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Common Core: 6th Grade Math : The Number System

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 #31 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{6.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{4} \overset{~\ }{6} \\ \hline \end{array}$

Possible Answers:

17.4

29.54

11.01

54.29

Correct answer:

54.29

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{3+6=9}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{6.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{4} \overset{~\ }{6} \\ \hline \space{} \, \space{\, } \space{\, }9\end{array}$

Add the numbers in the tenths place:

{8+4=12}

Because this sum is greater than 9, we write the 2 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{6.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{4} \overset{~\ }{6} \\ \hline \space{} \, \space{\,. }2\space{\, }9\end{array}$

Add the numbers in the ones place:

{6+7+1=14}

Because this sum is greater than 9, we write the 4 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ 1}{3} \overset{\ 1}{6.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{4} \overset{~\ }{6} \\ \hline \space{} \, 4\space{\,. }2\space{\, }9\end{array}$

Your final answer should be: 54.29

$\begin{array}{r}\overset{\ 1}{3} \overset{\ 1}{6.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{1}\overset{\ ~ }{7.}\overset{ }{4} \overset{~\ }{6} \\ \hline 5\space{} \, 4\space{\,. }2\space{\, }9\end{array}$

Report an Error

Example Question #36 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{7.}\overset{\ ~}{6}8\\ + \overset{\ ~ }{4}\overset{\ ~ }{7.}\overset{ }{5} \overset{~\ }{8} \\ \hline \end{array}$

Possible Answers:

10.05

41.9

15.25

95.26

Correct answer:

95.26

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{8+8=16}

Because this sum is greater than 9, we write the 6 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{7.}\overset{\ 1}{6}8\\ + \overset{\ ~ }{4}\overset{\ ~ }{7.}\overset{ }{5} \overset{~\ }{8} \\ \hline \space{} \, \space{\, } \space{\, }6\end{array}$

Add the numbers in the tenths place:

{6+5+1=11}

Because this sum is greater than 9, we write the 2 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

$\begin{array}{r}\overset{\ ~}{4} \overset{\ 1}{7.}\overset{\ 1}{6}8\\ + \overset{\ ~ }{4}\overset{\ ~ }{7.}\overset{ }{5} \overset{~\ }{8} \\ \hline \space{} \, \space{\,. }2\space{\, }6\end{array}$

Add the numbers in the ones place:

{7+7+1=15}

Because this sum is greater than 9, we write the 5 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ 1}{4} \overset{\ 1}{7.}\overset{\ 1}{6}8\\ + \overset{\ ~ }{4}\overset{\ ~ }{7.}\overset{ }{5} \overset{~\ }{8} \\ \hline \space{} \, 5\space{\,. }2\space{\, }6\end{array}$

Your final answer should be: 95.26

$\begin{array}{r}\overset{\ 1}{4} \overset{\ 1}{7.}\overset{\ 1}{6}8\\ + \overset{\ ~ }{4}\overset{\ ~ }{7.}\overset{ }{5} \overset{~\ }{8} \\ \hline 9\space{} \, 5\space{\,. }2\space{\, }6\end{array}$

Report an Error

Example Question #32 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{0.}\overset{\ ~}{2}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{7} \overset{~\ }{1} \\ \hline \end{array}$

Possible Answers:

23.45

86.92

41.49

48.16

Correct answer:

86.92

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{1+1=2}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{0.}\overset{\ ~}{2}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{7} \overset{~\ }{1} \\ \hline \space{} \, \space{\, } \space{\, }2\end{array}$

Add the numbers in the tenths place:

{2+7=9}

Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{0.}\overset{\ ~}{2}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{7} \overset{~\ }{1} \\ \hline \space{} \, \space{\,. }9\space{\, }2\end{array}$

Add the numbers in the ones place:

{0+6=6}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{0.}\overset{\ ~}{2}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{7} \overset{~\ }{1} \\ \hline \space{} \, 6\space{\,. }9\space{\, }2\end{array}$

Your final answer should be: 86.92

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{0.}\overset{\ ~}{2}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{7} \overset{~\ }{1} \\ \hline 8\space{} \, 6\space{\,. }9\space{\, }2\end{array}$

Report an Error

Example Question #38 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ ~}{3}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{6} \overset{~\ }{7} \\ \hline \end{array}$

Possible Answers:

66.98

40.56

37.57

17.52

Correct answer:

66.98

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{1+7=8}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ ~}{3}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{6} \overset{~\ }{7} \\ \hline \space{} \, \space{\, } \space{\, }8\end{array}$

Add the numbers in the tenths place:

{3+6=9}

Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ ~}{3}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{6} \overset{~\ }{7} \\ \hline \space{} \, \space{\,. }9\space{\, }8\end{array}$

