Common Core: 6th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

Example Question #112 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle - 12 m - 1 = n

Possible Answers:

Correct answer:

Explanation:

In the equation \displaystyle - 12 m - 1 = n\displaystyle {m} is the independent variable and \displaystyle {m} is the dependent variable. This means, as we manipulate \displaystyle {m}\displaystyle {n} will change.

Because we are given tables in our answer choices, we can plug in the given value for \displaystyle {m} from the table and use our equation from the question to see if that equals the value given for \displaystyle {n} in the table.

Let's start by testing values from the following table:

\displaystyle {-12(1)+-1=-12}

\displaystyle {-12+-1=-12}

\displaystyle {-13\neq -12}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {- 12 m - 1 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

\displaystyle {-12(1)-1=-13}

\displaystyle {-12-1=-13}

\displaystyle {-13=-13}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-12(4)-1=-98}

\displaystyle {-48-1=-98}

\displaystyle {-49\neq -98}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {- 12 m - 1 = n} ; thus, this answer choice is not correct and can be eliminated.

\displaystyle {-12(0)-1=-1}

\displaystyle {0-1=-1}

\displaystyle {-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-12(3)-1=-37}

\displaystyle {-36-1=-37}

\displaystyle {-37=-37}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-12(7)-1=-74}

\displaystyle {-84-1=-74}

\displaystyle {-85\neq -74}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {- 12 m - 1 = n} ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

\displaystyle {-12(7)-1=-85}

\displaystyle {-84-1=-85}

\displaystyle {-85=-85}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-12(15)-1=-181}

\displaystyle {-180-1=-181}

\displaystyle {-181=-181}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-12(17)-1=-205}

\displaystyle {-204-1=-205}

\displaystyle {-205=-205}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-12(19)-1=-229}

\displaystyle {-228+-1=-229}

\displaystyle {-229=-229}

All of these values were correct for our equation; thus, this table is our correct answer.

Example Question #116 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle - 18 m - 15 = n

Possible Answers:

Correct answer:

Explanation:

In the equation \displaystyle - 18 m - 15 = n\displaystyle {m} is the independent variable and \displaystyle {m} is the dependent variable. This means, as we manipulate \displaystyle {m}\displaystyle {n} will change.

Because we are given tables in our answer choices, we can plug in the given value for \displaystyle {m} from the table and use our equation from the question to see if that equals the value given for \displaystyle {n} in the table.

Let's start by testing values from the following table:

\displaystyle {-18(0)+-15=-14}

\displaystyle {0+-15=-14}

\displaystyle {-15\neq -14}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {- 18 m - 15 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

\displaystyle {-18(0)-15=-15}

\displaystyle {0-15=-15}

\displaystyle {-15=-15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-18(4)-15=-174}

\displaystyle {-72-15=-174}

\displaystyle {-87\neq -174}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {- 18 m - 15 = n} ; thus, this answer choice is not correct and can be eliminated.

\displaystyle {-18(0)-15=-15}

\displaystyle {0-15=-15}

\displaystyle {-15=-15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-18(6)-15=-123}

\displaystyle {-108-15=-123}

\displaystyle {-123=-123}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-18(8)-15=-148}

\displaystyle {-144-15=-148}

\displaystyle {-159\neq -148}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {- 18 m - 15 = n} ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

\displaystyle {-18(5)-15=-105}

\displaystyle {-90-15=-105}

\displaystyle {-105=-105}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-18(12)-15=-231}

\displaystyle {-216-15=-231}

\displaystyle {-231=-231}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-18(16)-15=-303}

\displaystyle {-288-15=-303}

\displaystyle {-303=-303}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {-18(18)-15=-339}

\displaystyle {-324+-15=-339}

\displaystyle {-339=-339}

All of these values were correct for our equation; thus, this table is our correct answer.

Example Question #117 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle 16 m + 15 = n

Possible Answers:

Correct answer:

Explanation:

In the equation \displaystyle 16 m + 15 = n\displaystyle {m} is the independent variable and \displaystyle {m} is the dependent variable. This means, as we manipulate \displaystyle {m}\displaystyle {n} will change.

Because we are given tables in our answer choices, we can plug in the given value for \displaystyle {m} from the table and use our equation from the question to see if that equals the value given for \displaystyle {n} in the table.

Let's start by testing values from the following table:

\displaystyle {16(9)+15=160}

\displaystyle {144+15=160}

\displaystyle {159\neq 160}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {16 m + 15 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

\displaystyle {16(7)+15=127}

\displaystyle {112+15=127}

\displaystyle {127=127}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {16(9)+15=318}

\displaystyle {144+15=318}

\displaystyle {159\neq 318}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {16 m + 15 = n} ; thus, this answer choice is not correct and can be eliminated.

\displaystyle {16(0)+15=15}

\displaystyle {0+15=15}

\displaystyle {15=15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {16(2)+15=47}

\displaystyle {32+15=47}

\displaystyle {47=47}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {16(3)+15=74}

\displaystyle {48+15=74}

\displaystyle {63\neq 74}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {16 m + 15 = n} ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

\displaystyle {16(0)+15=15}

\displaystyle {0+15=15}

\displaystyle {15=15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {16(3)+15=63}

\displaystyle {48+15=63}

\displaystyle {63=63}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {16(7)+15=127}

\displaystyle {112+15=127}

\displaystyle {127=127}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {16(18)+15=303}

\displaystyle {288+15=303}

\displaystyle {303=303}

All of these values were correct for our equation; thus, this table is our correct answer.

