Decimals: Add, Subtract, Multiply & Divide Lesson 1c

Adding & Subtracting Decimals If you know how to add & subtract whole numbers, you also know how to add & subtract decimals. Be sure to pay attention to place value, add or subtract in each place, and regroup when needed. Hundredths Thousandths Ones Tenths 8.784 + 2.56 + 6.721

Adding & Subtracting Decimals Fill in zeros where no digits are represented. Use rules of adding or subtracting. When adding or subtracting decimals: Line up the decimal points. Addition: Hundredths Thousandths Add up the thousandths. There are 5 thousandth. Add the tenths. There are 20 tenths. Since 20 hundredths is 2 ones 0 tenths, write 0 in the tenths place. Write 2 as an addend in the ones place. Add the ones. There are 18 ones. Add the hundredths. There are 16 hundredths. Since 16 hundredths is 1 tenth 6 hundredths, write 6 in the hundredths place. Write 1 as an addend in the tenths place. Ones Tenths 2 1 8.784 2.56 + 6.721 18. 6 5 So 8.784 + 2.56 + 6.721 = 18.065.

Adding & Subtracting Decimals When adding or subtracting decimals: Line up the decimal points. Fill in zeros where no digits are represented. Use rules of adding or subtracting. Subtraction: To subtract the thousandths, you will need more thousandths. Use one of the hundredths. Since 1 hundredth = 10 thousandths, change the number of the hundredths from 4 to 3 and the number of thousandths from 0 to 10. Hundredths Thousandths Ones Tenths Now subtract. There are 9 thousandths. 9 3 10 13 3 10 Try to subtract the hundredths. You will need more hundredths. There are no tenths to use, so use a one. Change the number of ones from 4 to 3. Raise the number of tenths from 0 to 9 and the number of hundredths from 3 to 13. 4.04 -2.681 Subtract the hundredths. There are 5 hundredths. 1. 3 5 9 Subtract the tenths. There are 3 tenths. Subtract the ones. There is 1 one. So 4.040 – 2.681 = 1.359

Addition Review 9.5 4.3 + 5.2 = 9.7 95 12.01 .10 + 12.1 12.2 13.1 103.01 .6 + 102.41 103.11 110.1

Subtraction Review 56.09 - 33.007 = 67.89 - 19.09 13.3 - 10.1 - 2.9 21.03 56.09 - 33.007 = 23.083 23.035 48.08 67.89 - 19.09 48.18 48.8 0.3 13.3 - 10.1 - 2.9 3.2 1.3

Multiplying with Decimals You multiply decimals the same way that you multiply whole numbers. The major difference is that you must correctly place the decimal point in your answer. Compare the two multiplications problems below: 29 x 55 1595 2.9 x 5.5 15.95 Each of the digits are the same. Each of the steps are the same. But the place values are different because of the decimal points.

Multiply with Decimals Placing the decimal point in the answer: One method to decide where to place the decimal point in the answer is by using an estimate. Tomatoes $1.85 Per Pound Example 1: You fill a bag with 2.30 pounds of tomatoes. The cost is $1.85 per pound. How much money do you spend? To solve the problem, you can multiply 2.30 x 1.85. Start with making an estimate. 2.30 x 1.85  2 x 2 = 4 We can see that the answer will have only one digit left of the decimal. Multiply as you would whole numbers. 185 x 230 42550 Use the estimate to place the decimal point. The estimate was 4, so the decimal point should go after the 4: 4.2550 The answer is 4.255. Since the answer needs to be in dollars and cents round to the nearest cent. You spend $4.26.

Multiply with Decimals Placing the decimal point in the answer: Another method to decide where to place the decimal point in the answer is by counting the number of places to the right of the decimal point in each number. The total tells you how many places there will be to the right of the decimal point in your final answer. Example 2: Multiply 0.04 x 0.03 Multiply as if the numbers where whole numbers. 4 x 3 = 12 Count the places to the right of the decimal point in each original number. Add. 0.04  2 decimal places 0.03  + 2 decimal places 4 decimal places Count the same number of places from right to left in the answer, then place the decimal point. (You may need to fill places with zeros.) 12 . . . . . . . . 0.04 x 0.03 = .0012

Multiplication Review 8.75 4.75 • 4 = 16.75 19 .008808 .734 • .12 .08808 .8808 24.185 12.95 • 2.9 37.555 126.13

Dividing with Decimals You divide decimals the same way that you divide whole numbers. The major difference is that you must correctly place the decimal point in your answer. Compare the two division problems below: Each of the digits are the same. Each of the steps are the same. But the place values are different because of the decimal points. -570 76 -76 -57 0 7 6 -7 6

Dividing with Decimals Dividing Decimals by Whole Numbers: To divide a decimal by a whole number, you place the decimal point for the answer directly above the decimal point in the dividend (the number you are dividing into). Then you divide the same way you divide whole numbers. Example 1: You and three friends rent a ski boat for the day. The total cost is $178.16. If you split the cost equally, how much does each person pay? To solve the problem, you can divide 178.16  4. Divide the same way you divide whole numbers. . 5 4 Write the decimal point for the answer directly above the decimal point in the dividend. 4 4 -16 1 8 Divisor Dividend . -16 2 1 -20 1 6 The answer is 44.54. Each person pays $44.54. -16

Dividing with Decimals Dividing by Decimals: To divide by a decimal, multiply the divisor (the number your dividing by) and the dividend (the number you are dividing into) by the same power of 10. You choose the power of ten that turns your divisor into a whole number. Write the decimal point on top directly above the new decimal point in the dividend. Divide the same way you divide whole numbers. Divisor Dividend Example 2: Divide 48  0.32 Multiply the divisor by a power of 10 to make it a whole number. 0.32 x 100 = 32 (whole number) Move the decimal point 2 places to show this. Multiply the dividend by the same power of 10. 1 5 . -32 16 48 x 100 = 4800 Move the decimal point 2 places to show this. . . 00 . . . . . . . . . . . . -160 48 x 0.32 = 150

Dividing with Decimals Rounding your final answer: When dividing decimals, you occasionally may need to round your final answer. To round your final answer you will always need to divide out the answer one decimal place past where you are rounding. Write the decimal point on top directly above the new decimal point in the dividend. Divide the same way you divide whole numbers. Example 3: Divide 53  0.7 Round your answer to the nearest tenth. 7 5 . 7 1 Multiply the divisor by a power of 10 to make it a whole number. 0.7 x 10 = 7 (whole number) Move the decimal point 1 place to show this. Multiply the dividend by the same power of 10. -49 4 53 x 10 = 530 Move the decimal point 1 place to show this. -35 5 . . . . . . . . . . . . -49 1

Dividing with Decimals Rounding your final answer: When dividing decimals, you occasionally may need to round your final answer. To round your final answer you will always need to divide out the answer one decimal place past where you are rounding. Write the decimal point on top directly above the new decimal point in the dividend. Divide the same way you divide whole numbers. Example 3: Divide 53  0.7 Round your answer to the nearest tenth. 7 5 . 7 1 Since our answer must be rounded to the nearest tenth, divide out to the hundredth. Since a 1 is in the hundredth spot and it is less than 5, then 75.71 rounds to 75.7 . -49 4 -35 5 53 x 0.7  75.7 -49 1

Division Review Round your answers to the nearest hundredth 63 3.09 = .05 63 3.09 = .66 21 30.09 .7 21.06 300.8 3008 .38 .2 .32 1.6 3.8

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