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Robert and May are competing in a track meet. The table at the right shows the results of their events.
9. Robert says his better jump was about 1 ft longer than May’s better jump. Is he correct?
10. Use the table above. If the school record for the softball throw is 78 ft, about how much farther must Robert throw the ball to match the record?
A 15 ft B 16 ft C 18 ft D 20 ft
11. Consider the sum of 3 _ 5 + 3 _ 4 . Round each fraction and estimate the sum. Add the two fractions using a common denominator and then round the result. Which estimate is closer to the actual answer?
10-1Bake SaleJill and her mother are going to prepare some foods for the school bake sale. They can choose to bake any of the foods in the chart. They can bake as many different things as they like. Use the chart to answer the questions.
1. Estimate to the nearest cup the amount of flour needed to make 4 pumpkin pies.
2. Jill wants to bake at least two different items. If Jill has 2 c of sugar and 3 c of flour, name a combination of baked goods that she could prepare.
3. Would it take more sugar and flour combined to make the cookies or the pumpkin pie?
4. Jill is thinking about baking 36 oatmeal cookies. How much flour would she and her mom need for this?
5. Estimate the amount of flour needed to bake everything listed in the chart.
Item Sugar Flour ServingsOatmeal cookies 1 1 _ 3 c 2 1 _ 4 c 18 cookies
15. Jerome’s rain gauge showed 13 9 __ 10 centimeters (cm) at the end of last month. At the end of this month, the rain gauge showed 15 3 __ 10 centimeters. How many more centimeters of rain fell this month?
A 29 2 ___ 10 cm B 15 3 ___ 10 cm C 2 4 ___ 10 cm D 1 4 ___ 10 cm
16. You are adding 3 2 _ 3 + 2 2 _ 3 using fraction strips. Explain how you rename the fraction part of the problem.
10-3Adding Mixed NumbersRandy talks on the telephone for 2 5 _ 6 hours, and then surfs the Internet for 3 3 _ 4 hours. How many hours does he spend on the two activities?
Step 1. Write equivalent fractions with the least common denominator. You can use fraction strips to show the equivalent fractions.
Step 2. Add the fraction part of the mixed number first. Then add the whole numbers.
9 ___ 12 + 10 ___ 12 = 19 ___ 12 3 + 2 = 5
19 ___ 12 + 5 = 5 19 ___ 12
Step 3. Simplify the sum if possible.
5 19 ___ 12 = 6 7 ___ 12 hours
So, 2 5 __ 6 + 3 3 __ 4 = 6 7 ___ 12 .
In 1 through 6, find each sum. Simplify if possible.
10-3Mixed Sums 1. Annie walked her dog 2 1 _ 4 miles from her house to the
dog park and 3 7 _ 8 miles around the park. Then she walked the same distance home. How many miles did she walk in all?
2. John’s full backpack weighs 5 1 _ 2 pounds, and Tyrone’s full backpack weighs 6 3 _ 5 pounds. What is the total weight of both boys’ backpacks?
3. Julie has two extension cords with lengths of 22 1 _ 6 feet and 26 3 _ 4 feet. How long a cord can she make by attaching them together?
4. Terry weighed his two cats at the veterinarian’s office. Boots weighed 12 9 __ 10 pounds, and Tiger weighed 13 1 _ 4 pounds. What is the total weight of both cats?
5. David ran 9 3 _ 4 miles on Saturday and 7 1 __ 10 miles on Sunday. How many miles did he run on the weekend?
6. Amanda’s library books weigh 4 3 _ 8 pounds, and her water bottle weighs 1 7 __ 16 pounds. What is the total weight of her books and water bottle?
10-4Subtracting Mixed NumbersThe Plainville Zoo has had elephants for 12 2 _ 3 years. The zoo has had zebras for 5 1 _ 2 years. How many years longer has the zoo had elephants?
For 1 through 4, find each difference. Simplify, if possible.Remember: You may have to rename a fraction in order to subtract.
1. 4 3 __ 5
− 2 1 __ 3
2. 5 6 __ 7
− 1 1 __ 2
3. 30
− 1 3 __ 4
4. 6 5 __ 6
− 5 1 __ 2
5. To find the difference of 7 − 3 5 __ 12 , how do you rename the 7?
6. Robyn ran 5 3 _ 4 miles last week. She ran 4 1 __ 10 miles this week. How many more miles did she run last week?
Step 1: Write equivalent fractions with the least common denominator. You can use fraction strips.
Step 2: Find the difference of 12 4 _ 6 − 5 3 _ 6 . Subtract the fractions. Then subtract the whole numbers. Simplify the difference if possible.
4 __ 6 − 3 __ 6 = 1 __ 6 12 − 5 = 7
So, 12 2 __ 3 − 5 1 __ 2 = 7 1 __ 6 years.
Example: Sometimes you may have to rename a fraction so you can subtract.Find the difference of 6 − 2 3 _ 8 .
10-4Mixed DifferencesAnswer each question. Write your answers in simplest form.
1. Jenna bought a spool of ribbon for her craft projects. It contained 5 3 _ 4 meters of ribbon. She used 3 2 _ 5 meters of ribbon for a project. How many meters of ribbon does Jenna have left?
2. Brandon has a male puppy with a mass of 3 1 _ 2 kilograms and a female puppy with a mass of 2 1 _ 5 kilograms. How much greater is the male puppy’s mass than the female puppy’s?
