Common Core: 6th Grade Math : The Number System

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

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Example Questions

Example Question #441 : Grade 6

Nicole decided to run from her house to her friend Alyssa's house. If we were to draw Nicole's house and Alyssa's house on a coordinate plane, Nicole lives at point  and Alyssa lives at point . Create a coordinate plane to help determine the distance, in units, that Nicole runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Nicole lives at point  and Alyssa lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 4
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Nicole ran {mathcode} units to Alyssa's house.

Example Question #112 : Solve Problems By Graphing Points In Quadrants Of A Coordinate Plane: Ccss.Math.Content.6.Ns.C.8

Kameron decided to run from her house to her friend Alyssa's house. If we were to draw Kameron's house and Alyssa's house on a coordinate plane, Kameron lives at point  and Alyssa lives at point . Create a coordinate plane to help determine the distance, in units, that Kameron runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Kameron lives at point  and Alyssa lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 6
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Kameron ran {mathcode} units to Alyssa's house.

Example Question #113 : Solve Problems By Graphing Points In Quadrants Of A Coordinate Plane: Ccss.Math.Content.6.Ns.C.8

Kameron decided to run from her house to her friend Linda's house. If we were to draw Kameron's house and Linda's house on a coordinate plane, Kameron lives at point  and Linda lives at point . Create a coordinate plane to help determine the distance, in units, that Kameron runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Kameron lives at point  and Linda lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 8
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Kameron ran {mathcode} units to Linda's house.

Example Question #442 : Grade 6

Jenny decided to run from her house to her friend Kathy's house. If we were to draw Jenny's house and Kathy's house on a coordinate plane, Jenny lives at point  and Kathy lives at point . Create a coordinate plane to help determine the distance, in units, that Jenny runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Jenny lives at point  and Kathy lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 9
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Jenny ran {mathcode} units to Kathy's house.

Example Question #443 : Grade 6

Jessica decided to run from her house to her friend Brittany's house. If we were to draw Jessica's house and Brittany's house on a coordinate plane, Jessica lives at point  and Brittany lives at point . Create a coordinate plane to help determine the distance, in units, that Jessica runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Jessica lives at point  and Brittany lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 10
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Jessica ran {mathcode} units to Brittany's house.

Example Question #444 : Grade 6

Mackenzie decided to run from her house to her friend Alex's house. If we were to draw Mackenzie's house and Alex's house on a coordinate plane, Mackenzie lives at point  and Alex lives at point . Create a coordinate plane to help determine the distance, in units, that Mackenzie runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Mackenzie lives at point  and Alex lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 12
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Mackenzie ran {mathcode} units to Alex's house.

Example Question #111 : Solve Problems By Graphing Points In Quadrants Of A Coordinate Plane: Ccss.Math.Content.6.Ns.C.8

Nicole decided to run from her house to her friend Cassie's house. If we were to draw Nicole's house and Cassie's house on a coordinate plane, Nicole lives at point  and Cassie lives at point . Create a coordinate plane to help determine the distance, in units, that Nicole runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Nicole lives at point  and Cassie lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 5
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Nicole ran {mathcode} units to Cassie's house.

Example Question #112 : Solve Problems By Graphing Points In Quadrants Of A Coordinate Plane: Ccss.Math.Content.6.Ns.C.8

Jenny decided to run from her house to her friend Miranda's house. If we were to draw Jenny's house and Miranda's house on a coordinate plane, Jenny lives at point  and Miranda lives at point . Create a coordinate plane to help determine the distance, in units, that Jenny runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Jenny lives at point  and Miranda lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 7
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Jenny ran {mathcode} units to Miranda's house.

Example Question #113 : Solve Problems By Graphing Points In Quadrants Of A Coordinate Plane: Ccss.Math.Content.6.Ns.C.8

Shelly decided to run from her house to her friend Linda's house. If we were to draw Shelly's house and Linda's house on a coordinate plane, Shelly lives at point  and Linda lives at point . Create a coordinate plane to help determine the distance, in units, that Shelly runs.

Possible Answers:

Correct answer:

Explanation:

From our question we know that Shelly lives at point  and Linda lives at point . We want to draw a coordinate plane and plot both of these points. Your coordinate plane should look something like the following:

Plot 11
Now that we have these points graphed, we can count the units between them. Now that we have these points graphed, we can count the units between them. Shelly ran {mathcode} units to Linda's house.

Example Question #1 : Dividing Multi Digit Decimals

Solve:

Possible Answers:

Correct answer:

Explanation:

The first thing that we want to do when dividing decimals is to turn the divisor into a whole number. We do this by moving the decimal place to the right: 

Screen shot 2020 10 08 at 11.52.33 am

If we move the decimal over one place in the divisor, we must also move the decimal over one place in the dividend:  

Screen shot 2020 10 08 at 11.52.37 am

The new division problem should look as follows:  

Screen shot 2020 10 08 at 11.52.40 am

*Notice how we've already placed the decimal in our answer. When we divide decimals, we place the decimal directly above the decimal in the dividend, but only after we've completed the first two steps of moving the decimal point in the divisor and dividend.

Now we can divide like normal:

Screen shot 2020 10 08 at 11.52.40 am

Think: how many times can 76 go into 197

76 can go into 197 two times so we write a 2 over the 7 in the dividend:

Screen shot 2020 10 08 at 11.52.50 am

Next, we multiply 2 and 76 and write that product underneath the 197 and subtract:

Screen shot 2020 10 08 at 11.52.54 am

Now we bring down the 6 from the dividend to make the 45 into a 456.

Think: how many times can 76 go into 456?

76 can go into 465 six times so we write a 6 above the 6 in the dividend:

Screen shot 2020 10 08 at 11.52.59 am

Next, we multiply 6 and 76 and write that product underneath the 456 and subtract:

Screen shot 2020 10 08 at 11.53.02 am

We are left with no remainder and a final quotient of 2.6

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