x10 x10 x10 x10 x10 x10 - gsiccharter.com
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BASE TEN SYSTEM
1 0 0 0 0 0 0, .x10x10x10x10x10x10
i Move to the left, the number is 10 times as large.b Move to the right and the number is 10 times less
or 1
10of the pervious number.
1,000,000 = 10 x 10 x 10 x 10 x 10 x 10
106The base is the number you are
multiplying repeatedly.
g
The exponent is the number of times you are multiplying the
base.
Value Exponent Form
1 , 0 00 , 000 1 0 6
1 0 0 , 000 1 0 5
1 0 , 0 00 1 0 4
1 , 0 00 1 0 3
1 0 0 1 0 2
1 0 1 0 1
1 1 0 2
Standard Form
5 4 7 , 2 6 4
Expanded Form
( 5 x 1 0 5 ) + ( 4 x 1 0 4 ) +( 7 x 1 0 3 ) + ( 2 x 1 0 2 ) +( 6 x 1 0 1 ) + ( 4 x 1 0 0 )
8 9 5 4 2 6 0 0 0•,Standard Form
8,954.26
Word Form
Eight thousand, nine hundred, fifty-four and twenty-six hundredths
Expanded Form
(8x1,000) + (9x100) + (5x10) + (4x1) + (2x0.1) + (6x0.01) = 8,954.26
Comparing decimals
1.254 2.254 0.602 0.452< >
0.235 1.235 3.258 3.258< =
exponentsbExponents show repeated multiplication.
bExponents represent how many times a number (the base) is multiplied by itself.
64 = 6x6x6x6exponent
base
1 time 3 times2 times 4 times
Exponential Form
25
Word Form
Two to the fifth power
Expanded Form
2 2 2 2 2
Standard Form
32
bAny number raised to the first power is itself. Example: 31 = 3 bAny number raised to the zero power is
always one. Example: 30 = 1
• • • •
exponentsbExponents show repeated multiplication.
bExponents represent how many times a number (the base) is multiplied by itself.
64 = 6x6x6x6exponent
base
1 time 3 times2 times 4 times
Exponential Form Word Form
Expanded Form Standard Form
bAny number raised to the first power is itself. Example: 31 = 3 bAny number raised to the zero power is
always one. Example: 30 = 1
MULTIPLICATIONmulti - digit
1
1 3
3 2 5
x 2 6
1 9 5 0
+ 6 5 0 0
8 4 5 0
1. Multiply 5x62. Multiply 6 x 2, add 33. Multiply 6 x 3, add 14. Put a zero as a place
holder5. Multiply 2 x 56. Multiply 2 x 2, add 17. Multiply 2 x 38. Add your answers
steps
Box and Cluster
300 20 5
20 6000 400 100
6 1800 120 30
MULTIPLICATIONmulti - digit
1
1 3
3 2 5
x 2 6
1 9 5 0
+ 6 5 0 0
8 4 5 0
1. Multiply 5x62. Multiply 6 x 2, add 33. Multiply 6 x 3, add 14. Put a zero as a place
holder5. Multiply 2 x 56. Multiply 2 x 2, add 17. Multiply 2 x 38. Add your answers
steps
Box and Cluster
300 20 5
20 6000 400 100
6 1800 120 30
division
)373515-30
249
73Q
-60135
-135000
DOES MCDONALDS SERVE BURGERS?
Step 2
Step 1
ADDING & SUBTRACTINGdecimals
5 6
- 2 4 3
6 7
+ 3 7 9
Step 1Line the
5.6 – 2.43 6.7 + 3.79
Step 2Put the decimal below
5 6
- 2 4 3
6 7
+ 3 7 9
decimals up.
in the answer row.
Step 4
Step 3
ADDING & SUBTRACTINGdecimals
5.6 – 2.43 6.7 + 3.79
5 6 0
- 2 4 3
6 7 0
+ 3 7 9
Step 3Fill in zeros as place holders.
Step 4 Add or subtract normally.
5 6 0
- 2 4 3
3 1 7
6 7 0
+ 3 7 9
1 0 4 9
5 110
thousandsHundred
thousandsTen
thousandsThousands
5 6 7
ones
Hundreds Tens Ones
4 9 3
decimals
Tenths Hundredths Thousandths
7 1 2
Decimalsvisual model
rounding
comparing
HUNDREDTHS
THOUSANDTTHS
0.482
6.35 =
6.40
Find the place value you are rounding to, look at the digit to the right. If the digit is 1, 2, 3, 4 then leave the place value number the same. If the digit is 5, 6, 7, 8, or 9, push the place value digit up to the next number.
