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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 #51 : Adding Multi Digit Decimals

Solve:

$\begin{array}{r}\overset{\ ~}{1} \overset{\ ~}{0.}\overset{\ ~}{3}1\\ + \overset{\ ~ }{2}\overset{\ ~ }{3.}\overset{ }{1} \overset{~\ }{8} \\ \hline \end{array}$

Possible Answers:

48.14

38.79

47.23

33.49

Correct answer:

33.49

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+8=9}

Your work should look something like this:

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

Add the numbers in the tenths place:

{3+1=4}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{0+3=3}

Your work should look something like this:

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

Your final answer should be: 33.49

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

Report an Error

Example Question #52 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

23.59

60.33

28.46

12.35

Correct answer:

60.33

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+1=3}

Your work should look something like this:

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

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.

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

Add the numbers in the ones place:

{7+3+1=11}

Because this sum is greater than 9, we write the 0 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

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

Your final answer should be: 60.33

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

Report an Error

Example Question #55 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

22.87

90.79

22.15

Correct answer:

90.79

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:

{7+2=9}

Your work should look something like this:

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

Add the numbers in the tenths place:

{0+7=7}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{6+4+1=11}

Because this sum is greater than 9, we write the 0 from the ones place and carry the 1 from the tens place over to the left. Your work should look something like this:

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

Your final answer should be: 90.79

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

Report an Error

Example Question #119 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

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

Possible Answers:

14.61

69.73

35.09

51.78

Correct answer:

69.73

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+2=3}

Your work should look something like this:

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

Add the numbers in the tenths place:

{0+7=7}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{1+8=9}

Your work should look something like this:

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

Your final answer should be: 69.73

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

Report an Error

Example Question #441 : The Number System

Solve:

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

Possible Answers:

53.34

59.98

38.3

88.43

Correct answer:

88.43

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:

{5+8=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:

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

Add the numbers in the tenths place:

{1+2+1=4}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{7+1=8}

Your work should look something like this:

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

Your final answer should be: 88.43

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

Report an Error

Example Question #57 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

12.49

66.17

55.04

31.49

Correct answer:

66.17

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+4=7}

Your work should look something like this:

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

Add the numbers in the tenths place:

{5+6=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:

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

Add the numbers in the ones place:

{7+8+1=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:

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

Your final answer should be: 66.17

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

Report an Error

Example Question #61 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

11.96

61.9

28.89

27.74

Correct answer:

61.9

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:

{0+0=0}

Your work should look something like this:

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

Add the numbers in the tenths place:

{1+8=9}

Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{4} \overset{\ ~}{6.}\overset{\ ~}{1}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{5.}\overset{ }{8} \overset{~\ }{0} \\ \hline \space{} \, \space{\,. }9\space{\, }0\end{array}$

Add the numbers in the ones place:

{6+5+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:

$\begin{array}{r}\overset{\ 1}{4} \overset{\ ~}{6.}\overset{\ ~}{1}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{5.}\overset{ }{8} \overset{~\ }{0} \\ \hline \space{} \, 1\space{\,. }9\space{\, }0\end{array}$

Your final answer should be: 61.90

$\begin{array}{r}\overset{\ 1}{4} \overset{\ ~}{6.}\overset{\ ~}{1}0\\ + \overset{\ ~ }{1}\overset{\ ~ }{5.}\overset{ }{8} \overset{~\ }{0} \\ \hline 6\space{} \, 1\space{\,. }9\space{\, }0\end{array}$

Report an Error

Example Question #62 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

44.47

36.44

65.47

59.48

Correct answer:

65.47

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:

{7+0=7}

Your work should look something like this:

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

Add the numbers in the tenths place:

{7+7=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:

Your work should look something like this:

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

Add the numbers in the ones place:

{2+2+1=5}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{4} \overset{\ 1}{2.}\overset{\ ~}{7}7\\ + \overset{\ ~ }{2}\overset{\ ~ }{2.}\overset{ }{7} \overset{~\ }{0} \\ \hline \space{} \, 5\space{\,. }4\space{\, }7\end{array}$

Your final answer should be: 65.47

$\begin{array}{r}\overset{\ ~}{4} \overset{\ 1}{2.}\overset{\ ~}{7}7\\ + \overset{\ ~ }{2}\overset{\ ~ }{2.}\overset{ }{7} \overset{~\ }{0} \\ \hline 6\space{} \, 5\space{\,. }4\space{\, }7\end{array}$

Report an Error

Example Question #63 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

53.62

14.73

28.21

39.78

Correct answer:

39.78

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:

{7+1=8}

Your work should look something like this:

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

Add the numbers in the tenths place:

{6+1=7}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{6+3=9}

Your work should look something like this:

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

Your final answer should be: 39.78

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

Report an Error

Example Question #64 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

43.63

10.4

59.34

78.98

Correct answer:

78.98

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:

{6+2=8}

Your work should look something like this:

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

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.

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

Add the numbers in the ones place:

{1+7=8}

Your work should look something like this:

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

Your final answer should be: 78.98

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

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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 #51 : Adding Multi Digit Decimals

Example Question #52 : Adding Multi Digit Decimals

Example Question #55 : Adding Multi Digit Decimals

Example Question #119 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Example Question #441 : The Number System

Example Question #57 : Adding Multi Digit Decimals

Example Question #61 : Adding Multi Digit Decimals

Example Question #62 : Adding Multi Digit Decimals

Example Question #63 : Adding Multi Digit Decimals

Example Question #64 : Adding Multi Digit Decimals

All Common Core: 6th Grade Math Resources

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