each of the following expressions when n = 15.


n/ (45)

(15)/(45)= 1/3

500

3f,j, page 9

(f) k - [(k)/6]=

     6 - (6)/6



(f)k - (k) - 6=                     (j) = 3k^2 + 20=

6 - [(6)/6] =                               3(6)^2 +20=

6 - 1 =                                        (18*18) + 20=

=5                                                =324 + 20=                                                            =344

500

Express the ratio as a fraction and with a colon:

There are 16 bees and 24 butterflies in the garden. Write the ratio of butterflies to bees.

24/16, 24:16

500

Replace a with 3, b with 4, and c with 6. Then find the value of the expression:

(b * a) + (b * c)

Then rewrite the above expression (using the letters) using the distributive property

(4 * 3) + (4 * 6)

= 12 + 24

=36


b * (a + c)

500

Name the property:

1. (3 * 2 ) * 6 = (3 * ( 2 * 6)

2. 0 / 12 = 0

3. 7 + 2 + 12 = 12 + 2 + 7

1. Associative Property of Multiplication

2. Properties of Zero

3. Commutative Property of Addition  

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