A. DIVISION of WHOLE NUMBERS

B. DECIMALS

a. PLACE VALUE of DECIMALS

PLACE VALUE|

Trillions| Billions| Millions| Thousands| Ones / Unit| Decimalpoint| .1| .01| .001| HUNDRED| TEN| TRILLIONS| HUNDRED| TEN| BILLIONS| HUNDRED| TEN| MILLIONS| HUNDRED| TEN| THOUSANDS| HUNDREDS| TENS| ONES| | TENTHS| HUNDREDTHS| THOUSANDTHS| 5| 8| 9,| 6| 1| 2,| 7| 4| 5,| 6| 1| 8,| 3| 2| 5| .| 1| 6| 2|

b. READING and WRITING DECIMALS

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c. =

=

COMPARING AND ORDERING DECIMALS

* >

>

<

<

Symbols used:

greater than less than equal * Two (2) Types of Ordering:

1. Ascending order – from smallest to largest

2. Descending Order – from largest to smallest

d. ADDITION of DECIMALS

Line the decimals up:| | | 1.452|

| | +| 1.3|

| | | |

"Pad" with zeros:| | | 1.452|

| | +| 1.300|

| | | |

Add:| | | 1.452|

| | +| 1.300|

| | | |

| | | 2.752|

e. SUBTRACTION of DECIMALS

f. MULTIPLCATION of DECIMALS

MULTIPLICATION PROPERTIES

1. Zero property – (ex: 4x0=0)

2. Commutative property – (Ex: 8x10=80 & 10x8=80)

3. Associative property –

4. Distributive property --

g. DIVISION of DECIMALS

h. SOLVING WORD PROBLEMS IN DECIMALS

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Top of Form

Solve the following word problems.

Julia cut a string 8.46 m long into 6 equal pieces. What is the length of each piece of string? m

The mass of a jar of sweets is 1.4 kg. What is the total mass of 7 such jars of sweets? kg

The watermelon bought by Peter is 3 times as heavy as the papaya bought by Paul. If the watermelon bought by Peter has a mass of 4.2 kg, what is the mass of the papaya? kg

There is 0.625 kg of powdered milk in each tin. If a carton contains 12 tins, find the total mass of powdered milk in the carton. kg

Marcus bought 8.6 kg of sugar. He poured the sugar equally into 5 bottles. There was 0.35 kg of sugar left over. What was the mass of sugar in 1 bottle? kg

Bottom of Form

C. NUMBER THEORY

i. DIVISIBILITY RULES

Rule #1: divisibility by 2

A number is divisible by 2 if it's last digit is 0,2,4,6,or 8. For instance, 8596742 is divisible by 2 because the las t digit is 2.

Rule # 2: divisibility by 3:

A number is divisible by 3 if the sum of its digits is divisible by 3 For instance, 3141 is divisible by 3 because 3+1+4+1 = 9 and 9 is divisible by 3.

Rule # 3: divisibility by 4

A number is divisible by 4 if the number represented by its last two digits is divisible by 4. For instance, 8920 is divisible by 4 because 20 is divisible by 4.

Rule #4: divisibility by 5

A number is divisible by 5 if its last digit is 0 ot 5.

For instance, 9564655 is divisible by 5 because the last digit is 5.

Rule # 5: divisibility by 6

A number is divisible by 6 if it is divisible by 2 and 3. Be careful! it is not one or the other. The number must be divisible by both 2 and 3 before you can conclude that it is divisible by 6.

Rule # 6: divisibility by 7

To check divisibility rules for 7, study carefully the following two examples: Is 348 divisible by 7?

Remove the last digit, which is 8. The number becomes 34. Then, Double 8 to get 16 and subtract 16from 34.

34 − 16 = 18 and 18 is not divisible by 7. Therefore, 348 is not divisible by 7 Is 37961 divisible by 7?

Remove the last digit, which is 1. The number becomes 3796. Then, Double 1 to get 2 and subtract 2 from 3796. 3796 − 2 = 3794, so still too big? Thus repeat the process. Remove the last digit, which is 4. The number becomes 379. Then, Double 4 to get 8 and subtract 8 from 379. 379 − 8 = 371, so still too big? Thus repeat the process.

Remove the last digit, which is 1. The number becomes 37. Then, Double 1 to get 2 and subtract...