Exercise 1-
Expressions
#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
#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
Express the following ratio is a fraction:
12 feet out of 30 feet
12/30 or 2/5
Indicate which property should be done first:
(3 * 4) + (3 * 6)
multiplication
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
#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
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
Express the ratio is a fraction then reduce:
3 dimes out of 18 dimes
3/18= 1/6
Indicate which operation should be done first:
8 * (5 + 2)
addition
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
(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
#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
#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
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)
5 * (3 + 5)
(3 * 4) + (3 * 3)
(5 * 3) + (5 * 5)
3 * (4 + 3)
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
#5h, page 7
5. Find the value of each of the following expressions when n = 15.
(h) 5n =
5(15) = 75
#3d, page 9
Find the value of each of the following expressions when k = 6
(d) 10 - (2k)/3
12/3
4
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
Write the missing number:
(8 * 2) + (n * 3) = 8 * (2 + 3)
n=?
n = 8
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
#5j, page 7
5j. Find the value of each of the following expressions when n = 15.
n/ (45)
(15)/(45)= 1/3
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
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
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)
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