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Common Core: 6th Grade Math : Grade 6

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

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All Common Core: 6th Grade Math Resources

6 Diagnostic Tests 186 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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.

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:

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

{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 #681 : Expressions & Equations

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

Possible Answers:

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

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

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

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

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.

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 9 m + 4 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 13\\ \hline 12 & 112\\ \hline 17 & 157\\ \hline 19& 175\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 14\\ \hline 12 & 114\\ \hline 17 & 160\\ \hline 19& 179\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 13\\ \hline 12 & 224\\ \hline 17 & 314\\ \hline 19& 350\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 67\\ \hline 10 & 94\\ \hline 12 & 123\\ \hline 19& 185\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 13\\ \hline 12 & 112\\ \hline 17 & 157\\ \hline 19& 175\\ \hline \end{tabular}}$

Explanation:

In the equation 9 m + 4 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 14\\ \hline 12 & 114\\ \hline 17 & 160\\ \hline 19& 179\\ \hline \end{tabular}}$

{9(1)+4=14}

{9+4=14}

${13\neq 14}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {9 m + 4 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 22\\ \hline 11 & 206\\ \hline 16 & 296\\ \hline 18& 332\\ \hline \end{tabular}}$

{9(2)+4=22}

{18+4=22}

{22=22}

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.

{9(11)+4=206}

{99+4=206}

${103\neq 206}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 67\\ \hline 10 & 94\\ \hline 12 & 123\\ \hline 19& 175\\ \hline \end{tabular}}$

{9(7)+4=67}

{63+4=67}

{67=67}

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.

{9(10)+4=94}

{90+4=94}

{94=94}

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.

{9(12)+4=123}

{108+4=123}

${112\neq 123}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 13\\ \hline 2 & 22\\ \hline 7 & 67\\ \hline 14& 130\\ \hline \end{tabular}}$

{9(1)+4=13}

{9+4=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.

{9(2)+4=22}

{18+4=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.

{9(7)+4=67}

{63+4=67}

{67=67}

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.

{9(14)+4=130}

{126+4=130}

{130=130}

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

Report an Error

Example Question #691 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if 3 m + 13 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 25\\ \hline 10 & 43\\ \hline 11 & 57\\ \hline 14& 65\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 16\\ \hline 6 & 31\\ \hline 14 & 55\\ \hline 18& 67\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 17\\ \hline 6 & 33\\ \hline 14 & 58\\ \hline 18& 71\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 16\\ \hline 6 & 62\\ \hline 14 & 110\\ \hline 18& 134\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 16\\ \hline 6 & 31\\ \hline 14 & 55\\ \hline 18& 67\\ \hline \end{tabular}}$

Explanation:

In the equation 3 m + 13 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 17\\ \hline 6 & 33\\ \hline 14 & 58\\ \hline 18& 71\\ \hline \end{tabular}}$

{3(1)+13=17}

{3+13=17}

${16\neq 17}$

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 + 13 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 28\\ \hline 8 & 74\\ \hline 12 & 98\\ \hline 15& 116\\ \hline \end{tabular}}$

{3(5)+13=28}

{15+13=28}

{28=28}

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)+13=74}

{24+13=74}

${37\neq 74}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 25\\ \hline 10 & 43\\ \hline 11 & 57\\ \hline 14& 55\\ \hline \end{tabular}}$

{3(4)+13=25}

{12+13=25}

{25=25}

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)+13=43}

{30+13=43}

{43=43}

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(11)+13=57}

{33+13=57}

${46\neq 57}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 13\\ \hline 2 & 19\\ \hline 16 & 61\\ \hline 19& 70\\ \hline \end{tabular}}$

{3(0)+13=13}

{0+13=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.

{3(2)+13=19}

{6+13=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.

{3(16)+13=61}

{48+13=61}

{61=61}

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)+13=70}

{57+13=70}

{70=70}

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

Report an Error

Example Question #691 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if - 18 m + 8 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -45\\ \hline 5 & -80\\ \hline 11 & -187\\ \hline 13& -222\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -46\\ \hline 5 & -82\\ \hline 11 & -190\\ \hline 13& -226\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 14 & -244\\ \hline 15 & -262\\ \hline 16 & -269\\ \hline 17& -288\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -46\\ \hline 5 & -164\\ \hline 11 & -380\\ \hline 13& -452\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -46\\ \hline 5 & -82\\ \hline 11 & -190\\ \hline 13& -226\\ \hline \end{tabular}}$

Explanation:

In the equation - 18 m + 8 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -45\\ \hline 5 & -80\\ \hline 11 & -187\\ \hline 13& -222\\ \hline \end{tabular}}$

{-18(3)+8=-45}

{-54+8=-45}

${-46\neq -45}$

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 {- 18 m + 8 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -28\\ \hline 13 & -452\\ \hline 14 & -488\\ \hline 16& -560\\ \hline \end{tabular}}$

{-18(2)+8=-28}

{-36+8=-28}

{-28=-28}

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.

