Decimals Add Subtract Multiply Divide Lesson 1 c

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

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. 8. 784 + 2. 56 + 6. 721

Adding & Subtracting Decimals When adding or subtracting decimals: 1. Line up the decimal points. 2. Fill in zeros where no digits are represented. 3. Use rules of adding or subtracting. Addition: Add up the thousandths. There are 5 thousandth. Add the hundredths. There are 16 hundredths. 2 1 8. 784 2. 56 0 + 6. 721 18. 06 5 • Since 16 hundredths is 1 tenth 6 hundredths, write 6 in the hundredths place. Write 1 as an addend in the tenths place. 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. So 8. 784 + 2. 56 + 6. 721 = 18. 065.

Adding & Subtracting Decimals When adding or subtracting decimals: 1. Line up the decimal points. 2. Fill in zeros where no digits are 3. 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. 9 3 10 13 3 10 4. 04 0 -2. 681 1. 35 9 Now subtract. There are 9 thousandths. 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. Subtract the hundredths. There are 5 hundredths. 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 . 10 + 12. 1 12. 01 = 12. 2 13. 1 103. 01 . 6 + 102. 41 = 103. 11 110. 1

Subtraction Review 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. 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. Tomatoes $1. 85 Per Pound ❶Start with making an estimate. ❷Multiply as you would whole ❸Use the estimate to place the numbers. decimal point. The estimate was 4, so the decimal 2. 30 x 1. 85 185 point should go after the 4: x 230 4. 2550 2 x 2 = 4 42550 We can see that the answer will have The answer is 4. 255. Since the answer needs to be in dollars only one digit left of the decimal. 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 ❶Multiply as if the numbers where whole numbers. 4 x 3 = 12 ❷Count 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 0. 04 x 0. 03 =. 0012 ❸Count 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. ) 0. 0. 0. 12. . .

Multiplication Review 8. 75 4. 75 • 4 = 16. 75 19 . 008808 . 734 • . 12 = . 08808 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: -570 76 -76 0 -57 0 76 -7 6 0 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.

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? ❷Divide the same way you To solve the problem, you can divide 178. 16 4. divide whole numbers. ❶Write the decimal point for the answer directly above the decimal point in the dividend. Divisor . Dividend The answer is 44. 54. Each person pays $44. 54. 4 4. 5 4 -16 18 -16 21 -20 16 -16 0

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 ❸Write the decimal point on divisor into a whole number. Example 2: Dividend Divisor Divide 48 0. 32 ❶Multiply the divisor by a power ❷Multiply the dividend by the of 10 to make it a whole number. same power of 10. 0. 32 x 100 = 32 (whole number) Move the decimal point 2 places to show this. . top directly above the new decimal point in the dividend. Divide the same way you divide whole numbers. 150. -32 Move the decimal point 2 places to 160 show this. -160. 00. . 48 x 0. 32 = 150 0 48 x 100 = 4800

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 ❸Write the decimal point on top directly above you are rounding. the new decimal point in the dividend. Example 3: Divide 53 0. 7 Divide the same way you divide whole numbers. Round your answer to the nearest tenth. ❶Multiply the divisor by a power ❷Multiply the dividend by the of 10 to make it a whole number. same power of 10. 0. 7 x 10 = 7 (whole number) Move the decimal point 1 place to show this. . . 53 x 10 = 530 Move the decimal point 1 place to show this. . 0. 75. 7 1 -49 40 -35 50 -49 10

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 ❸Write the decimal point on top directly above you are rounding. the new decimal point in the dividend. Example 3: Divide 53 0. 7 Divide the same way you divide whole numbers. Round your answer to the nearest tenth. 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. 53 x 0. 7 75. 7 1 -49 40 -35 50 -49 10

Division Review Round your answers to the nearest hundredth. 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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