Start with the digit all the way to the left and see which number is higher. If the digits are the same, move to the next place value to the right. Check the place of the decimal.
5.62 < 56.2
Visual models
ADDING & SUBTRACTINGdecimals1.26 + 0.32 = 1.58 c
Color in each decimal, then count all the
blocks colored.
0.52 – 0.23 = 0.29 c Color in the blocks for the first decimal, cross out the
second decimal and the
remaining color blocks are your
answer.
XXXXX
XXXXXXXXXX
XXXXX
XXX
visual model0.8 x 0.6 = 0.48
56.3 x 4.5 = ? 1 Multiply like you would
normally. 2 Count how many digits follow each decimal in the
problem.3 Move the decimal in the
answer the amount of
digits in the problem.
The answer is where the
colors overlap.
L The decimals DO NOT need to be lined up.
56.3x 4.5
281522520253.35
1312
+
1
standard algorithm
))
visual model0.4 ÷ 0.8 =
3.65 ÷ 0.5 = ?
1 Color in the amount in the first number (dividend).
2 The amount in each group is the second number (divisor).
3 The quotient (answer) is the amount of groups as a whole
number.
standard algorithm
5 groups
36.5-35
7.35
3.650.5 1 5- 1 5
0 0
Q
Move the decimal to make the dividend a
whole number.
Fraction=Equivalent Fractions
Fractions that represent the same amount.
H f=
vocabulary
h h kdenominator
numeratorMix
numberImproper fraction
E H
_ )
fractionsADDING
step 1: Find the least common denominator and change the
fractions to equivalent fractions.
E H+
Rewrite the problem with the new like denominators.
x4
x4
x3
x3
step 2:
+
step 3: Add the numerators.
8 + 6 = 14
step 4: C1412
=Convert to a mix number or the
simplest form of the fraction.
convertingImproper fractions to mix numbers
5 goes into 14 TWO times.
d=2Figure out how many times the denominator
can go into the numerator.
NThe remaining amount becomes the new numerator over the same denominator. 4
remains so it becomes 4/5
convertingMix numbers to improper fractions
1
2
3
Multiply the whole number by the denominator then add the numerator, and that is
your new denominator. The denominator in the mix
number stays the same.
fmultiply
2 x 8 + 7 = 23
add 8
=23
fractionssimplifyingSynonyms: simplifying, reducing
* Writing the fraction using the smallest numbers as the numerator and
denominator.
Find the LARGEST
number both the
numerator and
denominator are divisible by.
mdR
÷ 3
÷ 3
÷ 2
÷ 2
÷ 3
÷ 3
b
b
b
D
BD
8 dmix numbers
Add/subtract
Step 1: Change the denominators to a common
denominators.
+
IN bb
X5
X5
X4
X4
2015
2016
Step 2: Add the fractions and with the like denominators. 20
152016
+ =2031
Step 3: Convert the fraction into a mix number. 20
31 11201b
Step 4: Add the whole numbers.4+2+1
Step 5: Write the whole number and fraction and
reduce if needed. 7 1120
f H
D S
multiplyingfractions
USING A VISUALrows
X =
2
18columns
s i m p l i f y
4
18184c
Using the algorithm
GMultiply straight across for the numerator
and denominator.
c
cX
4x28x4
c 832c
g
multiplyingfractions
FRACTIONS AND a whole number
Put the whole number over one and multiply straight across.
X1 J10
Step 1. Convert the mix number to an improper
fraction
2 gX =2c8cdcE
FRACTIONS AND a mix number
k fX134 fX Step 2: Multiply straight
across.
Step 3: Convert back to a mix number. Simplify if
needed.
c
c
5232
=
20321 cK
c
c
G T
keep change
FRACTIONS AND a whole number
Keep the first
fraction the same.
Step 1. Put the whole number over one.
Step 2: Change the division to multiplication.
Fraction by a fraction
3 f
1X
Step 3: Flip the second fraction and multiply
straight across.
c
flip
÷
Flip the second fraction.
Change the
symbol to X
G DX =
620c 3
10
÷
3 84
244c6
D i v i d i n g F r a c t i on s
Converting measurements
CAPACITY1 cup = 8 fluid ounces
1 pint = 2 cups1 quart = 2 pints
1 gallon = 4 quarts1 liter = 1,000 milliliters
weight1 pound = 16 ounces1 ton = 2,000 pounds
1 kilogram = 1,000 grams
linear1 foot = 12 inches
1 yard = 3 feetI centimeter = 10 millimeters
1 meter = 100 centimeters1 kilometer = 1,000 meters
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