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## Add and subtract decimals by lining up the decimal points.

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#### Example 2

Round each value to the nearest tenth and then find the sum.

4.56,3.47,2.04,6.21\begin{align*}4.56, 3.47, 2.04, 6.21\end{align*}

First, round each number to the nearest tenth. Remember that the tenths place is the first digit to the right of the decimal point. Look at each digit in the tenths place and then the digit to the right of that to decide if you will need to round up the digit in the tenths place or keep it the same.

• 4.56 rounds to 4.6
• 3.47 rounds to 3.5
• 2.04 rounds to 2.0
• 6.21 rounds to 6.2

Now, find the sum of the four rounded numbers. Start by arranging the numbers vertically so that the decimal points line up.

4.63.52.0+6.2\begin{align*}4.6\\ 3.5\\ 2.0\\ \underline{+ 6.2}\end{align*}

Next, add from right to left. Start by adding 6, 5, 0, and 2 to make 13. Carry the 1 and add it with the 4, 3, 2, and 6 to make 16. Insert a decimal point into your answer directly under the decimal points in the original numbers.

4.63.52.0+6.216.3\begin{align*}4.6\\ 3.5\\ 2.0\\ \underline{+ 6.2}\\ 16.3\end{align*}

The answer is 4.6+3.5+2.0+6.2=16.3\begin{align*}4.6+3.5+2.0+6.2=16.3\end{align*}.

#### Example 3

4.56+1.2+37.89=\begin{align*}4.56+1.2+37.89=\underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, arrange the numbers vertically so that the decimal points line up.

4.56 1.2+37.89\begin{align*}& \quad \ 4.56\\ & \quad \ 1.2\\ & \underline{+ 37.89}\end{align*}

Next, add one zero after the 2 in the second number so that all numbers have two digits to the right of the decimal point.

4.561.20+37.89\begin{align*}4.56\\ 1.20\\ \underline{+ 37.89}\end{align*}

Now, add from right to left. Start by adding 6, 0 and 9 to make 15. Carry the 1 and add it with the 5, 2, and 8 to make 16. Once again carry the 1 and add it with the 4, 1, and 7 to make 13. Carry the 1 one more time and add it with the 3 to make 4. Insert a decimal point into your answer directly under the decimal points in the original numbers.

4.561.20+37.8943.65\begin{align*}4.56\\ 1.20\\ \underline{+ 37.89}\\ 43.65\end{align*}

The answer is 4.56+1.20+37.89=43.65\begin{align*}4.56+1.20+37.89=43.65\end{align*}.

#### Example 4

14.2+56.78+123.4=\begin{align*}14.2+56.78+123.4=\underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, arrange the numbers vertically so that the decimal points line up.

14.2 56.78+123.4\begin{align*}& \quad \ 14.2\\ & \quad \ 56.78\\ & \underline{+ 123.4 \;\;\;}\end{align*}

Next, add one zero after the 2 in the first number and one zero after the 4 in the third number so that all numbers have two digits to the right of the decimal point.

14.2056.78+123.40\begin{align*}14.20\\ 56.78\\ \underline{+ 123.40}\end{align*}

Now, add from right to left. Start by adding 0, 8, and 0 to make 8. Then add 2, 7, and 4 to make 13. Carry the 1 and add it with the 4, 6, and 3 to make 14. Once again carry the 1 and add it with the 1, 5, and 12 to make 19. Insert a decimal point into your answer directly under the decimal points in the original numbers.

14.2056.78+123.40194.38\begin{align*}14.20\\ 56.78\\ \underline{+ 123.40}\\ 194.38\end{align*}

The answer is 14.20+56.78+123.40=194.38\begin{align*}14.20+56.78+123.40=194.38\end{align*}.

#### Example 5

189.34+123.5+7.2=\begin{align*}189.34+123.5+7.2=\underline{\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, arrange the numbers vertically so that the decimal points line up.

189.34   123.5+  7.2\begin{align*}& \ \ \ 189.34\\ & \ \ \ 123.5\\ & \underline{\;\; + \ \ 7.2 \;\;}\end{align*}

Next, add one zero after the 5 in the second number and one zero after the 2 in the third number so that all numbers have two digits to the right of the decimal point.

189.34123.50+  7.20\begin{align*}189.34\\ 123.50\\ \underline{\;\; + \ \ 7.20}\end{align*}

Now, add from right to left. Start by adding 4, 0, and 0 to make 4. Then add 3, 5, and 2 to make 10. Carry the 1 and add it with the 9, 3, and 7 to make 20. Carry the 2 and add it with the 8 and 2 to make 12. Carry the 1 and add it with the 1 and 1 to make 3. Insert a decimal point into your answer directly under the decimal points in the original numbers.

189.34123.50+  7.20320.04\begin{align*}189.34\\ 123.50\\ \underline{\;\; + \ \ 7.20}\\ 320.04\end{align*}

The answer is 189.34+123.50+7.20=320.04\begin{align*}189.34+123.50+7.20=320.04\end{align*}.

### Review

Find each sum.

1. 29.451+711.36\begin{align*}29.451+711.36\end{align*}
2. 0.956+0.9885\begin{align*}0.956+0.9885\end{align*}
3. 13.69+42.23\begin{align*}13.69+42.23\end{align*}
4. 58.744+12.06+8.8\begin{align*}58.744+12.06+8.8\end{align*}
5. 67.90+1.2+3.456\begin{align*}67.90+1.2+3.456\end{align*}

Round to the nearest tenth, then find the sum.

1. 88.95+23.451\begin{align*}88.95+23.451\end{align*}
2. 690.026+831.163\begin{align*}690.026+831.163\end{align*}
3. 3.27+7.818\begin{align*}3.27+7.818\end{align*}
4. 0.99+0.909+0.048\begin{align*}0.99+0.909+0.048\end{align*}
5. 5.67+3.45+1.23\begin{align*}5.67+3.45+1.23\end{align*}

Round to the nearest hundredth, then find the sum.

1. 511.51109+99.0986\begin{align*}511.51109+99.0986\end{align*}
2. 0.744+7.005+0.7071\begin{align*}0.744+7.005+0.7071\end{align*}
3. 32.368+303.409\begin{align*}32.368+303.409\end{align*}
4. 1.0262+1.0242\begin{align*}1.0262+1.0242\end{align*}
5. 1.309+3.4590\begin{align*}1.309+3.4590\end{align*}

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Color Highlighted Text Notes

### Vocabulary Language: English

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).

Estimate

To estimate is to find an approximate answer that is reasonable or makes sense given the problem.

Rounding

Rounding is reducing the number of non-zero digits in a number while keeping the overall value of the number similar.