4th Grade Math Notes
Basic Fraction
Mixed Numbers and Improper Fractions
When converting a mixed number into an improper
numerator
denominator
- (the # of pieces shaded or unshaded)
fraction you multiply the denominator by the whole
number, then add the numerator.
- (the total number of pieces)
Example:
Example:
5
3
12
5
41
12 x 3 + 5 = 41
12
12
**Hint: The denominator does NOT change.**
When converting an improper fraction into a mixed
number you divide the numerator by the denominator.
**Hint: Zero can NEVER be a denominator.**
3 R5
41
12
12
41
5
3
- 36
12
5
**Hint: The dividend becomes the whole number
and the remainder becomes the numerator and
your denominator does NOT change.**
Equivalent Fraction
Adding Fractions
~ For the numerators add straight across.
~ The denominator does not change.
Ex.
12
24
=
+
2
4
The rule when converting fractions is that whatever
you do to the top you must also do to the bottom.
12
24
=
2
4
or
2
4
=
~ You divided 24 by 6 which equals 4.
~ Since you divided 24 by 6, you also have to divide
12
24
=
3
6
=
5
6
1
1
4
24
have to determine which operation was used.
~ 12 divided by 6 equals 2
+
Ex.
12
~ If your denominator is 24 and it changes to 4 you
12 by 6.
2
6
=
+
1
2
2
4
3
4
2
* Hint: Make sure you have a common
4
denominator before you add.
4th Grade Math Notes
Partial Product
Decimal Fraction and Decimal
23 x 48
20
3
40
800
120
8
160
24
75
100
800
120
160
+
24
1104
Area Model of Multiplication
14 x 12 = 168
+
2
0.75
~ To determine a fraction from a decimal put the
decimal in fraction form and simplify.
Ex.
75
3
0.75
=
=
100
4
Adding and Subtracting Decimals
2.25
4.32
+ 1.46
- 1.64
3.71
2.68
100
10
=
20
40
10
10 x 10 = 100
10 x 2 = 20
+
4
+ 8
~ make sure when adding or subtracting that the
168
decimal points are lined up
4 x 2 = 8
4 x 10 = 40
Division - Partial Quotient
3
Measuring Angles
369
- 300
100
69
- 60
20
9
-
9
3
0
123
Angles are measured in degrees using a tool called
a protractor. Angles can be seen in different
directions.
When we divide we can use our base 10 system to
help us determine out quotient. Multiplying by 1,
10, 100 and 1,000 we can easily find large chunks
to subtract from the dividend to find the total
quotient.
45°
45°
45°
Acute - an angle measuring less than 90
Obtuse - an angle measuring more than 90
Right - an angle measuring exactly 90
Straight - an angle measuring 180
4th Grade Math Notes
Measurement Conversions
12 inches = 1 foot
Math UNRAAVEL
U nderline the question
3 feet = 1 yard
1,760 yard = 1 mile
distance
5,280 feet = 1 mile
1 meter = 100 cm
1 kilometer = 1,000 meters
N ow predict what you need to do to solve the
problem
R ead the word problem
2,000 lb. = 1 T
A re the important words circled
16 oz. = 1 lb.
1
8 oz. =
lb.
2
1
4 oz. =
lb.
4
1000 g = 1 kg
weight
A pply the steps you choose to solve the problem
V erify your answer (Is it reasonable? Does it
make sense?)
E liminate wrong answers
L et the answer stay or rework the problem
**Double check your work!!!
Rounding Rap
Median, Mode and Range
Data: 23, 27, 25, 22, 29, 23, 26
Yo, find that place value
Circle that digit
Move to the right, underline get it.
0-4 circle stays the same
5-9 add one is the game
Now flex your muscles like a hero
Digits to the right change to zero
All the other digits stay the same
Yo! You’re the winner of the rounding
Median:
~ Put the numbers in numerical order and the
number in the middle is the median.
22, 23, 23, 25, 26, 27, 29
Median = 25
Mode:
~ The number that occurs most often.
Mode: 23
game!
Range:
~ The largest number subtract the lowest number.
Ex.
29 - 22 = 7
Range = 7
4th Grade Math Notes
,
ones
,
tens
(Since 18 is divisible by 3 then
495 is divisible by 3.)
hundreds
Example: 495
4+9+5 = 18
thousands
(Since 8 is divisible by two
then 4,368 is divisible by 2.)
ten thousands
If the sum of the digits is
divisible by three then the
original number is divisible
by 3.
Example: 4,368
millions
If the last digit is divisible
by 2 then the original
number is divisible
by 2.
Place Value
hundred thousands
Divisibility Rules 2-5
Parts of a
Whole Numbers
Divisibility Rules 6-10
If the number is divisible by
two and three then the
number is divisible by 6.
If the last three digits are
divisible by eight then the
original number is divisible
by 8.
If the sum of the digits is
divisible by nine then the
original number is divisible
by 9.
Example: 534
Is it divisible by 2? – yes
because 4 is divisible by 2
Is it divisible by 3? – yes
Example 7,328
hundredths
tenths
ones
(Since the last digit is a 5 then
3,695 is divisible by 5.)
tens
Example: 3,695
hundreds
(Since 28 is divisible by four
then 4,328 is divisible by 4.)
thousands
If the last digit is a five or a
zero then the number is
divisible by 5.
Example: 4,328
ten thousands
If the last two digits are
divisible by four then the
original number is divisible
by 4.
hundred thousands
Whole Numbers
Whole
Long Division
1 2 3 7 R 1
Divide
6 7 4 2 3
Multiply
Subtract
-6
Compare
1 4
Bring down
-1 2
0 2 2
(Since 328 is divisible by eight
then 7,328 is divisible by 8.)
-1 8
0 4 3
-4 2
Example: 495
4+9+5 = 18
0 1
(Since 18 is divisible by 9 then ~ Divide 6 into 7 one time so 1 goes above the 7.
495 is divisible by 9.)
~ Multiply 1 by 6 which equals 6 and subtract from 7 which
equals 1.
If the last digit is a zero then
the number is divisible by
10.
Example: 4,560
~ Compare - Is the amount less than the divisor? If not, go
(Since the last digit is a 0 then back and divide again.
4,560 is divisible by 10.)
~ Then bring down the 4 and the process begins again until
every number has been divided.
~ The final answer is 1,237 remainder 1.
**Hint: If you have to bring a number down, then you start
back over with divide.
4th Grade Math Notes
Number Line
Model Drawing
1. Read the whole problem.
2. Write a complete sentence at the bottom of
the problem. Leave a blank to fill in the
1
0
/4
1
/2
3
/4
0.25 0.50 0.75
1
25% 50% 75%
1 1/4
1 1/2
1 3/4
1.25
1.50
1.75
answer.
3. Figure out who and/or what is involved and
2
125% 150% 175%
draw a unit bar or unit bars.
4. Reread the problem using one sentence at a
time to solve it.
5. Do the computation.
6. Fill in the answer in the blank.
7. Check to make sure it is reasonable.
Resources
www.vectorkids.com/vkfractions
http://www.cobbk12.org/sites/literacy/math/mat
h2.htm
http://acworthelem.typepad.com/ms_myers_mat
h_class/4th.html
http://aaamath.com/
http://www.coolmath.com/
http://www.mathcats.com/
http://www.aplusmath.com/