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Common Core: 6th Grade Math : Expressions & Equations

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

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All Common Core: 6th Grade Math Resources

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Example Questions

Example Question #85 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 16 m - 14 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 114\\ \hline 10 & 146\\ \hline 16 & 253\\ \hline 17& 268\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 66\\ \hline 10 & 146\\ \hline 11 & 162\\ \hline 17& 258\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 67\\ \hline 10 & 148\\ \hline 11 & 165\\ \hline 17& 262\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 66\\ \hline 10 & 292\\ \hline 11 & 324\\ \hline 17& 516\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 66\\ \hline 10 & 146\\ \hline 11 & 162\\ \hline 17& 258\\ \hline \end{tabular}}$

Explanation:

In the equation 16 m - 14 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 67\\ \hline 10 & 148\\ \hline 11 & 165\\ \hline 17& 262\\ \hline \end{tabular}}$

{16(5)+-14=67}

{80+-14=67}

${66\neq 67}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {16 m - 14 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 10 & 146\\ \hline 13 & 388\\ \hline 15 & 452\\ \hline 19& 580\\ \hline \end{tabular}}$

{16(10)-14=146}

{160-14=146}

{146=146}

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.

{16(13)-14=388}

{208-14=388}

${194\neq 388}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 114\\ \hline 10 & 146\\ \hline 16 & 253\\ \hline 17& 268\\ \hline \end{tabular}}$

{16(8)-14=114}

{128-14=114}

{114=114}

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.

{16(10)-14=146}

{160-14=146}

{146=146}

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.

{16(16)-14=253}

{256-14=253}

${242\neq 253}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 2\\ \hline 11 & 162\\ \hline 16 & 242\\ \hline 17& 258\\ \hline \end{tabular}}$

{16(1)-14=2}

{16-14=2}

{2=2}

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.

{16(11)-14=162}

{176-14=162}

{162=162}

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.

{16(16)-14=242}

{256-14=242}

{242=242}

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.

{16(17)-14=258}

{272+-14=258}

{258=258}

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

Report an Error

Example Question #86 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 8 m + 2 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 34\\ \hline 8 & 66\\ \hline 16 & 141\\ \hline 17& 148\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 42\\ \hline 10 & 82\\ \hline 17 & 138\\ \hline 18& 146\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 43\\ \hline 10 & 84\\ \hline 17 & 141\\ \hline 18& 150\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 42\\ \hline 10 & 164\\ \hline 17 & 276\\ \hline 18& 292\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 42\\ \hline 10 & 82\\ \hline 17 & 138\\ \hline 18& 146\\ \hline \end{tabular}}$

Explanation:

In the equation 8 m + 2 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 43\\ \hline 10 & 84\\ \hline 17 & 141\\ \hline 18& 150\\ \hline \end{tabular}}$

{8(5)+2=43}

{40+2=43}

${42\neq 43}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {8 m + 2 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 2\\ \hline 5 & 84\\ \hline 9 & 148\\ \hline 14& 228\\ \hline \end{tabular}}$

{8(0)+2=2}

{0+2=2}

{2=2}

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.

{8(5)+2=84}

{40+2=84}

${42\neq 84}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 34\\ \hline 8 & 66\\ \hline 16 & 141\\ \hline 17& 138\\ \hline \end{tabular}}$

{8(4)+2=34}

{32+2=34}

{34=34}

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.

{8(8)+2=66}

{64+2=66}

{66=66}

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.

{8(16)+2=141}

{128+2=141}

${130\neq 141}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 34\\ \hline 6 & 50\\ \hline 16 & 130\\ \hline 17& 138\\ \hline \end{tabular}}$

{8(4)+2=34}

{32+2=34}

{34=34}

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.

{8(6)+2=50}

{48+2=50}

{50=50}

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.

{8(16)+2=130}

{128+2=130}

{130=130}

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.

