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

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Stephen went shopping to buy some new school supplies. He bought a backpack that cost $28.67 and a scientific calculator for$34.88. How much money did Stephen spend altogether?

When you add decimals you are adding whole numbers and like fraction parts. To make this process simpler, you should add decimal numbers using the vertical alignment method. The decimal points must be kept directly under each other and the digits in the same place value must be kept in line with each other. If the decimal numbers are signed numbers, the rules for adding integers are applied to the problem.

#### \begin{align*}87.296+48.6\end{align*}

Begin by writing the question using the vertical alignment method.

\begin{align*} 87.296 & \\ \underline{+48.6\phantom{00}}\end{align*}

Don't forget that the decimal points must be kept directly under one another. To ensure that the digits are aligned correctly, add zeros to 48.6.

\begin{align*} 87.296 & \\ \underline{+48.6{\color{blue}00}} & \end{align*}

\begin{align*} 87.296 & \\ \underline{+ 48.6{\color{blue}00}} & \\ 135.896 & \end{align*}

#### Now, let's try adding positive and negative decimals:

\begin{align*}(97.38)+(-45.17)\end{align*}

The first step is to write the problem using the vertical alignment method. The two decimal numbers that are being added have opposite signs. Apply the same rule that you used when adding integers that had opposite signs – subtract the numbers and use the sign of the larger number in the answer.

\begin{align*} 97.38 & \\ \underline{- 45.17} & \\ \quad 52.21 & \end{align*}

The larger number is 97.38 and it has a positive sign. This means that the sign of the answer will also be a positive value.

#### Finally, let's add two negative decimals together:

\begin{align*}(-168.8)+(-217.4536)\end{align*}

The first step is to write the problem using the vertical alignment method.

\begin{align*} -168.8\phantom{000} & \\ \underline{+-217.4536} & \end{align*}

To ensure that the digits are aligned correctly, add zeros to 168.8.

\begin{align*} -168.8{\color{blue}000} & \\ \underline{+-217.4536} & \end{align*}

\begin{align*} -168.8{\color{blue}000} & \\ \underline{+-217.4536} & \\ -386.2536 & \end{align*}

The numbers being added each had negative signs. This means that the sign of the answer is also a negative value.

### Examples

#### Example 1

Earlier, you were told that Stephen went shopping to buy some new school supplies and he bought a backpack that cost $28.67 and a scientific calculator for$34.88.

Stephen bought two items. To determine the total amount of money he spent, add the prices of the items.

The numbers and the decimal points have been correctly aligned. Now add the numbers.

Stephen spent 63.55 total. #### Example 2 Add the decimals: \begin{align*}45.36+15+137.692+32.8=?\end{align*} You can add all three numbers at once. \begin{align*}& \overset{2 1 \ \ 1}{\quad 45.36{\color{blue}0}}\\ & \quad 15.{\color{blue}000}\\ & \ 137.692\\ & \underline{+ 32.8{\color{blue}00}}\\ & \ 230.852\end{align*} #### Example 3 Add the decimals: \begin{align*}(53.69)+(-33.7)+(6.298)=?\end{align*} Add the two positive numbers together: \begin{align*} 53.69{\color{blue}0} & \\ \underline{+ \ \ 6.298} & \\ 59.988 & \end{align*} Subtract the negative number from the result: \begin{align*} 59.988 & \\ \underline{-33.7{\color{blue}00}} & \\ 26.288 & \end{align*} #### Example 4 Add the decimals: \begin{align*}14.68+39.217=?\end{align*} \begin{align*}14.68+39.217=53.897\end{align*} ### Review Add the following numbers. 1. \begin{align*}14.36+9.42\end{align*} 2. \begin{align*}52.72+27.163\end{align*} 3. \begin{align*}0.26+4.5+1.137\end{align*} 4. \begin{align*}37.231+14.567\end{align*} 5. \begin{align*}78.32+6.2+19.46\end{align*} 6. \begin{align*}65.23+12.75\end{align*} 7. \begin{align*}148.067+53.78+6.9\end{align*} 8. \begin{align*}56.75+14.9294+17.854\end{align*} 9. \begin{align*}18+26.87+65.358\end{align*} 10. \begin{align*}23.067+268.93+9.4\end{align*} 11. \begin{align*}(-24.69)+(-39.87)\end{align*} 12. \begin{align*}(76.35)+(-36.68)\end{align*} 13. \begin{align*}(-12.5)+(47.97)+(-21.653)\end{align*} 14. \begin{align*}(62.462)+(254.69)+(-427.9)\end{align*} 15. \begin{align*}(-37.76)+(-45.8)+(53.92)\end{align*} Determine the answer to the following problems. 1. When the owners of the Finest Fixer Co. completed a small construction job, they found that the following expenses had been incurred: labour,975.75; gravel, $88.79; sand,$43.51; cement, $284.96; and bricks$2214.85. What bill should they give the customer if they want to make a profit of $225 for the job? 2. A tile setter purchases the following supplies for the day: • One bag of thin-set mortar - $5.67 per bag • 44 sq ft of tile -$107.80 for 44 sq ft of tile • One gallon of grout - $17.97 per gallon • One container of grout sealer -$32.77 per container • 3 containers of grout and tile cleaner - $5.99 per container • 4 scrub pads -$2.78 each • One trowel - @$3.95 each
• 2 packages of tile spacers - $2.27 each • One grout bag -$2.79 each
• One grout float - $10.45 each What is the cost of these items before tax is added? 3. The four employees of the Broken Body Shop earned the following amounts last week: 815.86, 789.21, 804.18 and 888.35. What is the average weekly pay for the employees? 4. Jennifer bought the following school supplies: • 1000 sheets of paper -$14.67
• 36 pencils - @ $6.55 • 1 binder - @$18.48
• 1 backpack - @ $22.74 • 1 lunch bag - @$4.64

How much did Jennifer spend on these supplies before taxes?

5. A local seamstress needs to purchase fabric to sew curtains for the local theatre. She needs 123.75 yd. of black cotton for a backdrop, 217.4 yd. of white linen for stage curtains, 75 yd. for accessory curtains and 98.5 yd. for costumes. How many yards of fabric must be purchased to fill this order?

To see the Review answers, open this PDF file and look for section 1.3.

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### Vocabulary Language: English

Decimal point

A decimal point is a period that separates the complete units from the fractional parts in a decimal number.

Rounding

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