CCSS Math: 5.NBT.B.7
Start with simple problems like 0.2 + 0.4 and build to more complex problems like 10.3 + 36.75.
This article is designed to help you learn how to add decimals by letting you jump in and give it a try without being shown how to do it first.
The problems go from easier to more difficult, and along the way, there are examples and explanations for the times you get stuck. You'll learn the most if you look at the times you're confused as chances to learn!
Let's start by adding two tenths together.

Section 1: Adding tenths less than one

Example: 0.1+0.30.1 + 0.3
One strategy is to think in terms of tenths:
=0.1+0.3\phantom{=}0.1 + 0.3
=1=1 tenth + 3+ ~3 tenths
=4=4 tenths
=0.4=0.4
Another strategy is to use tenths grids:
0.1+0.3=0.4\blueD{0.1} + \greenD{0.3} = 0.4
Problem 1a
0.5+0.4=0.5 + 0.4 =
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Beautiful, let's move on to problems with whole numbers and tenths.

Section 2: Adding whole numbers and tenths

Example: 4+5.74 + 5.7
Let's break 5.75.7 down by place value:
4+5.7=4+5+0.7        Break 5.7 into 5 and 0.7.\begin{aligned}&\blueD{4}+\greenD{5.7}\\ \\ =&\blueD{4}+\greenD{5}+\greenD{0.7}~~~~~~~~\small{\gray{\text{Break 5.7 into 5 and 0.7.}}}\\\end{aligned}
=(4+5)+0.7        Group the whole numbers together.=9+0.7\begin{aligned} =&(\blueD{4}+\greenD{5})+\greenD{0.7}~~~~~~~~\small{\gray{\text{Group the whole numbers together.}}}\\ \\ =&9 + 0.7\\\end{aligned}
=9.7= 9.7
Problem 2a
6.4+2=6.4 + 2 =
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Excellent, next up are problems where both numbers have a whole number and a tenth.

Section 3: Adding tenths greater than one

Example: 14.3+5.214.3 + 5.2
Let's break both numbers down by place value.
14.3+5.2=14+0.3+5+0.2\begin{aligned}&\blueD{14.3}+\greenD{5.2}\\ \\ =&\blueD{14}+\blueD{0.3}+\greenD{5}+\greenD{0.2}\\\end{aligned}
=(14+5)+(0.3+0.2)        Group the whole numbers and the tenths.=19+0.5\begin{aligned} =&(\blueD{14}+\greenD{5})+(\blueD{0.3}+\greenD{0.2})~~~~~~~~{\gray{\text{Group the whole numbers and the tenths.}}}\\ \\ =&19 + 0.5\\\end{aligned}
=19.5= 19.5
So, 14.3+5.2=19.514.3 + 5.2 = 19.5.
Problem 3a
3.7+22.1=3.7 + 22.1 =
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Rockin'! Let's move on to adding hundredths.

Section 4: Adding hundredths

Example: 0.24+0.520.24 + 0.52
One strategy is to think in terms of hundredths:
=0.24+0.52\phantom{=}0.24 + 0.52
=24=24 hundredths + 52+ ~52 hundredths
=76=76 hundredths
=0.76=0.76
Another strategy is to use hundredths grids:
0.24+0.52=0.76\blueE{0.24} + \goldB{0.52} = 0.76
Problem 4a
0.31+0.64=0.31 + 0.64 =
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Sweet, now we're ready to solve problems with hundredths, tenths, and whole numbers.

Section 5: Adding whole numbers, tenths, and hundredths

Example: 5.21+8.685.21 + 8.68
Let's break both numbers down:
=5.21+8.68\phantom{=}\blueD{5.21}+\greenD{8.68}
=5+0.2+0.01+8+0.6+0.08=\blueD{5} + \blueD{0.2}+\blueD{0.01}+\greenD{8}+\greenD{0.6}+\greenD{0.08}
=(5+8)+(0.2+0.6)+(0.01+0.08)        Group by place value.=(\blueD{5} +\greenD{8})+(\blueD{0.2} +\greenD{0.6}) + (\blueD{0.01} +\greenD{0.08})~~~~~~~~\small{\gray{\text{Group by place value.}}}
=13+0.8+0.09=13 + 0.8 + 0.09
=13.89=13.89
Problem 5a
42+4.27=42 + 4.27=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Great, let's finish with a few more challenging problems.

Section 6: Challenge problems

Example: 10.16+36.7510.16 + 36.75
Let's break both numbers down by place value:
=10.16+36.75\phantom{=}\blueD{10.16}+\greenD{36.75}
=10+0.1+0.06+36+0.7+0.05=\blueD{10} + \blueD{0.1}+\blueD{0.06}+\greenD{36}+\greenD{0.7}+\greenD{0.05}
=(10+36)+(0.1+0.7)+(0.06+0.05)        Group by place value.=(\blueD{10}+\greenD{36})+(\blueD{0.1} +\greenD{0.7}) + (\blueD{0.06}+\greenD{0.05})~~~~~~~~\small{\gray{\text{Group by place value.}}}
=46+0.8+0.11=46 + 0.8 + 0.11
=46.91=46.91
Problem 6a
2.59+5.16=2.59 + 5.16=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}