Common Core: 6th Grade Math : Adding Multi-Digit Decimals

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

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1531 : Grade 6

Find the sum of 2.4, 55, and 6.21.

Possible Answers:

\(\displaystyle 7.00\)

\(\displaystyle 63.51\)

\(\displaystyle 700\)

\(\displaystyle 636.1\)

\(\displaystyle 63.61\)

Correct answer:

\(\displaystyle 63.61\)

Explanation:

To find the sum, you need to add. Line up all numbers vertically. Since one number has a decimal to the tenths place, one has a decimal to the hundredths place, and one has no decimal, be extra careful to line up the digits correctly! To help you, add a zero to the end of 2.4, and add two zeroes to the end of 55 so that all the digits line up correctly.

\(\displaystyle \begin{matrix} &\ 2.40 \\ & 55.00\\ + & \ 6.21 \end{matrix}\)

Now, add down each column, starting on the right side and moving to the left.

\(\displaystyle 2.40 + 55.00+ 6.21 = 63.61\)

The sum is 63.61.

Example Question #1 : Adding Multi Digit Decimals

Samantha went to the toy store and bought three things: 

2 bouncy balls: $0.49 each

1 coloring book: $4.75 each

How much money did Samantha spend at the toy store?

Possible Answers:

\(\displaystyle \$5.73\)

\(\displaystyle \$5.74\)

\(\displaystyle \$5.24\)

\(\displaystyle \$3.77\)

Correct answer:

\(\displaystyle \$5.73\)

Explanation:

To find the answer, you must add up all three items. Be careful to add $0.49 TWO times because Samantha bought 2 bouncy balls:

 \(\displaystyle 0.49+0.49+4.75=5.73\)

Samantha spent $5.73 at the toy store.

Example Question #3 : Adding Multi Digit Decimals

\(\displaystyle 33.4 + 22.7 =\)

Possible Answers:

\(\displaystyle 10.7\)

\(\displaystyle 56.1\)

\(\displaystyle 121.2\)

\(\displaystyle 34.8\)

\(\displaystyle 16.3\)

Correct answer:

\(\displaystyle 56.1\)

Explanation:

Add the "whole" parts of the numbers:  \(\displaystyle 33 + 22 = 55\)

Add the "decimal" parts of the numbers: \(\displaystyle 0.4 + 0.7 = 1.1\)

Add both parts together: \(\displaystyle 55 + 1.1 = 56.1\)

 

 

\(\displaystyle 33.4 + 22.7 = 56.1\)

Example Question #1 : How To Add And Subtract Decimals

If Susie bought a pair of shoes for \(\displaystyle \$ 75.98\), a shirt for \(\displaystyle \$23.48\), and a pair of pants for \(\displaystyle \$ 48.34\). How much did she spend in total?

Possible Answers:

\(\displaystyle \$ 146.80\)

\(\displaystyle \$$147.60\)

\(\displaystyle \$ 147.40\)

\(\displaystyle \$$148.80\)

\(\displaystyle \$ 147.80\)

Correct answer:

\(\displaystyle \$ 147.80\)

Explanation:

You add all three values and you get \(\displaystyle \$147.80\).

Example Question #7 : Decimals

Menu 1

Above is the menu at the concession stand at a school carnival. Ken wants to purchase a hamburger, a medium order of fries, and medium soda for himself, and a hot dog, a small order of fries, and a small soda for his friend Donna. He hands the clerk a $10 bill and a $5 bill. He has some $1 bills in his pocket; how many of them will he need to hand to the clerk along with the other two bills?

(No tax is charged, since this is a school event)

Possible Answers:

Three

One

None

Two

Correct answer:

Three

Explanation:

The items Ken purchases are as follows: 

Hamburger: $4.89

Medium fries: $2.79

Medium soda: $1.69

Hot dog: $4.39

Small fries: $2.29

Small soda: $1.09

The sum of the prices of these items:

  \(\displaystyle \$ 4.89\)

    \(\displaystyle 2.79\)

    \(\displaystyle 1.69\)

    \(\displaystyle 4.39\)

    \(\displaystyle 2.29\)

    \(\displaystyle \underline{1.09}\)

\(\displaystyle \$ 17.14\)

Subtract from $20:

\(\displaystyle \$20.00 - \$ 17.14 = \$ 2.86\)

Rounding this up - Ken needs to give the clerk three more $1 bills.