{-18(13)+8=-452}

{-234+8=-452}

${-226\neq -452}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 14 & -244\\ \hline 15 & -262\\ \hline 16 & -269\\ \hline 17& -298\\ \hline \end{tabular}}$

{-18(14)+8=-244}

{-252+8=-244}

{-244=-244}

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.

{-18(15)+8=-262}

{-270+8=-262}

{-262=-262}

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.

{-18(16)+8=-269}

{-288+8=-269}

${-280\neq -269}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -136\\ \hline 10 & -172\\ \hline 11 & -190\\ \hline 15& -262\\ \hline \end{tabular}}$

{-18(8)+8=-136}

{-144+8=-136}

{-136=-136}

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.

{-18(10)+8=-172}

{-180+8=-172}

{-172=-172}

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.

{-18(11)+8=-190}

{-198+8=-190}

{-190=-190}

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.

{-18(15)+8=-262}

{-270+8=-262}

{-262=-262}

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 12 m + 19 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 31\\ \hline 3 & 55\\ \hline 5 & 90\\ \hline 6& 101\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 31\\ \hline 4 & 134\\ \hline 10 & 278\\ \hline 14& 374\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 31\\ \hline 4 & 67\\ \hline 10 & 139\\ \hline 14& 187\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 32\\ \hline 4 & 69\\ \hline 10 & 142\\ \hline 14& 191\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 31\\ \hline 4 & 67\\ \hline 10 & 139\\ \hline 14& 187\\ \hline \end{tabular}}$

Explanation:

In the equation 12 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 32\\ \hline 4 & 69\\ \hline 10 & 142\\ \hline 14& 191\\ \hline \end{tabular}}$

{12(1)+19=32}

{12+19=32}

${31\neq 32}$

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 {12 m + 19 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 91\\ \hline 15 & 398\\ \hline 17 & 446\\ \hline 18& 470\\ \hline \end{tabular}}$

{12(6)+19=91}

{72+19=91}

{91=91}

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.

{12(15)+19=398}

{180+19=398}

${199\neq 398}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 31\\ \hline 3 & 55\\ \hline 5 & 90\\ \hline 6& 91\\ \hline \end{tabular}}$

{12(1)+19=31}

{12+19=31}

{31=31}

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.

{12(3)+19=55}

{36+19=55}

{55=55}

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.

{12(5)+19=90}

{60+19=90}

${79\neq 90}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 115\\ \hline 10 & 139\\ \hline 12 & 163\\ \hline 14& 187\\ \hline \end{tabular}}$

{12(8)+19=115}

{96+19=115}

{115=115}

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.

{12(10)+19=139}

{120+19=139}

{139=139}

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.

{12(12)+19=163}

{144+19=163}

{163=163}

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.

{12(14)+19=187}

{168+19=187}

{187=187}

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

Report an Error

Example Question #692 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if 16 m - 9 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 40\\ \hline 7 & 105\\ \hline 14 & 218\\ \hline 18& 283\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 39\\ \hline 7 & 103\\ \hline 14 & 215\\ \hline 18& 279\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 7\\ \hline 3 & 39\\ \hline 6 & 98\\ \hline 8& 129\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 39\\ \hline 7 & 206\\ \hline 14 & 430\\ \hline 18& 558\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 39\\ \hline 7 & 103\\ \hline 14 & 215\\ \hline 18& 279\\ \hline \end{tabular}}$

Explanation:

In the equation 16 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 40\\ \hline 7 & 105\\ \hline 14 & 218\\ \hline 18& 283\\ \hline \end{tabular}}$

{16(3)+-9=40}

{48+-9=40}

${39\neq 40}$

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 - 9 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 39\\ \hline 8 & 238\\ \hline 11 & 334\\ \hline 18& 558\\ \hline \end{tabular}}$

{16(3)-9=39}

{48-9=39}

{39=39}

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)-9=238}

{128-9=238}

${119\neq 238}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 7\\ \hline 3 & 39\\ \hline 6 & 98\\ \hline 8& 129\\ \hline \end{tabular}}$

{16(1)-9=7}

{16-9=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.

