3-1 Add and Subtract Decimals. Find the sum SOLUTION: Line up the decimal points and add as with whole numbers.

Transcription

1 Find the sum Line up the decimal points and add as with whole numbers Annex zeros so both number have the same number of decimal places. Line up the decimal points and add as with whole numbers Annex zeros so both number have the same number of decimal places. Line up the decimal points and add as with whole numbers. Find the difference Line up the decimal points and subtract as with whole numbers Annex zeros so both number have the same number of decimal places. Line up the decimal points and subtract as with whole numbers. esolutions Manual - Powered by Cognero Page 1

2 Line up the decimal points and subtract as with whole numbers. 7. The table shows the top three finishers in barrel racing. What is the time difference between Nicolas and Sancho? Understand: From the table, you know that Nicolas s time was seconds and Sancho s time was seconds. You need to find the difference between the two times. Plan: Subtract Nicolas s time (14.67) from Sancho s time (16.40). The time difference between Nicolas and Sancho is 1.73 seconds. 8. In two months, Mica spent a total of $ on groceries. She spent $ in the first month. How much did she spend in the second month? Understand: Mica spent a total of $ in two month on groceries. In the first month, she spent $ You need to find how much money she spent in the second month. Plan: Subtract the amount she spent in the first month ($213.20) from the total ($305.43). Mica spent $92.23 in the second month. esolutions Manual - Powered by Cognero Page 2

3 9. Financial Literacy A hat costs $10.95 and a T-shirt costs $ How much change will you receive if you pay for both items with a $50 bill? Understand: You know you have $50 and you spend $10.95 plus $ You need to find how much change you will get after paying for the two items. Plan: Add and and subtract the total from 50. You will receive $24.85 in change. esolutions Manual - Powered by Cognero Page 3

4 10. Use Math Tools The 4-by-100 meter relay is a track and field event involving four runners on each team. a. What is the combined time of Carter and Frater? b. How much faster did Powell run his leg of the race than Bolt? c. What is the combined time of all the runners? a. Understand: What is the combined time of Carter and Frater? Plan: Add Carter s time (13.4) and Frater s time (12). b. Understand: How much faster was Powell s time than Bolt s time? Plan: Subtract Powell s time (8.7) from Bolt s time (9). c. Understand: What is the combined time of all four runners? Plan: Add Carter s time (13.4), Frater s time (12), Bolt s time (12), and Powell s time (11.7). esolutions Manual - Powered by Cognero Page 4

5 11. Find the Error Luis is finding Find his mistake and correct it. Luis did not annex a zero before subtracting. 12. Reason Abstractly Write two different pairs of decimals whose sums are 14.1.One pair should involve regrouping. Select any decimal and subtract it from This will create the first pair. So, 50. and 9.1 are the first pair. The second pair should include regrouping. Subtract 7.7 from So, 7.7 and 6.4 are the second pair. 13. Reason Inductively Explain how you know that the sum of 12.6, 3.1, and 5.4 is greater than 20. The whole numbers are 12, 3, and 5. When you add the whole numbers the sum is 20. The sum of the decimals will be added on, which will make the sum greater than 20. esolutions Manual - Powered by Cognero Page 5

6 14. Persevere with Problems Josie found that = What is the missing factor in the related multiplication problem 3.28 = 9.84? Explain. Repeated addition is similar to multiplication. Josie added 3.28 three times to find the sum So, is Reason Abstractly Without subtracting , determine what digit will be in the hundredths place. Explain. A zero is annexed to subtract from 8.5. The 4 in the hundredths place of 4.64 is greater than the zero is annexed, so you need to regroup. You will subtract 10 4 to find the value in the hundredths place. 16. Reason Inductively Keira is buying items show in the table for her kitchen. Will $35 be enough to purchase all three items. Explain your reasoning. Line up the decimal points and add as with whole numbers $ $ Yes since $34.19<$35, $35 is enough for all the items. Find the sum Line up the decimal points and add as with whole numbers. esolutions Manual - Powered by Cognero Page 6

7 Annex zeros so both number have the same number of decimal places. Line up the decimal points and add as with whole numbers Line up the decimal points and add as with whole numbers. Find the difference Line up the decimal points and subtract as with whole numbers Annex zeros so both number have the same number of decimal places. Line up the decimal points and subtract as with whole numbers Line up the decimal points and subtract as with whole numbers. esolutions Manual - Powered by Cognero Page 7

8 23. Financial Literacy The current balance of Tami s checking account is $ Find the new balance after Tami writes a check for $ Understand: Tami has $ in the bank and takes out $ You need to find how much money she has left. Plan: Subtract the amount she took out (29.95) from the amount she had to begin with (237.80). Tami s new balance is $ The annual rainfall for Kayston Falls was inches in In 2013, the annual rainfall was inches. What is the difference in rainfall between the two years? Line up the decimal points and subtract as with whole numbers. The difference is 5.38 inches. esolutions Manual - Powered by Cognero Page 8

9 25. The melting point of sodium is 97.8 degrees Celsius. The melting point of potassium is degrees Celsius. How much higher is the melting point of sodium? Annex a zero so both number have the same number of decimal places. Line up the decimal points and subtract as with whole numbers. The melting point of sodium is degrees Celsius higher than the melting point of potassium. 26. Be Precise Collin needs three wooden boards to repair his porch. The lengths he needs are 2.2 meters, 2.82 meters, and 4.25 meters. He purchases a board that is 10 meters long and cuts the three sections. How much of the board that Collin purchased will be left? a. Understand: How much of the 10 meter board will be left after Collin cuts off the three lengths. Plan: Add the lengths of the three boards together, then subtract the total length from 10 meters. There will be 0.73 meter of the board left. esolutions Manual - Powered by Cognero Page 9

10 27. Dominic is traveling through the state of Oregon. He drove 66.4 miles from Salem to Eugene and then continued to Medford. The total distance of his trip was miles. How far is the distance from Eugene to Medford? Annex a zero. Line up the decimals points and subtract like with whole numbers. The distance from Eugene to Medford is miles. esolutions Manual - Powered by Cognero Page 10

11 28. The table shows the top four finishers for a swimming event. Determine if each statement is true or false. a. Will swam 0.32 seconds faster than Andrew. b. Ty swam 0.27 seconds faster than Will. c. Andrew swam 0.5 seconds slower than Ty. d. Will swam 0.11 seconds slower than Kendrick. Find the difference in time to determine which swimmer is faster or slower and by how much. A. Find the difference between Andrew and Will times. Will's time is a smaller value, so Will was faster. Will's time is 0.32 s faster, so the statement is true. B. Will's time is a smaller value, so Will was faster. So the statement is false. C. Andrew's time is a larger value, so Andrew was slower. Find the difference in times to find out how much slower. Andrew is 0.05 s slower, so the statement is false. D. Will's time is a larger value, so he was slower. Find the difference in times to find out how much slower. Will was 0.11 s slower than Kendrick so the statement is true. esolutions Manual - Powered by Cognero Page 11

12 Round the decimal to the nearest whole number is closer to one than zero so 4.75 rounds up to is closer to zero than one so 34.1 rounds down to is closer to zero than to one so rounds down to Plot the number 2.78 on the number line below. Each tick mark represents an increment of 0.01, so count 8 tick marks over from 2.7 to plot The table shows the distances Juliana biked several days this week. Which day of the week did she bike the greatest distance? 9.34 < 9.47; 9.47 < 9.74; 9.74 > 9.32 So, 9.74 is the greatest distance. Juliana biked this distance on Thursday. esolutions Manual - Powered by Cognero Page 12