3. Jeff’s sister drives 14 miles to her college, but his brother only drives 5 7 __ 10 miles to his college. How much farther does Jeff’s sister drive than his brother?
4. Montel bought a spool of string for making kites. It contained 10 3 __ 20 meters of string. He used 6 9 __ 10 meters of string for kites. How many meters of string does Montel have left?
5. Janet grew a pumpkin that weighs 13 1 _ 2 pounds and a melon that weighs 8 1 _ 4 pounds. How much heavier is the pumpkin than the melon?
6. Aidan roller-skated 3 1 __ 10 miles around the lake. Josh roller-skated 2 1 _ 2 miles around the park. How much farther did Aidan roller-skate than Josh?
10-5More Adding and Subtracting Mixed NumbersYou can use what you know about adding and subtracting with mixed numbers when you simplify expressions with mixed numbers.
Simplify ( 4 1 __ 8 + 6 1 __ 4 ) – 2 1 __ 2 .
Step 1 Add the mixed numbers in parentheses first. Find a common denominator.
Step 2 Subtract 2 1 __ 2 from the sum you found. Find a common denominator.
You can’t subtract 4 __ 8 from 3 __ 8 .
Step 3 Rename if possible.
In 1 through 9, simplify each expression. Remember to rename mixed numbers if possible.
10. Suzy spent 6 7 __ 8 days working on her English paper, 3 1 __ 6 days doing her science project, and 1 1 __ 2 days studying for her math test. How many more days did Suzy spend on her English paper and math test than on her science project?
15. What is a reasonable estimate for the sum of 4 1 __ 8 + 3 2 __ 3 + 5 1 __ 2 ?
16. Veronica is buying cubed cheese from Mr. Sand’s deli. She asks for 1 3 __ 4 pounds. When Mr. Sand places some cheese in a container and weighs it, the scale shows 1 1 __ 4 pounds. The container weighs 1 ___ 16 pound. How many more pounds of cheese would Mr. Sand need to add to the scale to get the amount that Veronica asked for? Explain how you solved the problem.
10-5Table TimeMake tables to solve. Write each answer in a complete sentence.
1. A train has 3 engines, 52 boxcars, and 1 caboose. At every stop, it picks up 8 more boxcars. How many total cars (engines, cars, and cabooses) will the train have after 5 stops?
2. Eileen likes to keep scrapbooks. She already has 4 scrapbooks filled with 40 pages each. If she fills 5 pages every month, how many months will it take her to fill up 2 more 40-page scrapbooks?
3. Phil’s Garage charges $50 for towing and $40 per hour to fix a car. Cliff’s Cars charges $60 for towing and $38 per hour to fix a car. After how many hours of working on a car will the cost of towing and fixing a car be the same at the two repair shops?
4. Dominic got a new video game. The first time he played the game he scored 80 points. After that, each time he played he increased his score by 60 points. How many times will he have to play before he scores 500 points?
5. A scientist is studying certain germs. She places 3 germs in a special solution that will help the germs grow. The number of germs doubles every hour. How many germs will there be after 8 hours?
6. Ed saved $50 one week. For the next 6 weeks, he saved $25 more than he saved the week before. How much did he save in all? One student solved this problem using the expression $50 ! 6($25) " $200. What error was made?
10-6Problem Solving: Draw a Picture and Write an EquationA jeweler has a strand of gold wire that is 1 3 _ 8 inches. He cuts 3 _ 4 of an inch of wire to make a loop. How long is the remaining piece of wire?
From his house, Jason rode his bike 1 1 _ 3 miles to the post office. He then rode in the same direction to the park, which is 1 _ 4 of a mile from the post office. How far did Jason ride?
1. To the right, draw a picture to represent the problem to be solved. Let x = the distance Jason rode from his house to the park.
2. Write an equation that represents this distance. Then solve for x.
Read and Understand
What do you know? The length of the wire is 1 3 _ 8 inches.
The length he cuts off is 3 _ 4 of an inch.
What are you trying to find? The length of the wire that is left over.
Plan and Solve
Draw a picture for what you know.
Write an equation. Let x = the length of wire left over.
10-6Problem Solving: Draw a Picture and Write an EquationDraw a picture and write an equation. Then solve.
3. Stewart draws a triangle, and each side is 2 1 _ 6 inches long. Judith draws a square, and each side is 1 5 _ 8 inches long. Which figure has the greater perimeter, the triangle or the square?
4. Cristoff practices playing his guitar for 1 1 _ 2 hours each weekday. He practices this amount of time plus an additional 1 1 _ 2 hours on Sundays. Let x = the number of hours Cristoff practices on Sundays. Draw a picture and write an equation and solve to find the number of hours he practices on Sundays.
5. Which of these fractions, when added to 2 1 _ 3 , will give you a sum greater than six?
A 3 1 __ 2 B 3 5 ___ 12 C 3 7 ___ 12 D 3 3 __ 4
6. Dennis says that 1 1 _ 2 , 1 2 _ 4 , and 1 3 _ 6 are all equivalent. Is he correct? Draw a picture and explain your answer.
1. Mr. Flanders drives 1 2 _ 3 miles to school and 1 2 _ 3 miles home each day. He also drives an extra 2 2 _ 7 miles to go to the gym. How many miles does he drive in one day?
2. Alison is making a 16-inch necklace. The first 4 1 _ 4 inches are filled with red beads and 8 3 _ 8 inches are filled with blue beads. The rest has white beads. How many inches are filled with white beads?