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Review
Numbers
What are Numbers?
-quantities
-amounts
What do we use numbers for?
-math
-measuring
-time
-money
-speed
-baking/cooking
Why are numbers important?
-to be accurate
Natural numbers
-whole numbers above zero
Ex. 1, 2, 3, …
Whole numbers
-numbers not divided into parts. No decimals
Ex. -1, 0, 1, 2, …
Rational numbers
-numbers that can be put into a fractional form. Numbers and thedecimals.
1
Ex. 1, , 1.33
3
Irrational numbers
-decimals that go on forever with no pattern.
Ex. π = 3.1415... pi goes on forever.
Addition
Combining values
Order doesn’t matters: you can add them in any order you want.
Ex. 5 + 7 = 7 + 5
Long Hand Addition

215
One Way: Add from left to right using place
value.
176
So
200 + 100 = 300
10 + 70 = 80
5 + 6 = 11
Then
300 + 80 + 11 = 391

215
176
Another Way: Add from right to left and use
regrouping (carrying)
1.
You can only put one number in each column in the “answer
row”. Put the last digit of your solution. Carry the first
number to the next column.
2.
Repeat Step 1, adding your original numbers and the “carried
number”.
3.
Repeat Step 2-3 until you have completed all the columns.
Subtraction
Taking a value away from another value
Order DOES matter
Ex. 5 – 7 ≠ 7 – 5
Long Hand Subtraction
** same rules as adding (one number per column until you hit the last column)

415
1.
236
2.
a.
b.
Start in column furthest to the right.
If the top number is greater than the bottom number simply subtract.
If not, borrow ten from the column next and place a ‘1’ next to the top number. Now subtract.
Move to next column and repeat Step 1. Do this until you have used all columns.
Multiplication



Repeated addition.
A certain number of groups of a certain value.
Order DOESN’T matter
Ex. 2 + 2 + 2 = 6
2x3=6
3x2=6
Long Hand Multiplication

29
54
x
20
9
50
4
1000
450
80
36
1.
2.
3.
Break the numbers into their place values. Ex. 29
becomes 20 and 9.
Multiply each value, putting the answer in the
corresponding grid.
Add all the grids together in your head.
1000
450
80
36 = 1566

29
54
same rules as adding (one number per column until you hit the last column)
1.
Multiply the numbers in the ones column farthest to the right.
2.
Put the last digit of the solution and “carry” the first to the second column.
3.
Multiply the tens on top with the ones on the bottom and ADD the “carried” number to your solution.
4.
Continue multiplying the top row with the ones digit on the bottom until you are done with the top row.
5.
Put a “zero (0)” as a place holder under the digit farthest to the right in your answer spot.
6.
Multiply the tens digit on the bottom with the each of the digits on the top following Steps 2 and 3.
7.
When finished with the tens on the bottom, you may need to continue into the hundreds, thousands, etc. putting a
placeholder whenever you switch columns.
8.
Add the solution rows together
Division




Repeated subtraction
The opposite of Multiplication
Splitting a number into EQUAL groups
Order MATTERS!!!
o Ex.
Ex.
6 3  36
6 3  2
Divisibility Rule – how to tell if a number is divisible by the BIG 10
2, 4, 6, 8, 10  even number
3  sum of digits is divisible by 3
45 – 4 + 5 = 9 and 9 is divisible by 3…so 45 is divisible by 3
4  last two digits are divisible by 4
340 – 40 is divisible by 4…so 340 is divisible by 4
5  ends in 5 or 0
6  divisible by 2 AND 3
8  last three digits divisible by 8 (like divisibility rule for 4)
9  sum of digits are divisible by 9 (like divisibility rule for 3)
10  ends in 0
Long Division
45  3
Inside the “house”
3 45
Outside the “house”
1. Divide – outside # with first digit(s) possible inside.
Put solution on top.
2. Multiply – solution digit(s) on top with outside #. Put
solution under first digit(s) inside.
3. Subtract – first digits inside and solution under it.
4. Bring Down – next digit inside.
5. Repeat – until you have a remainder of zero OR
three (3) decimal points.
With Decimals
3 764
= 254.67
6. Divide – outside # with first digit(s) possible inside.
Put solution on top.
7. Multiply – solution digit(s) on top with outside #. Put
solution under first digit(s) inside.
8. Subtract – first digits inside and solution under it.
9. Bring Down – next digit inside.
10. Repeat – until you have a remainder of zero OR
three (3) decimal points.