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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 #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 19 m + 2 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 21\\ \hline 5 & 97\\ \hline 7 & 135\\ \hline 19& 363\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 22\\ \hline 5 & 99\\ \hline 7 & 138\\ \hline 19& 367\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 21\\ \hline 5 & 97\\ \hline 7 & 146\\ \hline 13& 259\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 21\\ \hline 5 & 194\\ \hline 7 & 270\\ \hline 19& 726\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 21\\ \hline 5 & 97\\ \hline 7 & 135\\ \hline 19& 363\\ \hline \end{tabular}}$

Explanation:

In the equation 19 m + 2 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 22\\ \hline 5 & 99\\ \hline 7 & 138\\ \hline 19& 367\\ \hline \end{tabular}}$

{19(1)+2=22}

{19+2=22}

${21\neq 22}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 116\\ \hline 7 & 270\\ \hline 10 & 384\\ \hline 13& 498\\ \hline \end{tabular}}$

{19(6)+2=116}

{114+2=116}

{116=116}

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.

{19(7)+2=270}

{133+2=270}

${135\neq 270}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 21\\ \hline 5 & 97\\ \hline 7 & 146\\ \hline 13& 249\\ \hline \end{tabular}}$

{19(1)+2=21}

{19+2=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.

{19(5)+2=97}

{95+2=97}

{97=97}

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.

{19(7)+2=146}

{133+2=146}

${135\neq 146}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 2\\ \hline 7 & 135\\ \hline 8 & 154\\ \hline 13& 249\\ \hline \end{tabular}}$

{19(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.

{19(7)+2=135}

{133+2=135}

{135=135}

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.

{19(8)+2=154}

{152+2=154}

{154=154}

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.

{19(13)+2=249}

{247+2=249}

{249=249}

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

Report an Error

Example Question #699 : Expressions & Equations

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

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 3\\ \hline 11 & -1\\ \hline 12 & 9\\ \hline 19& 1\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 3\\ \hline 13 & -3\\ \hline 18 & -8\\ \hline 19& -9\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 3\\ \hline 13 & -6\\ \hline 18 & -16\\ \hline 19& -18\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 4\\ \hline 13 & -1\\ \hline 18 & -5\\ \hline 19& -5\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 3\\ \hline 13 & -3\\ \hline 18 & -8\\ \hline 19& -9\\ \hline \end{tabular}}$

Explanation:

In the equation - m + 10 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 4\\ \hline 13 & -1\\ \hline 18 & -5\\ \hline 19& -5\\ \hline \end{tabular}}$

{-1(7)+10=4}

{-7+10=4}

${3\neq 4}$

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 {- m + 10 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 8\\ \hline 6 & 8\\ \hline 14 & -8\\ \hline 16& -12\\ \hline \end{tabular}}$

{-1(2)+10=8}

{-2+10=8}

{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.

{-1(6)+10=8}

{-6+10=8}

${4\neq 8}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 3\\ \hline 11 & -1\\ \hline 12 & 9\\ \hline 19& -9\\ \hline \end{tabular}}$

{-1(7)+10=3}

{-7+10=3}

{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.

{-1(11)+10=-1}

{-11+10=-1}

{-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.

{-1(12)+10=9}

{-12+10=9}

${-2\neq 9}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 5\\ \hline 6 & 4\\ \hline 13 & -3\\ \hline 14& -4\\ \hline \end{tabular}}$

{-1(5)+10=5}

{-5+10=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.

{-1(6)+10=4}

{-6+10=4}

{4=4}

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)+10=-3}

{-13+10=-3}

{-3=-3}

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(14)+10=-4}

{-14+10=-4}

{-4=-4}

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

Report an Error

Example Question #102 : 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 + 5 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 21\\ \hline 13 & 213\\ \hline 17 & 288\\ \hline 19& 319\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 53\\ \hline 9 & 149\\ \hline 10 & 165\\ \hline 15& 245\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 54\\ \hline 9 & 151\\ \hline 10 & 168\\ \hline 15& 249\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 53\\ \hline 9 & 298\\ \hline 10 & 330\\ \hline 15& 490\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 53\\ \hline 9 & 149\\ \hline 10 & 165\\ \hline 15& 245\\ \hline \end{tabular}}$

Explanation:

In the equation 16 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 54\\ \hline 9 & 151\\ \hline 10 & 168\\ \hline 15& 249\\ \hline \end{tabular}}$

{16(3)+5=54}

{48+5=54}

${53\neq 54}$

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 + 5 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 37\\ \hline 9 & 298\\ \hline 13 & 426\\ \hline 17& 554\\ \hline \end{tabular}}$

{16(2)+5=37}

{32+5=37}

{37=37}

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(9)+5=298}

{144+5=298}

${149\neq 298}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 21\\ \hline 13 & 213\\ \hline 17 & 288\\ \hline 19& 309\\ \hline \end{tabular}}$

{16(1)+5=21}

{16+5=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.