Example Question #4 : Adding Multi Digit Decimals

Solve:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 4 } \overset{\ ~}{ 6 .}\overset{\ ~}{ 3 } 4 \\ + \overset{\ ~ }{ 4 }\overset{\ ~ }{ 6 .}\overset{ }{ 3 } \overset{~\ }{ 3 } \\ \hline \end{array}\)

Possible Answers:

\(\displaystyle 53.31\)

\(\displaystyle 92.67\)

 \(\displaystyle 12.62\)

\(\displaystyle 10.04\)

Correct answer:

\(\displaystyle 92.67\)

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:

\(\displaystyle 4 + 3 = 7\)

Your work should look something like this:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 4 } \overset{\ ~}{ 6 .}\overset{\ ~ }{ 3 } 4 \\ + \overset{\ ~ }{ 4 }\overset{\ ~ }{ 6 .}\overset{ }{ 3 } \overset{~\ }{ 3 } \\ \hline \space{} \, \space{\, } \space{\, } 7 \end{array}\)

Add the numbers in the tenths place:

\(\displaystyle 3 + 3 = 6\)

Your work should look something like this:

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

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 4 } \overset{\ ~ }{ 6 .}\overset{\ ~ }{ 3 } 4 \\ + \overset{\ ~ }{ 4 }\overset{\ ~ }{ 6 .}\overset{ }{ 3 } \overset{~\ }{ 3 } \\ \hline \space{} \, \space{\,. } 6 \space{\, } 7 \end{array}\)

Add the numbers in the ones place:

\(\displaystyle 6 + 6 = 12\)

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:

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

Add the numbers in the tens place including the one carried over:

\(\displaystyle 4 + 4 + 1 = 9\)

Your final answer should be: \(\displaystyle 92.67\)

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

Example Question #5 : Adding Multi Digit Decimals

Solve:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 3 } \overset{\ ~}{ 3 .}\overset{\ ~}{ 8 } 5 \\ + \overset{\ ~ }{ 4 }\overset{\ ~ }{ 3 .}\overset{ }{ 8 } \overset{~\ }{ 3 } \\ \hline \end{array}\)

 

 

Possible Answers:

\(\displaystyle 13.84\)

\(\displaystyle 30.72\)

\(\displaystyle 77.68\) 

\(\displaystyle 26.34\)

Correct answer:

\(\displaystyle 77.68\) 

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:

\(\displaystyle 5 + 3 = 8\) 

Your work should look something like this:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 3 } \overset{\ ~}{ 3 .}\overset{\ ~ }{ 8 } 5 \\ + \overset{\ ~ }{ 4 }\overset{\ ~ }{ 3 .}\overset{ }{ 8 } \overset{~\ }{ 3 } \\ \hline \space{} \, \space{\, } \space{\, } 8 \end{array}\)

Add the numbers in the tenths place:

\(\displaystyle 8 + 8 = 16\) 

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:

Your work should look something like this:

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

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

Add the numbers in the ones place including the one carried over:

\(\displaystyle 3 + 3 + 1 = 7\)

Your work should look something like this:

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

Add the numbers in the tens place:

\(\displaystyle 3 + 4 = 7\)

Your final answer should be: \(\displaystyle 77.68\)

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

 

Example Question #6 : Adding Multi Digit Decimals

Solve:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 3 } \overset{\ ~}{ 3 .}\overset{\ ~}{ 7 } 7 \\ + \overset{\ ~ }{ 1 }\overset{\ ~ }{ 5 .}\overset{ }{ 7 } \overset{~\ }{ 5 } \\ \hline \end{array}\)

 

Possible Answers:

\(\displaystyle 22.81\)

