Name: ______Ratios and Fraction ArithmeticOctober 30, 2015

  1. Harry was able to eat 1/4 of all of the chocolate frogs. Ron ate 2/7 of all of the chocolate frogs. What total fraction of the chocolate frogs got eaten?
  1. When Jack got to the top of the beanstalk, he saw an enormous giant who had a shadow of 15 feet. Jack was 5 feet tall and had a shadow of 3 feet. How tall was the giant?
  1. Mary and her brother Max had a contest to see who could swim the farthest in a short amount of time. They found that Mary could swim twice as far as Max. If the total distance they swam was 120 yards, how many yards was Mary able to swim?
  1. At Reynie’s birthday, his cake was cut into six equal pieces. Kate took one of the pieces, but only ate two-fifths of it. What fraction of the whole cake did Kate eat?
  1. In 16 minutes of jogging, 110 calories are burned. At this rate, how many calories are burned during a 90-minute jog?
  1. For every $3 Marisa spends, Andie spends $5. One weekend Andie spent a total $120 more than Marisa did. How many dollars did Andie spend?
  1. What is the value of N?

= +

  1. In lowest terms, what is the product of this multiplication expression?

×××××××××××

BONUS PROBLEMS

  1. It takes Melissa 2 hours to paint one car. It takes Dave 4 hours to paint one car. Kate also takes 4 hours to paint one car. If they all work together, how long will it take them to paint 2 cars?
  1. When placing the order for doughnuts for Math Club, the coach asked that for every 2 chocolate doughnuts, there would be 1 old-fashioned doughnut, 3 maple nut doughnuts, and 4 sprinkle doughnuts. If the coach ordered ten dozen doughnuts, how many were maple nut?
  1. A bus can hold 24 adults or 30 children. 25 children are already on the bus. What is the greatest number of adults that can still get on the bus?
  1. In simplest terms, what is the value of the following?

+

SOLUTIONS:

  1. 15/28

+ =

+ =

  1. 25 feet

The giant's shadow was 5 times Jack's shadow, so the giant must be 5 times Jack's height.

  1. 80 yards

Since Mary swims twice as fast, for every distance Max swims, Mary swims twice as far. So in this case, x (Max’s distance) + 2x (Mary’s distance) = 120, 3x = 120, x = 40, so Mary’s distance = 2x = 80.

  1. 1/15

× = =

  1. 618.75 calories

16 : 110 = 90 : x. 16x = (90) (110) = 9900. x = 9900/16 = 618.75.

  1. $300

Make a chart and look for a difference of $120.

Amount Andie Spent / $50 / $100 / $150 / $200 / $250 / $300
Amount Marisa Spent / $30 / $60 / $90 / $120 / $150 / $180
Difference / $20 / $40 / $60 / $80 / $100 / $120
  1. N = 30

- = - =

Cancel identical numerators and denominators with each other (that is, divide out each common factor greater than 1). This can be done 11 times. Then we are left with . In lowest terms, the product is .

  1. 2 hours

Dave paints ¼ of a car in an hour. Kate paints ¼ of a car in an hour. Melissa paints ½ of a car in an hour. The three fractions add up to one whole car; therefore it takes 2 hours to paint two cars.

  1. 36

The continued ratio of chocolate to old-fashioned to maple nut to sprinkles is 2:1:3:4. Then we let the number of chocolate, old-fashioned, maple nut and sprinkles be 2x, x, 3x, and 4x respectively. Since the total number of doughnuts is 120 (ten dozen), we have: 2x + x + 3x + 4x = 10x = 120, therefore x = 12. Since the question asks how many maple nut doughnuts there were, and the number of maple nut doughnuts is equal to 3x, the answer is 36.

  1. 4

24 adults require the same space as 30 children. Simplifying, 4 adults require the same space as 5 children. Since 5 more children could get on the bus to make 30 children, and 5 children require the same space as 4 adults, 4 adults can still get on the bus.

  1. 25

The meaning of any fraction is a b. Therefore, means 6 0.3, whose value is 20. Similarly, means 0.3 .06, whose value is 5. The value of the sum is 25.

Cascade Ridge PTSA Math Club1Show your work on a separate sheet of paper.