{16(13)+5=213}

{208+5=213}

{213=213}

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)+5=288}

{272+5=288}

${277\neq 288}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 4 & 69\\ \hline 8 & 133\\ \hline 18& 293\\ \hline \end{tabular}}$

{16(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.

{16(4)+5=69}

{64+5=69}

{69=69}

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(8)+5=133}

{128+5=133}

{133=133}

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)+5=293}

{288+5=293}

{293=293}

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 - 19 m + 19 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 1 & 0\\ \hline 7 & -228\\ \hline 15& -532\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 20\\ \hline 1 & 2\\ \hline 7 & -111\\ \hline 15& -262\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 0\\ \hline 2 & -19\\ \hline 12 & -198\\ \hline 15& -256\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 1 & 0\\ \hline 7 & -114\\ \hline 15& -266\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 1 & 0\\ \hline 7 & -114\\ \hline 15& -266\\ \hline \end{tabular}}$

Explanation:

In the equation - 19 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 20\\ \hline 1 & 2\\ \hline 7 & -111\\ \hline 15& -262\\ \hline \end{tabular}}$

{-19(0)+19=20}

{0+19=20}

${19\neq 20}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -19\\ \hline 3 & -76\\ \hline 12 & -418\\ \hline 15& -532\\ \hline \end{tabular}}$

{-19(2)+19=-19}

{-38+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.

{-19(3)+19=-76}

{-57+19=-76}

${-38\neq -76}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 0\\ \hline 2 & -19\\ \hline 12 & -198\\ \hline 15& -266\\ \hline \end{tabular}}$

{-19(1)+19=0}

{-19+19=0}

{0=0}

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.

{-19(2)+19=-19}

{-38+19=-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.

{-19(12)+19=-198}

{-228+19=-198}

${-209\neq -198}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -57\\ \hline 5 & -76\\ \hline 10 & -171\\ \hline 16& -285\\ \hline \end{tabular}}$

{-19(4)+19=-57}

{-76+19=-57}

{-57=-57}

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.

{-19(5)+19=-76}

{-95+19=-76}

{-76=-76}

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.

{-19(10)+19=-171}

{-190+19=-171}

{-171=-171}

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.

{-19(16)+19=-285}

{-304+19=-285}

{-285=-285}

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

Report an Error

Example Question #102 : 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 - 3 m - 2 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -4\\ \hline 5 & -15\\ \hline 7 & -20\\ \hline 16& -46\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -8\\ \hline 7 & -23\\ \hline 14 & -33\\ \hline 19& -49\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -5\\ \hline 5 & -17\\ \hline 7 & -23\\ \hline 16& -50\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -5\\ \hline 5 & -34\\ \hline 7 & -46\\ \hline 16& -100\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -5\\ \hline 5 & -17\\ \hline 7 & -23\\ \hline 16& -50\\ \hline \end{tabular}}$

Explanation:

In the equation - 3 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -4\\ \hline 5 & -15\\ \hline 7 & -20\\ \hline 16& -46\\ \hline \end{tabular}}$

{-3(1)+-2=-4}

{-3+-2=-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 {- 3 m - 2 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -2\\ \hline 2 & -16\\ \hline 11 & -70\\ \hline 16& -100\\ \hline \end{tabular}}$

{-3(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.

{-3(2)-2=-16}

{-6-2=-16}

${-8\neq -16}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -8\\ \hline 7 & -23\\ \hline 14 & -33\\ \hline 19& -49\\ \hline \end{tabular}}$

{-3(2)-2=-8}

{-6-2=-8}

{-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.

{-3(7)-2=-23}

{-21-2=-23}

{-23=-23}

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(14)-2=-33}

{-42-2=-33}

${-44\neq -33}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -5\\ \hline 3 & -11\\ \hline 10 & -32\\ \hline 16& -50\\ \hline \end{tabular}}$

{-3(1)-2=-5}

{-3-2=-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.

{-3(3)-2=-11}

{-9-2=-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.

