Challenging Fractions Questions (Primary 5)

 

1. Mixed Up Fractions: Ben ate 3/4 of a pizza and Sarah ate 5/8 of another pizza. They are the same size. Who ate the larger portion? (This requires comparing fractions with different denominators)

2. Fraction Race: There are 120 meters in a race. Michael ran 23/25 of the race, while Nadia ran 9/10 of it. Who ran further, and by how much? (This involves subtracting fractions with different denominators)

3. Pizza Party Percentages: A group of friends ordered 3 pizzas. They ate 75% of the first pizza, 60% of the second, and only half of the third. What fraction of the total pizzas did they eat? (This requires converting percentages to fractions and then adding fractions)

4. Fraction Word Problems: A rectangular garden is 10 meters long and 15 meters wide. If 3/5 of its width is occupied by a flower bed, what is the length of the flower bed? (This involves working with fractions of a whole number)

5. Equivalent Fractions Challenge: Find three different fractions that are equivalent to 7/12. (This tests understanding of simplifying and recognizing equivalent fractions)

6. Fraction on a Clock: If the hour hand of a clock points to 5, what fraction of the clock face has it covered? (This requires understanding fractions of a circle)

7. Fraction of a Recipe: A cake recipe requires 1 1/2 cups of flour. If you only want to make half the recipe, how much flour do you need? (This involves working with mixed numbers and fractions of a recipe)

8. Fraction Treasure Hunt: A pirate hides his treasure chest 2/3 of the way across a 60-meter long bridge. How far is the treasure chest from the beginning of the bridge? (This involves multiplying fractions by a whole number)

9. Fraction Shopping: A shirt costs $20. There is a 1/4 discount on it. How much will you pay after the discount? (This involves multiplying fractions by a whole number to find the discount)

10. Fraction Logic Puzzles: If 1/2 of a box of cookies is chocolate chip and 1/3 is oatmeal raisin, what fraction of the box is neither flavour? (This requires understanding how fractions represent parts of a whole)
    
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    Answer Key for Challenging Fractions Questions (Primary 5)

    1. Ben ate the larger portion. (6/8 is larger than 5/8 when comparing common denominators)

    2. Michael ran further. (Michael ran 115/125 while Nadia ran 108/120. Michael ran 7/125 further) Michael ran further in the race. Let's find out how much each person ran and then subtract the distances to see the difference.

       1. Convert fractions to have the same denominator:

       There are a couple of ways to approach this. We can find the least common denominator (the smallest number divisible by both 25 and 10) or convert one fraction to have the same denominator as the other.

       In this case, converting 9/10 to have a denominator of 25 is easier:

       • Multiply the top and bottom of 9/10 by 2.5 (because 2.5 x 4 = 25)
       • This becomes 22.5/25

       2. Find the distance each person ran:

       • Michael ran 23/25 * 120 meters (total race distance) = 115.2 meters
       • Nadia ran 22.5/25 * 120 meters = 108 meters

       3. Calculate the difference in distance:

       • Michael ran further by 115.2 meters - 108 meters = 7.2 meters

       Therefore, Michael ran further by 7.2 meters.

    3. Here's how to find the fraction of total pizzas the friends ate:

       1. Convert percentages to fractions:

          • 75% = 75/100 = 3/4 (of the first pizza)
          • 60% = 60/100 = 3/5 (of the second pizza)
          • Half = 50% = 50/100 = 1/2 (of the third pizza)

       2. Calculate the total fraction eaten:

          • Total fraction = 3/4 (1st pizza) + 3/5 (2nd pizza) + 1/2 (3rd pizza)

       3. Find a common denominator to add the fractions: The least common denominator (LCD) is the smallest number divisible by 4, 5, and 2. In this case, LCD = 20.

          • Convert 3/4 to twentieths: 3/4 * (5/5) = 15/20
          • Convert 3/5 to twentieths: 3/5 * (4/4) = 12/20

       4. Add the fractions with the common denominator:

          • Total fraction = 15/20 + 12/20 + 1/2 = 28/20

       Therefore, the friends ate a total of 28/20 of the pizzas.

       Optional simplification:

       Although less precise in this context, the fraction can be further simplified to 7/5 by dividing both numerator and denominator by 4.

    4. The flower bed is 6 meters long. (3/5 of 10 meters is 3/5 * 10 = 6 meters) With the additional information about the garden's width (15 meters), we can now determine the length of the flower bed.

       Here's how to solve it:

       1. Find the width of the flower bed:

          • We know the total garden width is 15 meters.

          • We are given that 3/5 of the width is occupied by the flower bed.

          • Therefore, the flower bed width is:

            Flower bed width = Total width * (Fraction of width occupied by flower bed) Flower bed width = 15 meters * (3/5) = 9 meters

       2. Flower bed length:

          The question asks for the length of the flower bed. In a rectangle, the length is independent of the width.

          Therefore, the length of the flower bed is the same as the overall garden length:

          Flower bed length = 10 meters

       So, the flower bed in this rectangular garden is 10 meters long.

    5. Possible answers include: 14/24, 21/36, 35/60 (all are equivalent to 7/12 by multiplying numerator and denominator by the same number)
       

       There are many fractions equivalent to 7/12. Here are three examples:

       1. Multiplying numerator and denominator by the same number:

       We can multiply both the top (numerator) and bottom (denominator) of 7/12 by the same number without changing the value of the fraction. For example, multiplying by 2 gives:

       • 7/12 * 2/2 = 14/24
       2. Dividing numerator and denominator by the same number (with a common divisor):

       If the numerator and denominator share a common divisor (a number that divides both without a remainder), we can divide by that number to get an equivalent fraction. In this case, 7 and 12 share a common divisor of 1. However, dividing by 1 doesn't change the fraction (7/12 divided by 1/1 is still 7/12).

       Here's an example with a different common divisor (3):

       • 7/12 * (3/3) = 21/36 (both numerator and denominator are divided by 3)
       3. Finding other simplified fractions with the same value:

       There might be other fractions with different numerators and denominators that represent the same value as 7/12. For example:

       • 1/2 (dividing both numerator and denominator by 7)

       While 1/2 is a simpler form, it's not achieved by multiplying or dividing by the same number as in the first two examples.

       These are just a few examples. You can find many other equivalent fractions to 7/12 by following the principles of multiplying/dividing by the same number (given a common divisor) or finding other simplified forms with the same value.

    6. The hour hand covers 5/12 of the clock face. (There are 12 hours, so each hour represents 1/12 of the circle) The hour hand on a clock covers a fraction of the clock face based on the number it points to. Here's how to find the fraction covered when it points to 5:

       1. Number of hours on a clock: There are 12 hours marked on a standard clock face.

       2. Space covered by each hour: Since the hour hand completes a full circle around the clock face in 12 hours, each hour on the clock face represents 1/12th of the total space.

       3. Hour hand pointing to 5: When the hour hand points to 5, it has moved 5 hours from the 12 o'clock position.

       4. Fraction of the clock face covered: Therefore, the hour hand covers 5/12 of the clock face when it points to 5.

       So, the answer is 5/12. The hour hand covers five out of the twelve equal parts representing the hours on the clock face.

    7. You need ¾ of a cup of flour. (Half of 1 ½ cups is ½ * (1 + ½) = ¾ cups) 

       
       
       

    8. The treasure chest is 40 meters from the beginning. (2/3 * 60 meters = 40 meters) 

       
       
       

    9. You will pay $15 after the discount. (Discount is ¼ * $20 = $5. Total price is $20 - $5 = $15) 
       

       
        

    10. The fraction of the box that is neither flavour is 1/6