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Introduction Adding and subtracting decimals is much like regular addition or subtraction. The most important thing to consider while solving these problems is to keep our decimal point in the same place, as well as adding or subtracting the correct units place together. We will be using long addition and long subtraction to solve these questions. Adding is fairly straight-forward however, when we subtract numbers we sometimes have to "borrow" a digit from the next units place which can be tricky. Let's take a look at a few examples and how to solve them. Adding Whole Numbers and Decimals In general the process for adding whole numbers and decimals is straight-forward. We simply line up the decimal points above and below each other and add each units place together. Adding Whole Numbers and Decimals If you have $29.30 and you earn an additional $21, how much do you have? We can figure this out by adding together the decimal number 29.3 and the whole number 21. 29.3 + 21 We should start by lining up the decimal points above each other. Even though there is no decimal point visible next to 21, it exists to the right of the ones unit place. Step 1 - Bring down the decimal point so it stays in the same location between the ones and tenths places. If you find it helpful, we can add a zero at the end of our whole number so that each units place has a digit. Step 2 - Add the two digits to the farthest right. 3 + 0 = 3 Be sure to keep the result beneath the tenths place since we added the tenths together. Step 3 - Work your way to the left adding the numbers that are in the same units place. 9 + 1 = 10 Since this is 10 is a two digit numbers, we carry the leftmost digit to the next unit place. Step 4 - Add the next units place together, and dont forget to also add the 1 we carried over from step 3. 1 + 2 + 2 = 5. Our final answer for this addition problem is 50.3. Solving Decimal Addition by Long Addition A driver has 12.65 tons of fruit in the back of their truck. On his way to the drop off point, he stops and loads an additional 14.50 tons of fruit. How much fruit total is the driver carrying in his truck? Adding Decimals to Decimals To solve our problem, we should add together the two values. 12.65 + 14.50 We can solve this by setting up a long addition problem. Remember to line up our decimal points directly above each other. Step 1 - Bring down the decimal point so it stays in the same location between the ones and tenths places. Step 2 - Add the two digits to the farthest right. 5 + 0 = 5 Be sure to keep the result beneath the hundredths place since we added the hundredths together. Step 3 - Work your way to the left adding the numbers that are in the same units place. 6 + 5 = 11 Since this is 11 is a two digit numbers, we carry the leftmost digit to the next unit place. Step 4 - Add the next units place together, and dont forget to also add the 1 we carried over from step 3. 1 + 2 + 4 = 7. Step 5 - Add the last units places together. 1 + 1 = 2. Our final answer is: 12.65 + 14.50 = 27.15 The truck driver is hauling 27.15 tons of fruit! Subtracting Whole Numbers and Decimals Subtracting Whole Numbers and Decimals Let's take a look at solving: 12 - 3.3 We should start by lining up the decimal points above each other. Even though there is no decimal point visible next to 12, it exists to the right of the ones unit place. Step 1 - Bring down the decimal point so it stays in the same location between the ones and tenths places. If you find it helpful, we can add a zero at the end of our whole number so that each units place has a digit. Step 2 - Subtract the two digits to the farthest right. Since 3 is larger than 0, we will have to borrow a 1 from the next units place. We will turn the 2 into a 1 and the zero into a 10. Step 3 - Work your way to the left subtracting the numbers that are in the same units place. Since 3 is larger than 1, we will have to borrow a 1 from the next units place. Our 1 will turn into an 11. 11 - 3 = 8 Solving Decimal Subtraction by Long Subtraction Subtracting decimals is much like adding them. One important technique we will use is to "borrow" a 1 from the units place to the left. Subtracting Decimals from Decimals You start off the week with $32.45 worth of allowance. After going out to the movie theater with your friends, you spend $14.50. How much money do you have left over? We can solve this problem by subtracting the amount spent from the amount you start off with. 32.45 - 14.5 We can solve this by setting up a long subtraction problem. Remember to line up the decimal points above each other. To keep things organized, we can add a zero at the end of 14.5 so that each unit space has a digit. Step 1 - Bring down the decimal point so it stays in the same location between the ones and tenths places. Step 2 - Subtract the two digits to the farthest right. 5 - 0 = 5 Be sure to keep the result beneath the hundredths place since we added the hundredths together. Step 3 - Work your way to the left subtracting the numbers that are in the same units place. 4 - 5 = ? When we are in this situation where we are subtracting a bigger number away, we want to borrow a 1 from the next unit space. We want to borrow a 1 from the ones unit place. We will change the 2 into a 1, and our 4 will turn into 14. 14 - 5 = 9 Step 4 - Our next step will be to subtract the ones unit place from eachother. If you notice, we are once again in the same situation where we will have to borrow a 1 from the next units place. 1 - 4 = ? We want to borrow a 1 from the tens unit place. We will change the 3 into a 2, and our 1 will turn into 11. 11 - 4 = 7 Step 5 - Our last step is to subtract our tens unit place. We need to keep track of how are digits change as we borrow numbers. 2 - 1 = 1 Our final answer is: 32.45 - 14.5 = 17.95 Adding and subtracting decimals and whole numbers is no different from regular whole number addition and subtraction. The key difference, is that we need to remember to line up the decimal points and the correct units places above and below each other.
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