{8(17)+2=138}

{136+2=138}

{138=138}

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

Report an Error

Example Question #1131 : Grade 6

Select the table of values that represent the relationship between {m} and {n} if - 3 m - 9 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -17\\ \hline 5 & -22\\ \hline 15 & -51\\ \hline 16& -53\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -18\\ \hline 5 & -24\\ \hline 15 & -54\\ \hline 16& -57\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -18\\ \hline 5 & -48\\ \hline 15 & -108\\ \hline 16& -114\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -33\\ \hline 10 & -39\\ \hline 15 & -43\\ \hline 19& -56\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -18\\ \hline 5 & -24\\ \hline 15 & -54\\ \hline 16& -57\\ \hline \end{tabular}}$

Explanation:

In the equation - 3 m - 9 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -17\\ \hline 5 & -22\\ \hline 15 & -51\\ \hline 16& -53\\ \hline \end{tabular}}$

{-3(3)+-9=-17}

{-9+-9=-17}

${-18\neq -17}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 3 m - 9 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -21\\ \hline 8 & -66\\ \hline 12 & -90\\ \hline 15& -108\\ \hline \end{tabular}}$

{-3(4)-9=-21}

{-12-9=-21}

{-21=-21}

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.

{-3(8)-9=-66}

{-24-9=-66}

${-33\neq -66}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -33\\ \hline 10 & -39\\ \hline 15 & -43\\ \hline 19& -56\\ \hline \end{tabular}}$

{-3(8)-9=-33}

{-24-9=-33}

{-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.

{-3(10)-9=-39}

{-30-9=-39}

{-39=-39}

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.

{-3(15)-9=-43}

{-45-9=-43}

${-54\neq -43}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -21\\ \hline 9 & -36\\ \hline 18 & -63\\ \hline 19& -66\\ \hline \end{tabular}}$

{-3(4)-9=-21}

{-12-9=-21}

{-21=-21}

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.

{-3(9)-9=-36}

{-27-9=-36}

{-36=-36}

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.

{-3(18)-9=-63}

{-54-9=-63}

{-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.

{-3(19)-9=-66}

{-57+-9=-66}

{-66=-66}

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

Report an Error

Example Question #88 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 13 m - 19 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 59\\ \hline 14 & 326\\ \hline 16 & 378\\ \hline 17& 404\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 20\\ \hline 8 & 85\\ \hline 10 & 122\\ \hline 13& 160\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 60\\ \hline 14 & 165\\ \hline 16 & 192\\ \hline 17& 206\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 59\\ \hline 14 & 163\\ \hline 16 & 189\\ \hline 17& 202\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 59\\ \hline 14 & 163\\ \hline 16 & 189\\ \hline 17& 202\\ \hline \end{tabular}}$

Explanation:

In the equation 13 m - 19 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 60\\ \hline 14 & 165\\ \hline 16 & 192\\ \hline 17& 206\\ \hline \end{tabular}}$

{13(6)+-19=60}

{78+-19=60}

${59\neq 60}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {13 m - 19 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -6\\ \hline 10 & 222\\ \hline 12 & 274\\ \hline 17& 404\\ \hline \end{tabular}}$

{13(1)-19=-6}

{13-19=-6}

{-6=-6}

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.

{13(10)-19=222}

{130-19=222}

${111\neq 222}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 20\\ \hline 8 & 85\\ \hline 10 & 122\\ \hline 13& 160\\ \hline \end{tabular}}$

{13(3)-19=20}

{39-19=20}

{20=20}

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.

{13(8)-19=85}

{104-19=85}

{85=85}

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.

{13(10)-19=122}

{130-19=122}

${111\neq 122}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 15 & 176\\ \hline 16 & 189\\ \hline 17 & 202\\ \hline 18& 215\\ \hline \end{tabular}}$

{13(15)-19=176}

{195-19=176}

{176=176}

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.

{13(16)-19=189}

{208-19=189}

{189=189}

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.

{13(17)-19=202}

{221-19=202}

{202=202}

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.

