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Multiplication of Fractions and Mixed Numbers Answer Sheet
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Hard
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Multiplication of Fractions and Mixed Numbers
Multiplication of Fractions and Mixed Numbers
Level:
Hard
No. of Questions10
Maximum Points10
- Question 1 of 10
1. Question
Marcus ate \(\frac{2}{8}\) of a large pizza. \(\frac{3}{4}\) of the remaining pizza was eaten by Lizzie. How much of the pizza did Lizzie eat?
IncorrectCorrectWOOHOO!
EXPLANATION
Fraction of Pizza eaten by Marcus = \(\frac{2}{8}\)
Remaining pizza = \(\frac{8}{8}\) – \(\frac{2}{8}\) = \(\frac{6}{8}\)
Amount of pizza eaten by Lizzie = \(\frac{3}{4}\) ×\(\frac{6}{8}\)
= \(\frac{18}{32}\)
= \(\frac{9}{16}\)
Hence, the amount of pizza eaten by Lizzie is \(\frac{9}{16}\).
WELL, IT’S ONLY A MATTER OF TIME TILL YOU ACE IT. KEEP TRYING!
EXPLANATION
Fraction of Pizza eaten by Marcus = \(\frac{2}{8}\)
Remaining pizza = \(\frac{8}{8}\) – \(\frac{2}{8}\) = \(\frac{6}{8}\)
Amount of pizza eaten by Lizzie = \(\frac{3}{4}\) ×\(\frac{6}{8}\)
= \(\frac{18}{32}\)
= \(\frac{9}{16}\)
Hence, the amount of pizza eaten by Lizzie is \(\frac{9}{16}\).
- Question 2 of 10
2. Question
Lindy ate 2\(\frac{4}{9}\) of a large pie. The same amount of pie was distributed to 45 others based on the quantity Lindy ate. What is the total amount of pies that would have been consumed?
IncorrectCorrectI KNEW YOU COULD DO IT! WELL DONE!
EXPLANATION:
Lindy ate 2\(\frac{4}{9}\) of a large pie. To find the total quantity of the pies that were distributed to the crowd,
2\(\frac{4}{9}\) should be multiplied by 45.
2\(\frac{4}{9}\) × 45
Using the Distributive Property,
= ( 2 × 45 ) + ( \(\frac{4}{9}\) × 45 )
Simplifying the equation further
= ( 90) + ( 4 × 5 )
= ( 90) + ( 20 )
= 110
Therefore, the total quantity of pies that would have to be distributed is 110.
A+ FOR EFFORT! KEEP TRYING.
EXPLANATION:
Lindy ate 2\(\frac{4}{9}\) of a large pie. To find the total quantity of the pies that were distributed to the crowd,
2\(\frac{4}{9}\) should be multiplied by 45.
2\(\frac{4}{9}\) × 45
Using the Distributive Property,
= ( 2 × 45 ) + ( \(\frac{4}{9}\) × 45 )
Simplifying the equation further
= ( 90) + ( 4 × 5 )
= ( 90) + ( 20 )
= 110
Therefore, the total quantity of pies that would have to be distributed is 110.
Hint
Multiply 2\(\frac{4}{9}\) with 45 to obtain the answer.
- Question 3 of 10
3. Question
A tiger is recorded to sleep for 4 hours in 1 day. A sloth sleeps 2\(\frac{2}{3}\) times more than the tiger on the same day. How many hours does the sloth sleep that day?
IncorrectCorrectYOU’RE DOING GREAT. KEEP GOING.
EXPLANATION
To find the number of hours the sloth sleeps, multiply the number of hours the tiger sleeps by 2\(\frac{2}{3}\).
= ( 4 × 2\(\frac{8}{3}\))
Using the distributive property we get the following
= (8) + (\(\frac{8}{3}\))
simplifying the equation further we get
= \(\frac{32}{3}\)
Therefore, the total number of hours a sloth slept that day is ( \(\frac{32}{3}\) ) hours
THAT WAS A GOOD ATTEMPT. DON’T EVER STOP TRYING!
EXPLANATION
To find the number of hours the sloth sleeps, multiply the number of hours the tiger sleeps by 2\(\frac{2}{3}\).
