Operations with Rational Numbers

Problems of the Day (Monday) 8 + (-2.25) = -3 ½ + ( -2 ¾) = - 4.5 + 4.5 = 1 ¼ + 2 1/6 = - 9.5 + 6 = One month Julia collected 8.4 gallons of rainwater. That month she used 5.2 gallons of rainwater for her garden and 6.5 gallons of rainwater for her flowers. How much supply was increased or decreased by the end of the month.

Adding & Subtracting Rational Numbers Practice Problems - 6.5 – 2 = 1 ½ - 2 = - ½ - ( - ¾) = ¼ + ½ = - 1 ½ + ( -1 ½ ) = ¼ + ( - ¾) = - 4 ½ + 2 = -8 + ( -1 1/8 ) = - 1/3 – ( - 5/6 ) =

Adding & Subtracting Rational Numbers Word Problems Renee hiked for 4 ¾ miles. After resting, Renee hiked back along the same route for 3 ¼ miles. How many more miles does Renee need to hike to return to the place where she started? A submarine submerged at a depth of – 35.25 meters dives an additional 8.5 meters. What is the new depth of the submarine? The first play of a football game resulted in a loss of 12 ½ yds. Then a penalty resulted in another loss of 5 yards. What is the total loss or gain? Jeremy is practicing some tricks on his skateboard. One trick takes him forward 5 feet, then he flips around and moves backward 7.2 feet, then moves forward again 2.2 feet. Write and solve an expression to find how far Jeremy is from his starting position when he finishes his trick. A diver dove to a location of 6 3/5 meters below sea level. He then dove to a second location 8 1/5 meters below sea level. How many meters are between location? ( This is a distance problem. Find the absolute value of the difference. Distance is never negative.)

Answer Key Problems of the Day 1. 5.75 2. - 6 1/4 3. 0 4. 3 5/12 5. - 3.5 6. - 3.3 gallons Adding and Subtracting Practice Problems Word Problems 1. - 8.5 1. 1 ½ miles 2. - ½ 2. - 43.75 m 3. ¼ 3. a loss of 17 ½ yds -17 ½) 4. ¾ 4. 5 – 7.2 + 2.2 = 0 (starting point) 5. -3 5. 6 3/5 – ( -8 1/5 ) = 1 3/5 m 6. - 1/2 7. - 2 1/2 8. - 9 1/8 9. 1/2

Problems of the Day (Tuesday) - 2/9 – (-3) = 1/3 – ( - 2/3) = 24 3/8 – ( -54 1/8 ) = Change the following mixed numbers into improper fractions 2 ¾ = 11 4/5 = 8 2/3 = 10 2/7 =

Multiplying Rational Numbers 6( -2/3) = -2 ½( -10) = (3/4)(-8/9) = -8 ¼( 2/11) = -3 1/5(- ½) = (-16)(3/4) = (4 1/3)(-3 3/8) = -8 2/5(- 2 1/7) =

Multplying Multiple Rational Numbers When you are multiplying multiple rational numbers, if there are an even number of negative signs, your answer will be positive. If there are an odd number of negative signs, your answer will be negative. Also, when you are multiplying multiple rational numbers, you can cancel numbers that are the same vertically and diagonally. ( -3/4)(1/2)(-2/3) = ( -2/3)( -3/4)( 4/5) = (2/3)( -9/10)( 5/6) = (-3/4)( -4/7)( -2/3) = (-3/5)( ½)( -2) = ( -2/7)(1/2)(14) =

Multiplying Rational Number Word Problems The price of one share of Acne Company declined $3.50 per day for 4 days in a row. What was the oveall change in the price of one share? If Sandy writes 6 checks for exactly $19.96, what is the expression that describes the change in her bank account? Wha is the balance in her account after the checks if she started with $200? Greg’s watch loses 3 ¼ minutes every week. If his watch continues to lose time at this rate, what would be the overall change in time after 8 weeks? Tina purchased a coat on sale. The original price was $180. The sale price was ¾ of the original price. How much did Tina pay for the coat? Dennis bought a new game for $36. Jenny spend 2 ½ times as much on the same game. How much did Jenny pay? How much more did Jenny spend? There are 220 students in the 7th grade at Penny Brook Middle School. If 2/5 of the students play sports, how many 7th graders participate in sports?

Answer Key Multiplying Rational Numbers (Slide 7) Multiplying Word Problems (Slide 9) -4 1. 14 25 2. $119.76 $80.24 -2/3 3. -26 -1 ½ 4. 135 1 3/5 5. $90 $54 -12 6. 88 -14 5/8 18 Multiplying Multiple Rational Numbers (Slide 8) ¼ 2/5 - ½ -2/7 3/5 -2

Dividing Rational Numbers Word Problems The price of one share of ABC company declined a total of $45.75 in 5 days. What was the average change of the price of one share per day? The running back for the Bulldogs football team carried the ball 9 times for a total loss of 15 ¾ yards. Find the average change in field position on each run. The 6:00 a.m. temperatures for four consecutive days in the town of Lincoln were -12.1 degrees C, -7.9 degrees C, -14.3 degrees C, and -5.7 degrees C. What was the average temperature for the 4 days? John buys a 6 ¼ lb bag of peanuts and shares it equally with four of his friends. How many pounds of peanuts does each person receive? Dana made 200 liters of fruit punch for the town fair, and she poured the punch into containers. If each container holds 2 ½ liters, how many containers will she need? A hot air balloon descended 99.6 meters in 12 seconds. What was the balloon’s average rate of descent in meters per second?

Answer Key – Dividing Rational Numbers Word Problems 1. -45.75/5 = -9.15 (The price of the share declined 9.15 per day.) 2. -15 ¾/ 9 = -63/4( 1/9) = -7/4 = -1 ¾ (The team lost 1 ¾ yds. each run.) 3. -40.0/4 = -10 (The average temperature was 10 degrees below zero.) 4. 6 ¼/5 = 25/4( 1/5) = 5/4 = 1 ¼ (Each person receives 1 ¼ lbs of peanuts.) 5. 200/2 ½ = 200/1(2/5) = 80 (She will need 80 containers.) 6. - 99.6/12 = -8.3 ( The balloon descended 8.3 meters per second.)