{13(18)-19=215}

{234+-19=215}

{215=215}

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

Report an Error

Example Question #89 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 17 m - 5 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 4 & 63\\ \hline 9 & 159\\ \hline 13& 226\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -4\\ \hline 6 & 99\\ \hline 8 & 134\\ \hline 18& 305\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 6 & 194\\ \hline 8 & 262\\ \hline 18& 602\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 6 & 97\\ \hline 8 & 131\\ \hline 18& 301\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 6 & 97\\ \hline 8 & 131\\ \hline 18& 301\\ \hline \end{tabular}}$

Explanation:

In the equation 17 m - 5 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -4\\ \hline 6 & 99\\ \hline 8 & 134\\ \hline 18& 305\\ \hline \end{tabular}}$

{17(0)+-5=-4}

{0+-5=-4}

${-5\neq -4}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {17 m - 5 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 80\\ \hline 8 & 262\\ \hline 9 & 296\\ \hline 18& 602\\ \hline \end{tabular}}$

{17(5)-5=80}

{85-5=80}

{80=80}

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.

{17(8)-5=262}

{136-5=262}

${131\neq 262}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 4 & 63\\ \hline 9 & 159\\ \hline 13& 226\\ \hline \end{tabular}}$

{17(0)-5=-5}

{0-5=-5}

{-5=-5}

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.

{17(4)-5=63}

{68-5=63}

{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.

{17(9)-5=159}

{153-5=159}

${148\neq 159}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 114\\ \hline 13 & 216\\ \hline 14 & 233\\ \hline 15& 250\\ \hline \end{tabular}}$

{17(7)-5=114}

{119-5=114}

{114=114}

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.

{17(13)-5=216}

{221-5=216}

{216=216}

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.

{17(14)-5=233}

{238-5=233}

{233=233}

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.

{17(15)-5=250}

{255+-5=250}

{250=250}

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

Report an Error

Example Question #1132 : Grade 6

Select the table of values that represent the relationship between {m} and {n} if m + 6 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 12\\ \hline 6 & 14\\ \hline 7 & 16\\ \hline 18& 28\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 11\\ \hline 6 & 12\\ \hline 7 & 13\\ \hline 18& 24\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 11\\ \hline 6 & 24\\ \hline 7 & 26\\ \hline 18& 48\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 7\\ \hline 11 & 17\\ \hline 13 & 30\\ \hline 14& 30\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 11\\ \hline 6 & 12\\ \hline 7 & 13\\ \hline 18& 24\\ \hline \end{tabular}}$

Explanation:

In the equation m + 6 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 12\\ \hline 6 & 14\\ \hline 7 & 16\\ \hline 18& 28\\ \hline \end{tabular}}$

{1(5)+6=12}

{5+6=12}

${11\neq 12}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {m + 6 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 15\\ \hline 11 & 34\\ \hline 14 & 40\\ \hline 16& 44\\ \hline \end{tabular}}$

{1(9)+6=15}

{9+6=15}

{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.

{1(11)+6=34}

{11+6=34}

${17\neq 34}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 7\\ \hline 11 & 17\\ \hline 13 & 30\\ \hline 14& 20\\ \hline \end{tabular}}$

{1(1)+6=7}

{1+6=7}

{7=7}

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.

{1(11)+6=17}

{11+6=17}

{17=17}

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.

{1(13)+6=30}

{13+6=30}

${19\neq 30}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 5 & 11\\ \hline 16 & 22\\ \hline 17& 23\\ \hline \end{tabular}}$

{1(0)+6=6}

{0+6=6}

{6=6}

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.

{1(5)+6=11}

{5+6=11}

{11=11}

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.

{1(16)+6=22}

{16+6=22}

{22=22}

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.