= ( 4 × 2\(\frac{8}{3}\))
Using the distributive property we get the following
= (8) + (\(\frac{8}{3}\))
simplifying the equation further we get
= \(\frac{32}{3}\)
Therefore, the total number of hours a sloth slept that day is ( \(\frac{32}{3}\) ) hours
Hint
Multiply the number of hours taken by the tiger and multiply it with 2\(\frac{2}{3}\).
- Question 4 of 10
4. Question
7 packages of meat were prepared by a deli worker. Each package contains 2\(\frac{6}{7}\) pounds of meat. How many pounds of meat were used?
IncorrectCorrectTHAT’S ANOTHER ONE FOR THE WIN! GOOD WORK!
EXPLANATION
7 × 2\(\frac{6}{7}\)
Using the distributive property we get the following
= ( 7 × 2 ) + ( 7 × \(\frac{6}{7}\) )
Simplifying further we get
= ( 14 ) + ( 7 × \(\frac{6}{7}\) )
= ( 14 ) + ( 6 )
= 20
Therefore, the deli worker used 20 pounds of meat.
KEEP UP THE WORK, AND YOU’LL GET IT!
EXPLANATION
7 × 2\(\frac{6}{7}\)
Using the distributive property we get the following
= ( 7 × 2 ) + ( 7 × \(\frac{6}{7}\) )
Simplifying further we get
= ( 14 ) + ( 7 × \(\frac{6}{7}\) )
= ( 14 ) + ( 6 )
= 20
Therefore, the deli worker used 20 pounds of meat.
Hint
Multiply the amount of meat in each packet with the total number of packets
- Question 5 of 10
5. Question
Fill in the blanks.
IncorrectCorrectSebastian planned his birthday party and he decided to divide one cake into eight pieces and distribute it among his friends. cakes are required if 48 of his friends came to the party.
A BUDDING MATHEMATICAL GENIUS AT WORK!
EXPLANATION
Since one cake is divided into eight slices, so, each slice is \(\frac{1}{8}\). to find the total number of slices required, \(\frac{1}{8}\) is multiplied by 48.
Total number of slices of cake required = \(\frac{1}{8}\) × 48
Simplifying the fraction we get
= 6
Therefore, Sebastian needs a total of 6 cakes.
THAT WAS A GOOD ATTEMPT. DON’T EVER STOP TRYING!
EXPLANATION
Since one cake is divided into eight slices, so, each slice is \(\frac{1}{8}\). to find the total number of slices required, \(\frac{1}{8}\) is multiplied by 48.
Total number of slices of cake required = \(\frac{1}{8}\) × 48
Simplifying the fraction we get
= 6
Therefore, Sebastian needs a total of 6 cakes.
Hint
Convert into fractions and then multiply.
- Question 6 of 10
6. Question
Arrange the following product of fractions in the increasing order of their value.
IncorrectCorrect- 2 \(\frac{1}{9}\)
- 3 \(\frac{7}{9}\)
- 2 \(\frac{8}{9}\)
- 3 \(\frac{2}{9}\)
View Answers:
BRAVO…KEEP GOING.
EXPLANATION
When simplifying each of the mixed fractions, we get the following results. Since all their denominators are equal, the numerator’s value is what determines which mixed fraction has the lowest and highest value among the mixed fractions of the given set. the following set of fractions is arranged in the increasing order of their values after simplification.
2 \(\frac{1}{9}\) = \(\frac{18}{9}\)
2 \(\frac{8}{9}\) = \(\frac{29}{9}\)
3 \(\frac{2}{9}\) = \(\frac{29}{9}\)
3 \(\frac{7}{9}\) = \(\frac{34}{9}\)
Therefore, the order of the mixed fractions is as given below.
2 \(\frac{1}{9}\)
2 \(\frac{8}{9}\)
3 \(\frac{2}{9}\)
3 \(\frac{7}{9}\)
Therefore, the order of the mixed numbers in the increasing order of their values is as provided here.
THERE’S ALWAYS NEXT TIME!
