Common Core: 7th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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Example Questions

Example Question #1 : How To Subtract Negative Numbers

Compute the following:  \(\displaystyle -12 -(-3)-(-4)+5\)

Possible Answers:

\(\displaystyle -14\)

\(\displaystyle 0\)

\(\displaystyle -24\)

\(\displaystyle -6\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 0\)

Explanation:

Convert all the double signs to a single sign before solving. Remember, two minus (negative) signs combine to form a plus (positive) sign, and a plus (positive) sign and a minus (negative) sign combine to form a minus (negative) sign.

\(\displaystyle -12 -(-3)-(-4)+5\)

\(\displaystyle -12+3+4+5=0\)

Example Question #1 : Describe Situations In Which Opposite Quantities Combine To Make 0: Ccss.Math.Content.7.Ns.A.1a

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 11+x=0\)

Possible Answers:

\(\displaystyle 1\)

\(\displaystyle -11\)

\(\displaystyle 10\)

\(\displaystyle 0\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle -11\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 11\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}11+x=0\\ -11\ \ \ \ -11\end{array}}{\\\\x=-11}\)

Example Question #2 : Describe Situations In Which Opposite Quantities Combine To Make 0: Ccss.Math.Content.7.Ns.A.1a

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 24+x=0\)

 

Possible Answers:

\(\displaystyle -24\)

\(\displaystyle 24\)

\(\displaystyle 20\)

\(\displaystyle 0\)

\(\displaystyle 1\)

Correct answer:

\(\displaystyle -24\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 24\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}24+x=0\\ -24\ \ \ \ -24\end{array}}{\\\\x=-24}\)

Example Question #1 : Describe Situations In Which Opposite Quantities Combine To Make 0: Ccss.Math.Content.7.Ns.A.1a

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 38+x=0\)

 

Possible Answers:

\(\displaystyle -38\)

\(\displaystyle 32\)

\(\displaystyle 1\)

\(\displaystyle 0\)

\(\displaystyle 38\)

Correct answer:

\(\displaystyle -38\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 38\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}38+x=0\\ -38\ \ \ \ -38\end{array}}{\\\\x=-38}\)

Example Question #1 : The Number System

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 62+x=0\)

 

Possible Answers:

\(\displaystyle 1\)

\(\displaystyle 60\)

\(\displaystyle -62\)

\(\displaystyle 0\)

\(\displaystyle 62\)

Correct answer:

\(\displaystyle -62\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 62\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}62+x=0\\ -62\ \ \ \ -62\end{array}}{\\\\x=-62}\)

Example Question #1 : The Number System

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 70+x=0\)

 

Possible Answers:

\(\displaystyle -10\)

\(\displaystyle -70\)

\(\displaystyle 1\)

\(\displaystyle 70\)

\(\displaystyle 0\)

Correct answer:

\(\displaystyle -70\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 70\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}70+x=0\\ -70\ \ \ \ -70\end{array}}{\\\\x=-70}\)

Example Question #2 : The Number System

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 86+x=0\)

 

Possible Answers:

\(\displaystyle 86\)

\(\displaystyle 1\)

\(\displaystyle -1\)

\(\displaystyle -86\)

\(\displaystyle 0\)

Correct answer:

\(\displaystyle -86\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 86\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}86+x=0\\ -86\ \ \ \ -86\end{array}}{\\\\x=-86}\)

Example Question #5 : Describe Situations In Which Opposite Quantities Combine To Make 0: Ccss.Math.Content.7.Ns.A.1a

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 99+x=0\)

 

Possible Answers:

\(\displaystyle -1\)

\(\displaystyle -90\)

\(\displaystyle -99\)

\(\displaystyle 99\)

\(\displaystyle 0\)

Correct answer:

\(\displaystyle -99\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 99\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}99+x=0\\ -99\ \ \ \ -99\end{array}}{\\\\x=-99}\)

Example Question #1 : The Number System

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 59+x=0\)

 

Possible Answers:

\(\displaystyle 0\)

\(\displaystyle 50\)

\(\displaystyle 1\)

\(\displaystyle -59\)

\(\displaystyle 59\)

Correct answer:

\(\displaystyle -59\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 59\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}59+x=0\\ -59\ \ \ \ -59\end{array}}{\\\\x=-59}\)

Example Question #5 : Describe Situations In Which Opposite Quantities Combine To Make 0: Ccss.Math.Content.7.Ns.A.1a

For the equation provided, what value when substituted for \(\displaystyle x\), will equal \(\displaystyle 0?\)

\(\displaystyle 19+x=0\)

 

Possible Answers:

\(\displaystyle 0\)

\(\displaystyle -19\)

\(\displaystyle 19\)

\(\displaystyle 1\)

\(\displaystyle -1\)

Correct answer:

\(\displaystyle -19\)

Explanation:

In order to answer this question, we can solve for \(\displaystyle x\). When solving for \(\displaystyle x\) we need to isolate the \(\displaystyle x\) variable on one side of the equation. 

We can subtract \(\displaystyle 19\) to both sides in order to isolate the variable, \(\displaystyle x\).

\(\displaystyle \frac{\begin{array}[b]{r}19+x=0\\ -19\ \ \ \ -19\end{array}}{\\\\x=-19}\)

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