Download 6th Grade Test Prep

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6
Grade Test Prep
Number Sense
6.N.1
Read & Write whole numbers to trillions
Write 268,745,320,709 in expanded form.
Write 7,185,403,629 in word form.
Write 53,602,015,008 in short word form.
6.N.2
6.N.3
6.N.4
6.N.5
Commutative, Associative, Distributive, Identity, Inverse, and Zero properties
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Distributive Property
Identity Property of Addition
Identity Property of Multiplication
Inverse Property of Addition
Inverse Property of Multiplication
Zero Property
a+b=b+a
a*b=b*a
(a + b) + c = a + (b + c)
(a * b) * c = a * (b * c)
a(b + c) = a(b) + a(c)
a+0=a
a×1=a
a + (-a) = 0
a * (1/a) = a
a×0=0
6.N.6
6.N.7
6.N.8
6.N.9
Rate, Ratio, & Proportion
RATIO
Compares two
numbers.
2 to 3,
5:4
7
9
RATE
A ratio that
compares quantities
of different units
miles
426

hours
8
PROPORTION
Compares two
different ratios and
determines if they
are equal, by using
cross-multiplication.
6.N.10
6.N.6
6.N.7
6.N.8
6.N.9
Rate, Ratio, & Proportion
6.N.10
What is the ratio of red triangles to green triangles?
What is the ratio of green triangles to red triangles?
Julia traveled 426 miles in 8 hours. What is the unit
rate for the number of miles Julia traveled?
Mrs. Winters bought 8 pounds of ham for $18.88.
What was the cost per pound of the ham?
Pencils are on sale, 3 for 36 cents. How much
money does Allie need to buy 8 pencils?
6.N.11
6.N.12
Percent
Determine the percent
of the grid that is
shaded?
Shade in 88% of the
given grid.
Write 45% as a decimal and a simplified fraction.
6.N.11
6.N.12
Percent
What is 53% of 114?
= .53 * 114
Method 1: Translate
60.42
Rate * base = Part
Method 2: Formula
.53 * 114 = 60.42
53
x

. 100 114
53 * 114 = 100x
6,042 = 100x
60.42 = x
Method 3: Proportion
6.N.26
Estimating Percent
A recent survey found that 41% of the 300 people surveyed
forgot to turn off their cell phones before boarding an airplane.
About how many people forgot to turn off their cell phones?
Step 1:
Round 41% to the nearest 10 percent.
41% rounds to 40%
Step 2:
Use mental math to find 10% of 300.
10% of 300 is 30
Step 3:
Find 40% of 300.
40% of 300 is 4 times 10% of 300.
4 * 30 = 120
About 120 people forgot to turn off their cell phones.
6.N.26
Estimating Percent
The Harris family wants to leave a 15% tip for their waiter.
The cost of their meal is about $45.85. About how much tip
should the Harris family leave for the waiter?
For the premier of a new movie, 745 people lined up to buy
tickets. 67% of those in line were able to purchase a ticket
for the movie. About how many tickets were sold to the
movie?
Sally had to answer 93% of the test questions correctly to
earn an A. About how many of the 80 questions on the test
did she need to answer correctly to earn an A?
6.N.11
6.N.12
Percent
What is 40% of 30?
123 is what percent of 150?
What percent of 1,000 is 5?
New York is the 27th largest state in the United States. What
percent of the 50 states in the U.S. are larger than New York?
Of the 36 students in Florence’s class, 27 have been inside the
Empire State Building. What percent of the class has not been
inside the Empire State Building?
6.N.13
Absolute Value
The absolute value of a number is the distance from 0 to the number on a number line.
|4| means a distance of 4 units from 0 on the number line.
|-8| means a distance of 8 units from 0 on the number line.
What does |-22| mean?
Which of the following has the least value?
|-50|
|5|
|-1|
|10|
Which of the following has a value equal to the value of |-12|?
-12
|-1.20|
|1.20|
|12|
6.N.20
6.N.21
Convert fractions to repeating / terminating decimals
Terminating decimals are decimals that end.
Non -Terminating decimals are decimals that go on forever.
Repeating decimals are decimals where the decimal digits repeat forever in order.
Non-Repeating decimals are decimals where the decimal digits repeat forever without
any order.
What kind of a decimal is 0.36?
Express 0.36 as a fraction in simplest form?
Represent 3/11 as a decimal.
What kind of a decimal does 3/11 convert into?
When written in decimal form, which of the following is a terminating decimal?
1/8
2/9
3/7
6.N.14
6.N.15
Locate and order Rational numbers
Which of the following shows the integers in order from least to greatest?
a)
-4, -5, -7, 3
b)
3, -4, -5, -7
c)
-7, -5, -4, 3
d)
3, -7, -5, -4
Place the following numbers in order from greatest to least.
-8
80%
8/50
8.6012
6.N.19
Multiplicative Inverse of a number
To find the multiplicative inverse (reciprocal) of a fraction, “flip” the
fraction.
The numerator takes the denominators place and the denominator takes
the numerators place.
Complete the following table:
Fraction
2/5
3
-3/4
2
5
3
Reciprocal
6.N.16
6.N.17
6.N.18
Add, subtract, multiply & divide fractions and mixed numbers
To Add or Subtract Fractions:
- Convert all fractions to equivalent fractions with the same denominator
- Add or subtract the numerator
- Simplify the fraction or turn it into a mixed number if possible.
1 2
 