EXPLANATION
When simplifying each of the mixed fractions, we get the following results. Since all their denominators are equal, the numerator’s value is what determines which mixed fraction has the lowest and highest value among the mixed fractions of the given set. the following set of fractions is arranged in the increasing order of their values after simplification.
2 \(\frac{1}{9}\) = \(\frac{18}{9}\)
2 \(\frac{8}{9}\) = \(\frac{29}{9}\)
3 \(\frac{2}{9}\) = \(\frac{29}{9}\)
3 \(\frac{7}{9}\) = \(\frac{34}{9}\)
Therefore, the order of the mixed fractions is as given below.
2 \(\frac{1}{9}\)
2 \(\frac{8}{9}\)
3 \(\frac{2}{9}\)
3 \(\frac{7}{9}\)
Therefore, the order of the mixed numbers in the increasing order of their values is as provided here.
- Question 7 of 10
7. Question
Which among the following mixed fractions are equal to the other set of fractions.
(Note: There can be more than one correct options)
IncorrectCorrectWELL DONE! YOU GOT IT RIGHT.
EXPLANATION
When the mixed fractions are simpolified we get the following values.
9 \(\frac{6}{9}\) =\(\frac{87}{9}\)
7 \(\frac{13}{4}\) = \(\frac{41}{4}\)
8 \(\frac{3}{8}\)= \(\frac{67}{8}\)
5 \(\frac{12}{9}\)= \(\frac{57}{9}\)
Out of these mixed fractions the answers of 9 \(\frac{6}{9}\) and 5 \(\frac{12}{9}\) are correct. The remaining answers are incorrect, therefore, these are the correct answers.
KEEP THINKING, AND KEEP TRYING!
EXPLANATION
When the mixed fractions are simpolified we get the following values.
9 \(\frac{6}{9}\) =\(\frac{87}{9}\)
7 \(\frac{13}{4}\) = \(\frac{41}{4}\)
8 \(\frac{3}{8}\)= \(\frac{67}{8}\)
5 \(\frac{12}{9}\)= \(\frac{57}{9}\)
Out of these mixed fractions the answers of 9 \(\frac{6}{9}\) and 5 \(\frac{12}{9}\) are correct. The remaining answers are incorrect, therefore, these are the correct answers.
Hint
First simplify each mixed number and verify if the answer you get matches the answers provided here.
- Question 8 of 10
8. Question
The product of a whole number and fraction is \(\frac{24}{5}\). What are the possible pairs of whole number and fractions out of the given sets of numbers?
(Note: There can be more than one correct options)
IncorrectCorrectIT’S AMAZING TO SEE HOW FAR YOU’VE COME! YOU ARE ABSOLUTELY RIGHT.
SOLUTION
3, \(\frac{8}{5}\) as well as 4, \(\frac{6}{5}\) are two of the opinion which provide the answer as \(\frac{24}{5}\). The other two options do not give the answer as \(\frac{24}{5}\).
UH-OH!
SOLUTION
3, \(\frac{8}{5}\) as well as 4, \(\frac{6}{5}\) are two of the opinion which provide the answer as \(\frac{24}{5}\). The other two options do not give the answer as \(\frac{24}{5}\).
- Question 9 of 10
9. Question
The product of 7 and \(\frac{2}{9}\) is-
IncorrectCorrectYOU’VE ALWAYS HAD IT IN YOU, KEEP UP THE GOOD WORK!
EXPLANATION
7 × \(\frac{2}{9}\) = \(\frac{14}{9}\)
YOU’RE ALMOST THERE.
EXPLANATION
7 × \(\frac{2}{9}\) = \(\frac{14}{9}\)
- Question 10 of 10
10. Question
The product of a 9 and \(\frac{9}{2}\) is-
IncorrectCorrectYOU’VE ALWAYS HAD IT IN YOU, KEEP UP THE GOOD WORK!
EXPLANATION
The product of 9 and \(\frac{9}{2}\) is \(\frac{81}{2}\).
YOU’RE ALMOST THERE.
EXPLANATION
The product of 9 and \(\frac{9}{2}\) is \(\frac{81}{2}\).
Level:
Hard
No. of Questions
10
Maximum Points
10