Example Question #113 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle -1 = n

Possible Answers:

Correct answer:

Explanation:

In the equation \displaystyle -1 = n\displaystyle {m} is the independent variable and \displaystyle {m} is the dependent variable. This means, as we manipulate \displaystyle {m}\displaystyle {n} will change.

Because we are given tables in our answer choices, we can plug in the given value for \displaystyle {m} from the table and use our equation from the question to see if that equals the value given for \displaystyle {n} in the table.

Let's start by testing values from the following table:

\displaystyle {0(11)+-1=0}

\displaystyle {0+-1=0}

\displaystyle {-1\neq 0}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {-1 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

\displaystyle {0(8)-1=-1}

\displaystyle {0-1=-1}

\displaystyle {-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {0(10)-1=-2}

\displaystyle {0-1=-2}

\displaystyle {-1\neq -2}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {-1 = n} ; thus, this answer choice is not correct and can be eliminated.

\displaystyle {0(1)-1=-1}

\displaystyle {0-1=-1}

\displaystyle {-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {0(11)-1=-1}

\displaystyle {0-1=-1}

\displaystyle {-1=-1}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {0(14)-1=10}

\displaystyle {0-1=10}

\displaystyle {-1\neq 10}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {-1 = n} ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

\displaystyle {0(0)-1=-1}

\displaystyle {0-1=-1}

\displaystyle {-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {0(7)-1=-1}

\displaystyle {0-1=-1}

\displaystyle {-1=-1}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {0(10)-1=-1}

\displaystyle {0-1=-1}

\displaystyle {-1=-1}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {0(13)-1=-1}

\displaystyle {0+-1=-1}

\displaystyle {-1=-1}

All of these values were correct for our equation; thus, this table is our correct answer.

Example Question #119 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle 9 m - 10 = n

Possible Answers:

Correct answer:

Explanation:

In the equation \displaystyle 9 m - 10 = n\displaystyle {m} is the independent variable and \displaystyle {m} is the dependent variable. This means, as we manipulate \displaystyle {m}\displaystyle {n} will change.

Because we are given tables in our answer choices, we can plug in the given value for \displaystyle {m} from the table and use our equation from the question to see if that equals the value given for \displaystyle {n} in the table.

Let's start by testing values from the following table:

\displaystyle {9(0)+-10=-9}

\displaystyle {0+-10=-9}

\displaystyle {-10\neq -9}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {9 m - 10 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

\displaystyle {9(2)-10=8}

\displaystyle {18-10=8}

\displaystyle {8=8}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(9)-10=142}

\displaystyle {81-10=142}

\displaystyle {71\neq 142}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {9 m - 10 = n} ; thus, this answer choice is not correct and can be eliminated.

\displaystyle {9(2)-10=8}

\displaystyle {18-10=8}

\displaystyle {8=8}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(4)-10=26}

\displaystyle {36-10=26}

\displaystyle {26=26}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(9)-10=82}

\displaystyle {81-10=82}

\displaystyle {71\neq 82}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {9 m - 10 = n} ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

\displaystyle {9(1)-10=-1}

\displaystyle {9-10=-1}

\displaystyle {-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(4)-10=26}

\displaystyle {36-10=26}

\displaystyle {26=26}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(5)-10=35}

\displaystyle {45-10=35}

\displaystyle {35=35}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(15)-10=125}

\displaystyle {135+-10=125}

\displaystyle {125=125}

All of these values were correct for our equation; thus, this table is our correct answer.

Example Question #120 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle 9 m - 12 = n

Possible Answers:

Correct answer:

Explanation:

In the equation \displaystyle 9 m - 12 = n\displaystyle {m} is the independent variable and \displaystyle {m} is the dependent variable. This means, as we manipulate \displaystyle {m}\displaystyle {n} will change.

Because we are given tables in our answer choices, we can plug in the given value for \displaystyle {m} from the table and use our equation from the question to see if that equals the value given for \displaystyle {n} in the table.

Let's start by testing values from the following table:

\displaystyle {9(7)+-12=52}

\displaystyle {63+-12=52}

\displaystyle {51\neq 52}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {9 m - 12 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

\displaystyle {9(5)-12=33}

\displaystyle {45-12=33}

\displaystyle {33=33}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(6)-12=84}

\displaystyle {54-12=84}

\displaystyle {42\neq 84}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {9 m - 12 = n} ; thus, this answer choice is not correct and can be eliminated.

\displaystyle {9(1)-12=-3}

\displaystyle {9-12=-3}

\displaystyle {-3=-3}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(5)-12=33}

\displaystyle {45-12=33}

\displaystyle {33=33}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(12)-12=107}

\displaystyle {108-12=107}

\displaystyle {96\neq 107}

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between \displaystyle {m} and \displaystyle {n} if \displaystyle {9 m - 12 = n} ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

\displaystyle {9(6)-12=42}

\displaystyle {54-12=42}

\displaystyle {42=42}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(8)-12=60}

\displaystyle {72-12=60}

\displaystyle {60=60}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(14)-12=114}

\displaystyle {126-12=114}

\displaystyle {114=114}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

\displaystyle {9(19)-12=159}

\displaystyle {171+-12=159}

\displaystyle {159=159}

All of these values were correct for our equation; thus, this table is our correct answer.

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