Mental Math. Name. There are several ways that you can add and subtract decimals mentally to solve a problem.

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1 Mental Math 2-1 There are several ways that you can add and subtract decimals mentally to solve a problem. Commutative Property of Addition Associative Property of Addition You can add two decimal numbers in any order You can change the groupings of addends. 1.7 (1.3 7) ( ) 7 Compatible numbers are numbers that are easy to compute mentally and 7.4 are compatible because they are easy to add ( ) With compensation, you adjust one or both decimal numbers to make computations easier and compensate to get the final answer Add or subtract mentally How much heavier is a Hippo than a Moose? 6. How heavy are the Elephant and the Rhino combined? Weight of Zoo Animals Animal Weight (Tons) Hippo 2.5 Elephant 3.85 Rhino 2.15 Moose.5 7. What is the total weight of all four animals?

2 Rounding Whole Numbers and Decimals 2-2 You can use the number line below to help you round 8,237,650 to the nearest million. Is 8,237,650 closer to 8,000,000 or 9,000,000? 8,237,650 is less than halfway to 9,000,000. 8,237,650 is closer to 8,000,000. The number line can also help you round to the nearest tenth. Is closer to 7.7 or 7.8? halfway is more than halfway to is closer to 7.8. Round each number to the place of the underlined digit. 1. 4,725, ,023, Round the number of connected computers in Year 2 to the nearest ten million. 6. Marc earned $9.37 per hour working at the library. Round his wage to the nearest ten cents. Number of Computers Connected to the Internet Year 1 30,979,376 Year 2 42,199,279 Year 3 63,592,854 R 2 2

3 Estimating Sums and Differences 2-3 During one week, Mr. Graham drove a truck to five different towns to make deliveries. Estimate how far he drove in all. Mr. Graham s Mileage Log Cities Mileage Mansley to Mt. Hazel 243 Mt. Hazel to Perkins 303 Perkins to Alberton 279 Alberton to Fort Maynard 277 Fort Maynard to Mansley 352 To estimate the sum, you can round each number to the nearest hundred miles Estimate each sum or difference ,500 mi Mr. Graham drove about 1,500 mi. You can estimate differences in a similar way. Estimate You can round each number to the nearest whole number The difference is about Estimation Brigid worked h. Kevin worked h. About how many more hours did Brigid work than Kevin? R 2 3

4 Modeling Addition and Subtraction of Decimals 2-4 Adding decimals using a hundredths grid: Add Subtracting decimals using a hundredths grid: Subtract Step 1: Shade 32 squares to show Step 1: Shade 61 squares to show Step 2: Use a different color. Shade 17 squares to show Step 3: Count all the squares that are shaded. How many hundredths are shaded in all? Write the decimal for the total shaded squares: Step 2: Cross out 42 squares to show Step 3: Count the squares that are shaded but not crossed out. Write the decimal: So, = So, = Add or subtract. You may use hundredths grids to help = = R 2 4

5 Problem Solving: Draw a Picture and Write an Equation 2-5 A community center is raising funds to buy a computer. Here is a picture of the sign they put outside the center. How much more money must the center raise? How to write an equation number sentence for a problem: One Way The goal is $1,600. So far, $1,000 has been raised. The amount yet to be raised is the unknown. Think: The amount raised so far and the amount yet to be raised will reach the goal. Write an equation. 1,000 x 1,600 Think: What number added to 1,000 will result in 1,600? 1, ,600 The amount yet to be raised is $600. Another Way The goal is $1,600. So far, $1,000 has been raised. The amount yet to be raised is the unknown. Think: The difference between the goal and what has been raised so far is the amount yet to be raised. Write an equation. 1,600 1,000 x Think: What number will result if 1,000 is subtracted from 1,600? 1,600 1, The amount yet to be raised is $600. A mason needs 22 bricks to make a stoop. So far he has carried 15 to the site. How many more bricks must he carry? Draw a picture. Write an equation. Write a number sentence. Solve. R 2 5

6 Adding Decimals 2-6 In February, Chantell ran a 5K race in 0.6 hour. She ran another 5K race in May in 0.49 hour. What was her combined time for the two races? Step 1: Write the numbers, lining up the decimal points. Include the zeros to show place value You can use decimal squares to represent this addition problem. Step 2: Add the hundredths Step 3: Add the tenths. Remember to write the decimal point in your answer Chantell s combined time for the two races was 1.09 hours. Add Is 16.7 a reasonable sum for ? Explain. 6. How much combined snowfall was there in Milwaukee and Oklahoma City? City Snowfall (inches) in 2000 Milwaukee, WI 87.8 Baltimore, MD 27.2 Oklahoma City, OK 17.3 R 2 6

7 Subtracting Decimals 2-7 Mr. Montoya bought 3.5 lb of ground beef. He used 2.38 lb to make hamburgers. How much ground beef does he have left? Step 1: Write the numbers, lining up the decimal points. Include the zeros to show place value You can use decimal squares to represent this subtraction problem. Step 2: Subtract the hundredths. Regroup if you need to Step 3: Subtract the tenths and the ones. Remember to write the decimal point in your answer Mr. Montoya has 1.12 lb of ground beef left over. Subtract R 2 7

8 Problem Solving: Multiple-Step Problems 2-8 Kim has a $10 bill, a $20 bill, and 2 $5 gift certificates. She uses the gift certificates toward the purchase of a CD for $ How much money does Kim have left after buying the CD? Read and Understand What do you know? What are you trying to find? Kim has a ten-dollar bill, a twenty-dollar bill, and two five-dollar gift certificates. She uses the 2 certificates toward the purchase of a CD that costs $ How much money does Kim have left after she buys the CD? Plan and Solve Answer these hidden questions. How much money does Kim have? $20.00 $10.00 $30.00 How much are the two $5.00 $5.00 $10.00 certificates worth? How much cash will Kim need to $14.00 $10.00 $4.00 buy the CD? Solve the problem. Write the answer in a complete sentence. Money cash paid for CD Money left $30.00 $4.00 $26.00 Kim has $26 left after buying the CD. Look Back and Check Is your answer correct? Yes, $4.00 $26.00 $ You can also find how much money Kim has left by completing the following expression. $10.00 $20.00 $5.00 $5.00 R 2 8