{16(3)-9=39}

{48-9=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.

{16(6)-9=98}

{96-9=98}

${87\neq 98}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 39\\ \hline 12 & 183\\ \hline 17 & 263\\ \hline 18& 279\\ \hline \end{tabular}}$

{16(3)-9=39}

{48-9=39}

{39=39}

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(12)-9=183}

{192-9=183}

{183=183}

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)-9=263}

{272-9=263}

{263=263}

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(18)-9=279}

{288+-9=279}

{279=279}

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

Report an Error

Example Question #96 : 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 - 20 m - 2 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -22\\ \hline 14 & -282\\ \hline 16 & -322\\ \hline 18& -362\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -21\\ \hline 14 & -280\\ \hline 16 & -319\\ \hline 18& -358\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -162\\ \hline 12 & -242\\ \hline 14 & -271\\ \hline 18& -352\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -22\\ \hline 14 & -564\\ \hline 16 & -644\\ \hline 18& -724\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -22\\ \hline 14 & -282\\ \hline 16 & -322\\ \hline 18& -362\\ \hline \end{tabular}}$

Explanation:

In the equation - 20 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -21\\ \hline 14 & -280\\ \hline 16 & -319\\ \hline 18& -358\\ \hline \end{tabular}}$

{-20(1)+-2=-21}

{-20+-2=-21}

${-22\neq -21}$

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 {- 20 m - 2 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -2\\ \hline 1 & -44\\ \hline 3 & -124\\ \hline 11& -444\\ \hline \end{tabular}}$

{-20(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.

{-20(1)-2=-44}

{-20-2=-44}

${-22\neq -44}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -162\\ \hline 12 & -242\\ \hline 14 & -271\\ \hline 18& -352\\ \hline \end{tabular}}$

{-20(8)-2=-162}

{-160-2=-162}

{-162=-162}

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.

{-20(12)-2=-242}

{-240-2=-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.

{-20(14)-2=-271}

{-280-2=-271}

${-282\neq -271}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -22\\ \hline 4 & -82\\ \hline 6 & -122\\ \hline 7& -142\\ \hline \end{tabular}}$

{-20(1)-2=-22}

{-20-2=-22}

{-22=-22}

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.

{-20(4)-2=-82}

{-80-2=-82}

{-82=-82}

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.

{-20(6)-2=-122}

{-120-2=-122}

{-122=-122}

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.

{-20(7)-2=-142}

{-140+-2=-142}

{-142=-142}

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

Report an Error

Example Question #101 : 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 + 6 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 78\\ \hline 11 & 188\\ \hline 15 & 252\\ \hline 18& 300\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 79\\ \hline 11 & 96\\ \hline 15 & 129\\ \hline 18& 154\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 78\\ \hline 11 & 94\\ \hline 15 & 126\\ \hline 18& 150\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 5 & 46\\ \hline 12 & 113\\ \hline 19& 168\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 78\\ \hline 11 & 94\\ \hline 15 & 126\\ \hline 18& 150\\ \hline \end{tabular}}$

Explanation:

In the equation 8 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 79\\ \hline 11 & 96\\ \hline 15 & 129\\ \hline 18& 154\\ \hline \end{tabular}}$

{8(9)+6=79}

{72+6=79}

${78\neq 79}$

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 + 6 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 2 & 44\\ \hline 5 & 92\\ \hline 16& 268\\ \hline \end{tabular}}$

{8(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.

{8(2)+6=44}

{16+6=44}

${22\neq 44}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 5 & 46\\ \hline 12 & 113\\ \hline 19& 158\\ \hline \end{tabular}}$

{8(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.

{8(5)+6=46}

{40+6=46}

{46=46}

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(12)+6=113}

{96+6=113}

${102\neq 113}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 62\\ \hline 10 & 86\\ \hline 12 & 102\\ \hline 14& 118\\ \hline \end{tabular}}$

{8(7)+6=62}

{56+6=62}

{62=62}

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(10)+6=86}

{80+6=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.

{8(12)+6=102}

{96+6=102}

{102=102}

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(14)+6=118}

{112+6=118}

{118=118}

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 : Grade 6

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

All Common Core: 6th Grade Math Resources

Example Questions

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

Example Question #681 : Expressions & Equations

Example Question #94 : 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 #691 : Expressions & Equations

Example Question #691 : Expressions & Equations

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

Example Question #692 : Expressions & Equations

Example Question #96 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #101 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

All Common Core: 6th Grade Math Resources

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