\(\displaystyle 46.52\)

\(\displaystyle 49.52\)

\(\displaystyle 11.33\)

Correct answer:

\(\displaystyle 49.52\)

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:

\(\displaystyle 7 + 5 = 12\) 

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:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 3 } \overset{\ ~}{ 3 .}\overset{\ 1 }{ 7 } 7 \\ + \overset{\ ~ }{ 1 }\overset{\ ~ }{ 5 .}\overset{ }{ 7 } \overset{~\ }{ 5 } \\ \hline \space{} \, \space{\, } \space{\, } 2 \end{array}\)

Add the numbers in the tenths place including the one carried over:

\(\displaystyle 7 + 7 + 1 = 15\)

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:

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

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 3 } \overset{\ 1 }{ 3 .}\overset{\ 1 }{ 7 } 7 \\ + \overset{\ ~ }{ 1 }\overset{\ ~ }{ 5 .}\overset{ }{ 7 } \overset{~\ }{ 5 } \\ \hline \space{} \, \space{\,. } 5 \space{\, } 2 \end{array}\)

Add the numbers in the ones place including the one carried over:

\(\displaystyle 3 + 5 + 1 = 9\)

 Your work should look something like this: 

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

Add the numbers in the tens place:

\(\displaystyle 3 + 1 = 4\)

Your final answer should be: \(\displaystyle 49.52\)

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

 

 

 

Example Question #2 : Adding Multi Digit Decimals

Solve:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 3 } \overset{\ ~}{ 7 .}\overset{\ ~}{ 4 } 5 \\ + \overset{\ ~ }{ 3 }\overset{\ ~ }{ 8 .}\overset{ }{ 8 } \overset{~\ }{ 3 } \\ \hline \end{array}\)

 

 

Possible Answers:

\(\displaystyle 33.68\)

\(\displaystyle 42.81\)

\(\displaystyle 40.83\)

\(\displaystyle 76.28\)

Correct answer:

\(\displaystyle 76.28\)

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: 

\(\displaystyle 5 + 3 = 8\)

Your work should look something like this:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 3 } \overset{\ ~}{ 7 .}\overset{\ ~ }{ 4 } 5 \\ + \overset{\ ~ }{ 3 }\overset{\ ~ }{ 8 .}\overset{ }{ 8 } \overset{~\ }{ 3 } \\ \hline \space{} \, \space{\, } \space{\, } 8 \end{array}\) 

Add the numbers in the tenths place: 

\(\displaystyle 4 + 8 = 12\)

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:

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

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

Add the numbers in the ones place including the one carried over: 

\(\displaystyle 7 + 8 + 1 = 16\)

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:

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

Add the numbers in the tens place including the one carried over:

\(\displaystyle 3 + 3 + 1 = 7\)

Your final answer should be: \(\displaystyle 76.28\) 

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

 

Example Question #72 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3

Solve:

\(\displaystyle \begin{array}{r}\overset{\ ~}{ 1 } \overset{\ ~}{ 2 .}\overset{\ ~}{ 6 } 2 \\ + \overset{\ ~ }{ 3 }\overset{\ ~ }{ 6 .}\overset{ }{ 8 } \overset{~\ }{ 4 } \\ \hline \end{array}\)

 

 

Possible Answers:

\(\displaystyle 46.14\)

\(\displaystyle 49.46\)

\(\displaystyle 59.37\)

\(\displaystyle 49.27\)

Correct answer:

\(\displaystyle 49.46\)

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:

\(\displaystyle 2 + 4 = 6\)

Your work should look something like this:

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

Add the numbers in the tenths place:

\(\displaystyle 6 + 8 = 14\)

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:

Your work should look something like this:

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

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

Add the numbers in the ones place including the one carried over:

\(\displaystyle 2 + 6 + 1 = 9\)

Your work should look something like this:

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

Add the numbers in the tens place:

\(\displaystyle 1 + 3 = 4\)

Your final answer should be: \(\displaystyle 49.46\)

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

 

 

Learning Tools by Varsity Tutors