{1(17)+6=23}

{17+6=23}

{23=23}

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

Report an Error

Example Question #91 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 2 m - 5 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -1\\ \hline 5 & 5\\ \hline 7 & 9\\ \hline 12& 19\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 7\\ \hline 9 & 13\\ \hline 10 & 26\\ \hline 19& 43\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 0\\ \hline 5 & 7\\ \hline 7 & 12\\ \hline 12& 23\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -1\\ \hline 5 & 10\\ \hline 7 & 18\\ \hline 12& 38\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -1\\ \hline 5 & 5\\ \hline 7 & 9\\ \hline 12& 19\\ \hline \end{tabular}}$

Explanation:

In the equation 2 m - 5 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 0\\ \hline 5 & 7\\ \hline 7 & 12\\ \hline 12& 23\\ \hline \end{tabular}}$

{2(2)+-5=0}

{4+-5=0}

${-1\neq 0}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {2 m - 5 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 13\\ \hline 14 & 46\\ \hline 16 & 54\\ \hline 19& 66\\ \hline \end{tabular}}$

{2(9)-5=13}

{18-5=13}

{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.

{2(14)-5=46}

{28-5=46}

${23\neq 46}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 7\\ \hline 9 & 13\\ \hline 10 & 26\\ \hline 19& 43\\ \hline \end{tabular}}$

{2(6)-5=7}

{12-5=7}

{7=7}

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.

{2(9)-5=13}

{18-5=13}

{13=13}

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.

{2(10)-5=26}

{20-5=26}

${15\neq 26}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 11\\ \hline 11 & 17\\ \hline 12 & 19\\ \hline 15& 25\\ \hline \end{tabular}}$

{2(8)-5=11}

{16-5=11}

{11=11}

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.

{2(11)-5=17}

{22-5=17}

{17=17}

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.

{2(12)-5=19}

{24-5=19}

{19=19}

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.

{2(15)-5=25}

{30+-5=25}

{25=25}

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

Report an Error

Example Question #92 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 15 m - 19 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -19\\ \hline 5 & 56\\ \hline 13 & 187\\ \hline 14& 201\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 116\\ \hline 12 & 322\\ \hline 17 & 472\\ \hline 19& 532\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 116\\ \hline 12 & 161\\ \hline 17 & 236\\ \hline 19& 266\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 117\\ \hline 12 & 163\\ \hline 17 & 239\\ \hline 19& 270\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 116\\ \hline 12 & 161\\ \hline 17 & 236\\ \hline 19& 266\\ \hline \end{tabular}}$

Explanation:

In the equation 15 m - 19 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 117\\ \hline 12 & 163\\ \hline 17 & 239\\ \hline 19& 270\\ \hline \end{tabular}}$

{15(9)+-19=117}

{135+-19=117}

${116\neq 117}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {15 m - 19 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 11\\ \hline 7 & 172\\ \hline 8 & 202\\ \hline 19& 532\\ \hline \end{tabular}}$

{15(2)-19=11}

{30-19=11}

{11=11}

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.

{15(7)-19=172}

{105-19=172}

${86\neq 172}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -19\\ \hline 5 & 56\\ \hline 13 & 187\\ \hline 14& 201\\ \hline \end{tabular}}$

{15(0)-19=-19}

{0-19=-19}

{-19=-19}

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.

{15(5)-19=56}

{75-19=56}

{56=56}

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.

{15(13)-19=187}

{195-19=187}

${176\neq 187}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 11\\ \hline 6 & 71\\ \hline 7 & 86\\ \hline 12& 161\\ \hline \end{tabular}}$

{15(2)-19=11}

{30-19=11}

{11=11}

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.

{15(6)-19=71}

{90-19=71}

{71=71}

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.

{15(7)-19=86}

{105-19=86}

{86=86}

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.