5 3
3 1
 
5 2
3 7
 
7 3
6 2
 
7 3
6.N.16
6.N.17
6.N.18
Add, subtract, multiply & divide fractions and mixed numbers
To Add or Subtract Mixed Numbers:
- Convert the mixed numbers into improper fractions
- Convert all fractions to equivalent fractions with the same denominator
- Add or subtract the numerator
- Simplify the fraction or turn it into a mixed number if possible.
1 2
2  
5 3
1
7
1 3 
2
3
3
5 4
5
6 2
1  
7 3
6.N.16
6.N.17
6.N.18
Add, subtract, multiply & divide fractions and mixed numbers
To Multiply Fractions / Mixed Numbers:
- Convert the mixed numbers into improper fractions
- Multiply the two numerators
- Multiply the denominators
- Simplify the fraction or turn it into a mixed number if possible.
2 3
 
3 4
1 1
3 
2 3
2
2 3 
7
6
7
1 2 
7
6
6.N.16
6.N.17
6.N.18
Add, subtract, multiply & divide fractions and mixed numbers
To Divide Fractions / Mixed Numbers:
- Convert the mixed numbers into improper fractions
- Find the reciprocal of the second fraction
- Rewrite the problem by changing the division sign into multiplication
- Multiply the numerator by the numerator.
- Multiply the denominator by the denominator
- Simplify the fraction or turn it into a mixed number if possible.
3 7
 
5 10
1 1
3  
3 2
2
82 
7
6
6
1 2 
7
21
6.N.23
6.N.24
Exponents & Repeated multiplication
To write the numbers in exponential form
6×6×6×6
- The base in exponential form is the
number itself.
6
- Count the number of times the number is
repeated.
4
- Write the four as an exponent.
64
6.N.23
6.N.24
Exponents & Repeated multiplication
To write the numbers in repeated
multiplication form
35
- Write the base, followed by a
multiplication sign
3×
- Repeat the number as many times as the
exponent
3×3×3×3×3
- Simplify (if the question asks for it)
243
6.N.22
6.N.25
Order of Operations
To simplify, using order of operations
62 - (17 · 5) ÷ 5 + 3²
- Do the operations inside the parentheses
first and bring everything else down
62 - 85 ÷ 5 + 3²
- Simplify any exponents, and bring
everything else down
62 – 85 ÷ 5 + 9
- Multiply /divide in order from left to
right, and bring everything else down
62 – 17 + 9
- Add / Subtract in order from left to
right, and bring everything else down
45 + 9
54
20 – 5 + (13 – 3)
96 ÷ (4 × 4) ÷ 3
3 * 15 ÷ 5²
72 · 6 ÷ 3 + 48 - 29
6.N.27
Justify reasonableness using estimation
Jenny spent $39.90 for a pair of shoes, $26.95 for a dress, and $4.15 for a
bottle of shampoo. She estimates, that she spent $60. Is $60 a reasonable
estimate for the amount of money she spent?
To estimate an answer:
$39.90 rounds to $40
-Round each amount to the nearest dollar
$26.95 rounds to $27
$4.15 rounds to $4
- Complete the indicated operation to
estimate
40 + 27 + 4 = $71
- Write your answer
Jenny spent about $71,
thus her estimate of
$60 is incorrect.