Add the numbers in the ones place:

{6+0=6}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ ~}{3}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{6} \overset{~\ }{7} \\ \hline \space{} \, 6\space{\,. }9\space{\, }8\end{array}$

Your final answer should be: 66.98

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{6.}\overset{\ ~}{3}1\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{6} \overset{~\ }{7} \\ \hline 6\space{} \, 6\space{\,. }9\space{\, }8\end{array}$

Report an Error

Example Question #101 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{4.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{8.}\overset{ }{3} \overset{~\ }{6} \\ \hline \end{array}$

Possible Answers:

73.19

37.47

34.37

53.63

Correct answer:

73.19

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{3+6=9}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{4.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{8.}\overset{ }{3} \overset{~\ }{6} \\ \hline \space{} \, \space{\, } \space{\, }9\end{array}$

Add the numbers in the tenths place:

{8+3=11}

Because this sum is greater than 9, we write the 1 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{4.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{8.}\overset{ }{3} \overset{~\ }{6} \\ \hline \space{} \, \space{\,. }1\space{\, }9\end{array}$

Add the numbers in the ones place:

{4+8+1=13}

Because this sum is greater than 9, we write the 3 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ 1}{3} \overset{\ 1}{4.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{8.}\overset{ }{3} \overset{~\ }{6} \\ \hline \space{} \, 3\space{\,. }1\space{\, }9\end{array}$

Your final answer should be: 73.19

$\begin{array}{r}\overset{\ 1}{3} \overset{\ 1}{4.}\overset{\ ~}{8}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{8.}\overset{ }{3} \overset{~\ }{6} \\ \hline 7\space{} \, 3\space{\,. }1\space{\, }9\end{array}$

Report an Error

Example Question #1571 : Grade 6

Solve:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{1.}\overset{\ ~}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{0} \overset{~\ }{3} \\ \hline \end{array}$

Possible Answers:

45.19

19.9

16.94

57.6

Correct answer:

45.19

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{6+3=9}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{1.}\overset{\ ~}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{0} \overset{~\ }{3} \\ \hline \space{} \, \space{\, } \space{\, }9\end{array}$

Add the numbers in the tenths place:

{1+0=1}

Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{1.}\overset{\ ~}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{0} \overset{~\ }{3} \\ \hline \space{} \, \space{\,. }1\space{\, }9\end{array}$

Add the numbers in the ones place:

{1+4=5}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{1.}\overset{\ ~}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{0} \overset{~\ }{3} \\ \hline \space{} \, 5\space{\,. }1\space{\, }9\end{array}$

Your final answer should be: 45.19

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{1.}\overset{\ ~}{1}6\\ + \overset{\ ~ }{3}\overset{\ ~ }{4.}\overset{ }{0} \overset{~\ }{3} \\ \hline 4\space{} \, 5\space{\,. }1\space{\, }9\end{array}$

Report an Error

Example Question #1571 : Grade 6

Solve:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{3.}\overset{\ ~}{6}4\\ + \overset{\ ~ }{1}\overset{\ ~ }{1.}\overset{ }{3} \overset{~\ }{4} \\ \hline \end{array}$

Possible Answers:

19.94

45.57

24.98

25.37

Correct answer:

24.98

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{4+4=8}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{3.}\overset{\ ~}{6}4\\ + \overset{\ ~ }{1}\overset{\ ~ }{1.}\overset{ }{3} \overset{~\ }{4} \\ \hline \space{} \, \space{\, } \space{\, }8\end{array}$

Add the numbers in the tenths place:

{6+3=9}

Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{3.}\overset{\ ~}{6}4\\ + \overset{\ ~ }{1}\overset{\ ~ }{1.}\overset{ }{3} \overset{~\ }{4} \\ \hline \space{} \, \space{\,. }9\space{\, }8\end{array}$

Add the numbers in the ones place:

{3+1=4}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{3.}\overset{\ ~}{6}4\\ + \overset{\ ~ }{1}\overset{\ ~ }{1.}\overset{ }{3} \overset{~\ }{4} \\ \hline \space{} \, 4\space{\,. }9\space{\, }8\end{array}$

Your final answer should be: 24.98

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{3.}\overset{\ ~}{6}4\\ + \overset{\ ~ }{1}\overset{\ ~ }{1.}\overset{ }{3} \overset{~\ }{4} \\ \hline 2\space{} \, 4\space{\,. }9\space{\, }8\end{array}$

Report an Error

Example Question #103 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{5.}\overset{\ ~}{1}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{8} \\ \hline \end{array}$

Possible Answers:

11.67

21.09

27.4

61.51

Correct answer:

61.51

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{3+8=11}

Because this sum is greater than 9, we write the 1 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{5.}\overset{\ 1}{1}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{8} \\ \hline \space{} \, \space{\, } \space{\, }1\end{array}$

Add the numbers in the tenths place:

{1+3+1=5}

Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{5.}\overset{\ 1}{1}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{8} \\ \hline \space{} \, \space{\,. }5\space{\, }1\end{array}$

Add the numbers in the ones place:

{5+6+1=12}

Because this sum is greater than 9, we write the 1 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ 1}{2} \overset{\ ~}{5.}\overset{\ 1}{1}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{8} \\ \hline \space{} \, 1\space{\,. }5\space{\, }1\end{array}$

Your final answer should be: 61.51

$\begin{array}{r}\overset{\ 1}{2} \overset{\ ~}{5.}\overset{\ 1}{1}3\\ + \overset{\ ~ }{3}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{8} \\ \hline 6\space{} \, 1\space{\,. }5\space{\, }1\end{array}$

Report an Error

Example Question #43 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{0.}\overset{\ ~}{6}2\\ + \overset{\ ~ }{3}\overset{\ ~ }{3.}\overset{ }{5} \overset{~\ }{2} \\ \hline \end{array}$

Possible Answers:

52.86

14.73

32.71

64.14

Correct answer:

64.14

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{2+2=4}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{0.}\overset{\ ~}{6}2\\ + \overset{\ ~ }{3}\overset{\ ~ }{3.}\overset{ }{5} \overset{~\ }{2} \\ \hline \space{} \, \space{\, } \space{\, }4\end{array}$

Add the numbers in the tenths place:

{6+5=11}

Because this sum is greater than 9, we write the 1 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{0.}\overset{\ ~}{6}2\\ + \overset{\ ~ }{3}\overset{\ ~ }{3.}\overset{ }{5} \overset{~\ }{2} \\ \hline \space{} \, \space{\,. }1\space{\, }4\end{array}$

Add the numbers in the ones place:

{0+3+1=4}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{0.}\overset{\ ~}{6}2\\ + \overset{\ ~ }{3}\overset{\ ~ }{3.}\overset{ }{5} \overset{~\ }{2} \\ \hline \space{} \, 4\space{\,. }1\space{\, }4\end{array}$

Your final answer should be: 64.14

$\begin{array}{r}\overset{\ ~}{3} \overset{\ 1}{0.}\overset{\ ~}{6}2\\ + \overset{\ ~ }{3}\overset{\ ~ }{3.}\overset{ }{5} \overset{~\ }{2} \\ \hline 6\space{} \, 4\space{\,. }1\space{\, }4\end{array}$

Report an Error

Example Question #44 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{5.}\overset{\ ~}{0}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{4} \\ \hline \end{array}$

Possible Answers:

81.38

10.67

53.55

Correct answer:

81.38

Explanation:

When we add with multi-digit numbers with decimals, we start with the numbers furthest to the right and work our way towards the left.

Add the numbers in the hundredths place:

{4+4=8}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{5.}\overset{\ ~}{0}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{4} \\ \hline \space{} \, \space{\, } \space{\, }8\end{array}$

Add the numbers in the tenths place:

{0+3=3}

Your work should look something like this:

*Notice that the decimal moves directly down when we are adding decimal numbers.

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{5.}\overset{\ ~}{0}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{4} \\ \hline \space{} \, \space{\,. }3\space{\, }8\end{array}$

Add the numbers in the ones place:

{5+6+1=12}

Because this sum is greater than 9, we write the 1 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

$\begin{array}{r}\overset{\ 1}{3} \overset{\ ~}{5.}\overset{\ ~}{0}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{4} \\ \hline \space{} \, 1\space{\,. }3\space{\, }8\end{array}$

Your final answer should be: 81.38

$\begin{array}{r}\overset{\ 1}{3} \overset{\ ~}{5.}\overset{\ ~}{0}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{6.}\overset{ }{3} \overset{~\ }{4} \\ \hline 8\space{} \, 1\space{\,. }3\space{\, }8\end{array}$

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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

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Common Core: 6th Grade Math : The Number System

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

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #31 : Adding Multi Digit Decimals

Example Question #36 : Adding Multi Digit Decimals

Example Question #32 : Adding Multi Digit Decimals

Example Question #38 : Adding Multi Digit Decimals

Example Question #101 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Example Question #1571 : Grade 6

Example Question #1571 : Grade 6

Example Question #103 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Example Question #43 : Adding Multi Digit Decimals

Example Question #44 : Adding Multi Digit Decimals

All Common Core: 6th Grade Math Resources

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