Chapter Two Test Review: Multiplying & Dividing Decimals
Lesson 2-1: Multiplication Properties
There are five properties of multiplication introduced in this section. They are
1. The Commutative Property
ORDER DOES NOT MATTER! 3*5=5*3 7*8=8*7 therefore a*b=b*a ORDER DOES NOT MATTER!
2. The Zero Property
Any number multiplied by zero equals zero, therefore n * 0= 0
3. The Identity Property
Any number multiplied by one equals that number. 3*1=3 6*1=6 therefore a*1=a
4. The Associative Property
GROUPING DOES NOT MATTER! (2*3)*4= 2*(3*4) therefore a*(b*c)=(a*b)*c GROUPING DOES NOT MATTER!
5. The Distributive Property
*View the Diagram below for a explanation of the distributive property and proof that it works!
COMPLETE PROBLEMS
#7, #10, #12 on page 76 (SET A)
There are five properties of multiplication introduced in this section. They are
1. The Commutative Property
ORDER DOES NOT MATTER! 3*5=5*3 7*8=8*7 therefore a*b=b*a ORDER DOES NOT MATTER!
2. The Zero Property
Any number multiplied by zero equals zero, therefore n * 0= 0
3. The Identity Property
Any number multiplied by one equals that number. 3*1=3 6*1=6 therefore a*1=a
4. The Associative Property
GROUPING DOES NOT MATTER! (2*3)*4= 2*(3*4) therefore a*(b*c)=(a*b)*c GROUPING DOES NOT MATTER!
5. The Distributive Property
*View the Diagram below for a explanation of the distributive property and proof that it works!
COMPLETE PROBLEMS
#7, #10, #12 on page 76 (SET A)
Lesson 2-2: Multiplying Whole Numbers & Decimals
When multiplying decimals by decimals or whole numbers remember to count the number of decimal places in both factors in order to determine the number of decimal places in the product.
For ex.
1. 20 (zero decimal places) * 15 (zero decimal places) = 300 (zero decimal places)
2. 0.02 (two decimal places) * 1.5 (one decimal place) = .300 (two+one = three decimal places)
3. 0.2 (one decimal place) * .015 (three decimal places) = .0030 (one + three = four decimal places)
NOTE: Add zeros as decimal places when needed
COMPLETE PROBLEMS
#1, #5, #10 on page 76 (SET B)
Lesson 2-4/2-5: Dividing by Whole Numbers, Dividing a Decimal by a Decimal
1. When dividing a decimal by a whole number PLACE the decimal point in the quotient first. It should be directly over the decimal point in the dividend. After the decimal is placed, complete the long division problem.
2. When dividing a decimal or whole number by a decimal, multiply the divisor by 10 until it is a whole number. In other words shift the decimal to the right until the divisor is a whole number. You must then multiply the dividend by the same power of ten.
For example 345/23.8 Shift the decimal in 23.8 to the right one time. 23.8 becomes 238. You must then shift the decimal of the dividend once to the right as well. Therefore 345 would become 3450. Then complete the long division problem.
For example 760.56/0.234 Shift the decimal in 0.234 to the right three times. 0.234 becomes 234. You must then shift the decimal of the dividend three times to the right as well. Therefore 760.56 would become 760560. Then complete the long division problem.
COMPLETE PROBLEMS
#1, #6 (SET C)
#3, #5 (SET D)
on page 77
Lesson 2-7: Solving Multiplication & Division Equations
Division and Multiplication are inverse operations. Therefore to solve a one-step problem involving one of these operations, you must use the other.
For example
3x=12 3 is being multiplied times x to equal 12
3x/3=12/3 work backwards! Instead of multiplying divide both sides by three
x=4 SOLVE!
5x=25 5 is being multiplied times x to equal 25
5x/5=25/5 work backwards! Instead of multiplying divide both sides by five
x=5 SOLVE!
x/2=12 x is being divided by 2 to equal 12
(2)x/2=12(2) work backwards! Instead of dividing, multiply both sides by two
x=24 SOLVE!
x/10=12 x is being divided by 10 to equal 12
(10)x/10=12(10) work backwards! Instead of dividing, multiply both sides by ten
x=120 SOLVE!
COMPLETE PROBLEMS
#2-#6 (SET E)
on page 77
When multiplying decimals by decimals or whole numbers remember to count the number of decimal places in both factors in order to determine the number of decimal places in the product.
For ex.
1. 20 (zero decimal places) * 15 (zero decimal places) = 300 (zero decimal places)
2. 0.02 (two decimal places) * 1.5 (one decimal place) = .300 (two+one = three decimal places)
3. 0.2 (one decimal place) * .015 (three decimal places) = .0030 (one + three = four decimal places)
NOTE: Add zeros as decimal places when needed
COMPLETE PROBLEMS
#1, #5, #10 on page 76 (SET B)
Lesson 2-4/2-5: Dividing by Whole Numbers, Dividing a Decimal by a Decimal
1. When dividing a decimal by a whole number PLACE the decimal point in the quotient first. It should be directly over the decimal point in the dividend. After the decimal is placed, complete the long division problem.
2. When dividing a decimal or whole number by a decimal, multiply the divisor by 10 until it is a whole number. In other words shift the decimal to the right until the divisor is a whole number. You must then multiply the dividend by the same power of ten.
For example 345/23.8 Shift the decimal in 23.8 to the right one time. 23.8 becomes 238. You must then shift the decimal of the dividend once to the right as well. Therefore 345 would become 3450. Then complete the long division problem.
For example 760.56/0.234 Shift the decimal in 0.234 to the right three times. 0.234 becomes 234. You must then shift the decimal of the dividend three times to the right as well. Therefore 760.56 would become 760560. Then complete the long division problem.
COMPLETE PROBLEMS
#1, #6 (SET C)
#3, #5 (SET D)
on page 77
Lesson 2-7: Solving Multiplication & Division Equations
Division and Multiplication are inverse operations. Therefore to solve a one-step problem involving one of these operations, you must use the other.
For example
3x=12 3 is being multiplied times x to equal 12
3x/3=12/3 work backwards! Instead of multiplying divide both sides by three
x=4 SOLVE!
5x=25 5 is being multiplied times x to equal 25
5x/5=25/5 work backwards! Instead of multiplying divide both sides by five
x=5 SOLVE!
x/2=12 x is being divided by 2 to equal 12
(2)x/2=12(2) work backwards! Instead of dividing, multiply both sides by two
x=24 SOLVE!
x/10=12 x is being divided by 10 to equal 12
(10)x/10=12(10) work backwards! Instead of dividing, multiply both sides by ten
x=120 SOLVE!
COMPLETE PROBLEMS
#2-#6 (SET E)
on page 77