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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 #1601 : Grade 6

Solve:

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

Possible Answers:

42.81

56.45

11.97

27.89

Correct answer:

56.45

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+1=5}

Your work should look something like this:

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

Add the numbers in the tenths place:

{1+3=4}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{3+3=6}

Your work should look something like this:

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

Your final answer should be: 56.45

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

Report an Error

Example Question #131 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

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

Possible Answers:

34.3

29.54

53.8

49.91

Correct answer:

53.8

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+6=10}

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:

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

Add the numbers in the tenths place:

{3+4+1=8}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{3+0=3}

Your work should look something like this:

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

Your final answer should be: 53.80

$\begin{array}{r}\overset{\ ~}{3} \overset{\ ~}{3.}\overset{\ 1}{3}4\\ + \overset{\ ~ }{2}\overset{\ ~ }{0.}\overset{ }{4} \overset{~\ }{6} \\ \hline 5\space{} \, 3\space{\,. }8\space{\, }0\end{array}$

Report an Error

Example Question #451 : The Number System

Solve:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{8.}\overset{\ ~}{5}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{1} \overset{~\ }{2} \\ \hline \end{array}$

Possible Answers:

11.35

38.79

45.13

68.66

Correct answer:

68.66

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+2=6}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{8.}\overset{\ ~}{5}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{1} \overset{~\ }{2} \\ \hline \space{} \, \space{\, } \space{\, }6\end{array}$

Add the numbers in the tenths place:

{5+1=6}

Your work should look something like this:

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

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{8.}\overset{\ ~}{5}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{1} \overset{~\ }{2} \\ \hline \space{} \, \space{\,. }6\space{\, }6\end{array}$

Add the numbers in the ones place:

{8+0=8}

Your work should look something like this:

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{8.}\overset{\ ~}{5}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{1} \overset{~\ }{2} \\ \hline \space{} \, 8\space{\,. }6\space{\, }6\end{array}$

Your final answer should be: 68.66

$\begin{array}{r}\overset{\ ~}{2} \overset{\ ~}{8.}\overset{\ ~}{5}4\\ + \overset{\ ~ }{4}\overset{\ ~ }{0.}\overset{ }{1} \overset{~\ }{2} \\ \hline 6\space{} \, 8\space{\,. }6\space{\, }6\end{array}$

Report an Error

Example Question #72 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

61.42

29.17

40.88

48.21

Correct answer:

61.42

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+7=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:

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

Add the numbers in the tenths place:

{5+8+1=13}

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:

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

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

Add the numbers in the ones place:

{5+5+1=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:

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

Your final answer should be: 61.42

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

Report an Error

Example Question #72 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

59.8

42.68

58.94

46.29

Correct answer:

46.29

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:

{7+2=9}

Your work should look something like this:

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

Add the numbers in the tenths place:

{1+1=2}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{5+1=6}

Your work should look something like this:

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

Your final answer should be: 46.29

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

Report an Error

Example Question #73 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

25.21

41.92

40.56

28.33

Correct answer:

41.92

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:

{5+7=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:

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

Add the numbers in the tenths place:

{1+7+1=9}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{7+4+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:

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

Your final answer should be: 41.92

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

Report an Error

Example Question #75 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

57.55

30.05

31.1

11.86

Correct answer:

31.1

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:

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

Add the numbers in the tenths place:

{0+1=1}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{4+7+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:

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

Your final answer should be: 31.10

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

Report an Error

Example Question #76 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

63.04

15.57

47.79

55.81

Correct answer:

63.04

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+8=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:

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

Add the numbers in the tenths place:

{1+8+1=9}

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:

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

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

Add the numbers in the ones place:

{6+6+1=13}

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:

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

Your final answer should be: 63.04

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

Report an Error

Example Question #77 : Adding Multi Digit Decimals

Solve:

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

Possible Answers:

24.71

45.57

10.22

56.56

Correct answer:

45.57

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+6=7}

Your work should look something like this:

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

Add the numbers in the tenths place:

{1+4=5}

Your work should look something like this:

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

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

Add the numbers in the ones place:

{0+5=5}

Your work should look something like this:

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

Your final answer should be: 45.57

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

Report an Error

Example Question #1 : Subtracting Multi Digit Decimals

Find the difference.

7.26-5.83=

Possible Answers:

1.43

2.43

1.53

1.33

1.48

Correct answer:

1.43

Explanation:

Finding a difference means to subtract.

In the hundredths column, we can easily subtract 6-3=3 .

In the tenths column we must borrow from the 7 (making it 6) and also making the 2 a 12. Now we can subtract 12-8=4 .

Finally in the ones column we can subtract 6-5=1 .

Thus the final answer is 1.43.

Report an Error

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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 : Grade 6

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

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #1601 : Grade 6

Example Question #131 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Example Question #451 : The Number System

Example Question #72 : Adding Multi Digit Decimals

Example Question #72 : Adding Multi Digit Decimals

Example Question #73 : Adding Multi Digit Decimals

Example Question #75 : Adding Multi Digit Decimals

Example Question #76 : Adding Multi Digit Decimals

Example Question #77 : Adding Multi Digit Decimals

Example Question #1 : Subtracting Multi Digit Decimals

All Common Core: 6th Grade Math Resources

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