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Addition and Subtraction with Decimal Numbers
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Addition and subtraction with decimals are just the same as addition and subtraction with the whole number. The most important thing to remember is to line up the decimal points so that when you stack them, they are directly on top of each other. Doing this stacks the place values so that the ones are on top of the ones, the tens on the tens, the tenths on the tenths, and so forth. If there are any times when there aren’t as many digits after the decimal place in one number as there are in another, remember that you can fill in any places to the right of the decimal with a 0. In numbers, this looks like 3.15 = 3.150 = 3.150000000 and so on.

### Steps for Addition (Combining Two Positive or Two Negative Numbers)

1. Stack the numbers according to place value. (This will line up the decimals.)
2. Add the numbers in the columns starting with the column on the right.
3. Carry numbers into the next place value to the left as needed.
4. Repeat this pattern for each remaining column.
5. Bring the decimal down.
6. Check the sign. (If both numbers were positive, the answer is positive. If both numbers were negative the answer is negative.)

### Steps for Subtraction (Combining a Positive and Negative Number)

1. Place the biggest number on top.
2. Stack in columns according to place value. (This will line up the decimals.)
3. Regroup when needed.
4. Subtract in columns by place value starting on the right and going left.
5. Bring the decimal down.
6. The strongest wins. (If the bigger number was negative then the answer is negative. If the bigger number was positive then the answer is positive.)
Subtraction with decimals

### Practice Problems

Evaluate the following expression:
1. $$2.4 + 8.8 = ?$$ (
Solution
Solution: $$11.2$$
Details:
Using place values, we will add $$2.4$$ and $$8.8$$. Line up the numbers in their corresponding places. Next, add the numbers in the tenth column. Since $$4 + 8 = 12$$, place the 2 below the tenths place and the 1 on the ones place. Finally, add the numbers in the ones place. Include the 1 carried over from the tenths place.
$$1 + 2 + 8 = 11$$ Our final answer: $$11.2$$
Be sure to include the decimal point between the tenths place and the ones place.
)
2. $$8.12 + 9.81 = ?$$ (
Solution
Solution: $$17.93$$
Details:
Using place values, we will add $$8.12$$ and $$9.81$$. Line up the numbers in their corresponding place values. Next, add the numbers in the hundredths column. Since $$2 + 1 = 3$$, place the 3 below the hundredths place. Next, add the numbers in the tenths column. Since $$1 + 8 = 9$$, place the 9 below the tenths place. Finally, add the numbers in the ones column. Since $$8 + 9 = 17$$, we put a 7 in the ones place and the 1 in the tens place. Our final answer: $$17.93$$
Be sure to include the decimal point between the tenths place and the ones place.
)
3. $$5.92 + 3.22 = ?$$ (
Video Solution
Solution: $$9.14$$
Details:

(Video Source | Transcript)
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4. $$7.2 - 1.5 = ?$$ (
Solution
Solution:
$$5.7$$
)
5. $$5.2 - 5.4 = ?$$ (
Solution
Solution:
$$-0.2$$
)
6. $$39.6 - 88.88 = ?$$ (
Video Solution
Solution: $$-49.28$$
Details:

(Video Source | Transcript)
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