{-3(10)-2=-32}

{-30-2=-32}

{-32=-32}

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)-2=-50}

{-48+-2=-50}

{-50=-50}

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

Report an Error

Example Question #701 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if 6 m - 4 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 2\\ \hline 4 & 20\\ \hline 11 & 73\\ \hline 15& 96\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 26\\ \hline 12 & 68\\ \hline 17 & 98\\ \hline 18& 104\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 26\\ \hline 12 & 136\\ \hline 17 & 196\\ \hline 18& 208\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 27\\ \hline 12 & 70\\ \hline 17 & 101\\ \hline 18& 108\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 26\\ \hline 12 & 68\\ \hline 17 & 98\\ \hline 18& 104\\ \hline \end{tabular}}$

Explanation:

In the equation 6 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 27\\ \hline 12 & 70\\ \hline 17 & 101\\ \hline 18& 108\\ \hline \end{tabular}}$

{6(5)+-4=27}

{30+-4=27}

${26\neq 27}$

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 {6 m - 4 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -4\\ \hline 1 & 4\\ \hline 5 & 52\\ \hline 14& 160\\ \hline \end{tabular}}$

{6(0)-4=-4}

{0-4=-4}

{-4=-4}

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.

{6(1)-4=4}

{6-4=4}

${2\neq 4}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 2\\ \hline 4 & 20\\ \hline 11 & 73\\ \hline 15& 96\\ \hline \end{tabular}}$

{6(1)-4=2}

{6-4=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.

{6(4)-4=20}

{24-4=20}

{20=20}

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.

{6(11)-4=73}

{66-4=73}

${62\neq 73}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 8\\ \hline 6 & 32\\ \hline 9 & 50\\ \hline 18& 104\\ \hline \end{tabular}}$

{6(2)-4=8}

{12-4=8}

{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.

{6(6)-4=32}

{36-4=32}

{32=32}

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.

{6(9)-4=50}

{54-4=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.

{6(18)-4=104}

{108+-4=104}

{104=104}

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

Report an Error

Example Question #701 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if - 3 m - 18 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -30\\ \hline 8 & -42\\ \hline 10 & -37\\ \hline 16& -56\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -18\\ \hline 3 & -27\\ \hline 8 & -42\\ \hline 17& -69\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -17\\ \hline 3 & -25\\ \hline 8 & -39\\ \hline 17& -65\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -18\\ \hline 3 & -54\\ \hline 8 & -84\\ \hline 17& -138\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -18\\ \hline 3 & -27\\ \hline 8 & -42\\ \hline 17& -69\\ \hline \end{tabular}}$

Explanation:

In the equation - 3 m - 18 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -17\\ \hline 3 & -25\\ \hline 8 & -39\\ \hline 17& -65\\ \hline \end{tabular}}$

{-3(0)+-18=-17}

{0+-18=-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 - 18 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -27\\ \hline 9 & -90\\ \hline 14 & -120\\ \hline 16& -132\\ \hline \end{tabular}}$

{-3(3)-18=-27}

{-9-18=-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.

{-3(9)-18=-90}

{-27-18=-90}

${-45\neq -90}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -30\\ \hline 8 & -42\\ \hline 10 & -37\\ \hline 16& -56\\ \hline \end{tabular}}$

{-3(4)-18=-30}

{-12-18=-30}

{-30=-30}

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)-18=-42}

{-24-18=-42}

{-42=-42}

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(10)-18=-37}

{-30-18=-37}

${-48\neq -37}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -45\\ \hline 11 & -51\\ \hline 12 & -54\\ \hline 14& -60\\ \hline \end{tabular}}$

{-3(9)-18=-45}

{-27-18=-45}

{-45=-45}

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)-18=-51}

{-33-18=-51}

{-51=-51}

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(12)-18=-54}

{-36-18=-54}

{-54=-54}

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(14)-18=-60}

{-42+-18=-60}

{-60=-60}

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

Report an Error

Example Question #702 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if 2 m + 15 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 17\\ \hline 6 & 27\\ \hline 7 & 29\\ \hline 18& 51\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 17\\ \hline 6 & 54\\ \hline 7 & 58\\ \hline 18& 102\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 23\\ \hline 15 & 45\\ \hline 16 & 58\\ \hline 18& 61\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 18\\ \hline 6 & 29\\ \hline 7 & 32\\ \hline 18& 55\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 17\\ \hline 6 & 27\\ \hline 7 & 29\\ \hline 18& 51\\ \hline \end{tabular}}$

Explanation:

In the equation 2 m + 15 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 18\\ \hline 6 & 29\\ \hline 7 & 32\\ \hline 18& 55\\ \hline \end{tabular}}$

{2(1)+15=18}

{2+15=18}

${17\neq 18}$

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 + 15 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 23\\ \hline 6 & 54\\ \hline 10 & 70\\ \hline 19& 106\\ \hline \end{tabular}}$

{2(4)+15=23}

{8+15=23}

{23=23}

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(6)+15=54}

{12+15=54}

${27\neq 54}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 23\\ \hline 15 & 45\\ \hline 16 & 58\\ \hline 18& 51\\ \hline \end{tabular}}$

{2(4)+15=23}

{8+15=23}

{23=23}

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)+15=45}

{30+15=45}

{45=45}

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(16)+15=58}

{32+15=58}

${47\neq 58}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 33\\ \hline 10 & 35\\ \hline 16 & 47\\ \hline 18& 51\\ \hline \end{tabular}}$

{2(9)+15=33}

{18+15=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.