{15(12)-19=161}

{180+-19=161}

{161=161}

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

Report an Error

Example Question #91 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 10 m + 7 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 10 & 107\\ \hline 17 & 177\\ \hline 18 & 198\\ \hline 19& 207\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 37\\ \hline 11 & 234\\ \hline 15 & 314\\ \hline 18& 374\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 37\\ \hline 11 & 117\\ \hline 15 & 157\\ \hline 18& 187\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 38\\ \hline 11 & 119\\ \hline 15 & 160\\ \hline 18& 191\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 37\\ \hline 11 & 117\\ \hline 15 & 157\\ \hline 18& 187\\ \hline \end{tabular}}$

Explanation:

In the equation 10 m + 7 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 38\\ \hline 11 & 119\\ \hline 15 & 160\\ \hline 18& 191\\ \hline \end{tabular}}$

{10(3)+7=38}

{30+7=38}

${37\neq 38}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {10 m + 7 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 97\\ \hline 16 & 334\\ \hline 18 & 374\\ \hline 19& 394\\ \hline \end{tabular}}$

{10(9)+7=97}

{90+7=97}

{97=97}

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.

{10(16)+7=334}

{160+7=334}

${167\neq 334}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 10 & 107\\ \hline 17 & 177\\ \hline 18 & 198\\ \hline 19& 197\\ \hline \end{tabular}}$

{10(10)+7=107}

{100+7=107}

{107=107}

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.

{10(17)+7=177}

{170+7=177}

{177=177}

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.

{10(18)+7=198}

{180+7=198}

${187\neq 198}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 27\\ \hline 8 & 87\\ \hline 12 & 127\\ \hline 15& 157\\ \hline \end{tabular}}$

{10(2)+7=27}

{20+7=27}

{27=27}

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.

{10(8)+7=87}

{80+7=87}

{87=87}

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.

{10(12)+7=127}

{120+7=127}

{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.

{10(15)+7=157}

{150+7=157}

{157=157}

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

Report an Error

Example Question #94 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 16 m - 17 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -97\\ \hline 6 & -226\\ \hline 12 & -418\\ \hline 15& -514\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -97\\ \hline 6 & -113\\ \hline 12 & -209\\ \hline 15& -257\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -145\\ \hline 11 & -193\\ \hline 17 & -278\\ \hline 18& -295\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -96\\ \hline 6 & -111\\ \hline 12 & -206\\ \hline 15& -253\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -97\\ \hline 6 & -113\\ \hline 12 & -209\\ \hline 15& -257\\ \hline \end{tabular}}$

Explanation:

In the equation - 16 m - 17 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -96\\ \hline 6 & -111\\ \hline 12 & -206\\ \hline 15& -253\\ \hline \end{tabular}}$

{-16(5)+-17=-96}

{-80+-17=-96}

${-97\neq -96}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 16 m - 17 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -97\\ \hline 13 & -450\\ \hline 16 & -546\\ \hline 19& -642\\ \hline \end{tabular}}$

{-16(5)-17=-97}

{-80-17=-97}

{-97=-97}

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.

{-16(13)-17=-450}

{-208-17=-450}

${-225\neq -450}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -145\\ \hline 11 & -193\\ \hline 17 & -278\\ \hline 18& -295\\ \hline \end{tabular}}$

{-16(8)-17=-145}

{-128-17=-145}

{-145=-145}

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.

{-16(11)-17=-193}

{-176-17=-193}

{-193=-193}

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.

{-16(17)-17=-278}

{-272-17=-278}

${-289\neq -278}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -49\\ \hline 8 & -145\\ \hline 15 & -257\\ \hline 16& -273\\ \hline \end{tabular}}$

{-16(2)-17=-49}

{-32-17=-49}

{-49=-49}

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.

{-16(8)-17=-145}

{-128-17=-145}

{-145=-145}

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.

{-16(15)-17=-257}

{-240-17=-257}

{-257=-257}

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.

{-16(16)-17=-273}

{-256+-17=-273}

{-273=-273}

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

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Common Core: 6th Grade Math : Expressions & Equations

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

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Example Question #85 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #86 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #1131 : Grade 6

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Example Question #1132 : Grade 6

Example Question #91 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #92 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #91 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

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All Common Core: 6th Grade Math Resources

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