{2(10)+15=35}

{20+15=35}

{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.

{2(16)+15=47}

{32+15=47}

{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.

{2(18)+15=51}

{36+15=51}

{51=51}

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

Report an Error

Example Question #703 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if - 7 m + 17 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 17\\ \hline 5 & -18\\ \hline 11 & -60\\ \hline 18& -109\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 18\\ \hline 5 & -16\\ \hline 11 & -57\\ \hline 18& -105\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 17\\ \hline 8 & -39\\ \hline 10 & -42\\ \hline 14& -71\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 17\\ \hline 5 & -36\\ \hline 11 & -120\\ \hline 18& -218\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 17\\ \hline 5 & -18\\ \hline 11 & -60\\ \hline 18& -109\\ \hline \end{tabular}}$

Explanation:

In the equation - 7 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 18\\ \hline 5 & -16\\ \hline 11 & -57\\ \hline 18& -105\\ \hline \end{tabular}}$

{-7(0)+17=18}

{0+17=18}

${17\neq 18}$

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 {- 7 m + 17 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 3\\ \hline 15 & -176\\ \hline 18 & -218\\ \hline 19& -232\\ \hline \end{tabular}}$

{-7(2)+17=3}

{-14+17=3}

{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.

{-7(15)+17=-176}

{-105+17=-176}

${-88\neq -176}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 17\\ \hline 8 & -39\\ \hline 10 & -42\\ \hline 14& -81\\ \hline \end{tabular}}$

{-7(0)+17=17}

{0+17=17}

{17=17}

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.

{-7(8)+17=-39}

{-56+17=-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.

{-7(10)+17=-42}

{-70+17=-42}

${-53\neq -42}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 10\\ \hline 13 & -74\\ \hline 17 & -102\\ \hline 19& -116\\ \hline \end{tabular}}$

{-7(1)+17=10}

{-7+17=10}

{10=10}

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.

{-7(13)+17=-74}

{-91+17=-74}

{-74=-74}

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.

{-7(17)+17=-102}

{-119+17=-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.

{-7(19)+17=-116}

{-133+17=-116}

{-116=-116}

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

Report an Error

Example Question #111 : 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 3 m - 13 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -12\\ \hline 9 & 16\\ \hline 13 & 29\\ \hline 14& 33\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 5\\ \hline 11 & 20\\ \hline 12 & 34\\ \hline 14& 39\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -13\\ \hline 9 & 28\\ \hline 13 & 52\\ \hline 14& 58\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -13\\ \hline 9 & 14\\ \hline 13 & 26\\ \hline 14& 29\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -13\\ \hline 9 & 14\\ \hline 13 & 26\\ \hline 14& 29\\ \hline \end{tabular}}$

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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -12\\ \hline 9 & 16\\ \hline 13 & 29\\ \hline 14& 33\\ \hline \end{tabular}}$

{3(0)+-13=-12}

{0+-13=-12}

${-13\neq -12}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -7\\ \hline 10 & 34\\ \hline 11 & 40\\ \hline 12& 46\\ \hline \end{tabular}}$

{3(2)-13=-7}

{6-13=-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.

{3(10)-13=34}

{30-13=34}

${17\neq 34}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 5\\ \hline 11 & 20\\ \hline 12 & 34\\ \hline 14& 39\\ \hline \end{tabular}}$

{3(6)-13=5}

{18-13=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.

{3(11)-13=20}

{33-13=20}

{20=20}

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(12)-13=34}

{36-13=34}

${23\neq 34}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -13\\ \hline 6 & 5\\ \hline 12 & 23\\ \hline 19& 44\\ \hline \end{tabular}}$

{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(6)-13=5}

{18-13=5}

{5=5}

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(12)-13=23}

{36-13=23}

{23=23}

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=44}

{57+-13=44}

{44=44}

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

Report an Error

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

Example Question #699 : Expressions & Equations

Example Question #102 : 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

Example Question #102 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #701 : Expressions & Equations

Example Question #701 : Expressions & Equations

Example Question #702 : Expressions & Equations

Example Question #703 : Expressions & Equations

Example Question #111 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

All Common Core: 6th Grade Math Resources

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