Written Instructions:
For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
| 1) Anand has two pieces of yarn, one 12 feet long and the other 9 feet long. For a craft project, he wants to cut them up to produce many pieces of yarn that are all of the same length, with no yarn left over. What is the greatest length, in feet, that he can make them feets Answer:_______________ |
| 2) At a party, the cheese pizza is cut into 15 slices and the veggie pizza is cut into 5 slices. If the host wants to serve identical platters that contain the same combination of cheese and veggie slices, with no slices left over, what is the greatest number of platters the host can prepare platters Answer:_______________ |
| 3) Stanley is thinking of a number that is divisible by both 7 and 10. What is the smallest possible number that Stanley could be thinking of {short;ans} Answer:_______________ |
| 4) Savithri has pieces of construction paper that are 12 centimetres long and 5 centimetres wide. For an art project, she wants to create the smallest possible square, without cutting or overlapping any of the paper. How long will each side of the square be centimetre Answer:_______________ |
| 5) Mrs. Kalai, the maths teacher, has 10 logic puzzles and 18 visual puzzles that she wants to group into sets for students who finish their tests early. Mrs. Kalai wants each set to be identical, containing the same combination of logic puzzles and visual puzzles, with no puzzles left over. What is the greatest number of sets she can create sets Answer:_______________ |
| 6) Haritha has 15 commemorative plates and 10 commemorative spoons. She wants to display them in groups throughout her house, each with the same combination of plates and spoons, with none left over. What is the greatest number of groups Haritha can display groups Answer:_______________ |
| 7) Kumar and his friends made dinner reservations at two local restaurants on two different days. While the first restaurant sat all the friends in groups of 7, the second restaurant sat all the friends in groups of 6. What is the smallest number of people that could be in the group groups Answer:_______________ |
| 8) Prem has two pieces of twine, one 18 feet long and the other 9 feet long. If he wants to cut them up to produce many pieces of twine that are all of the same length, with no twine left over, what is the greatest length, in feet, that he can make them feets Answer:_______________ |
| 9) With flu season coming up, Charmaine decides to make get-well-soon kits. She has 9 cans of chicken soup and 15 boxes of tissue, which she wants to use to make identical kits with no materials left over. What is the greatest number of get-well-soon kits Charmaine can make kits Answer:_______________ |
| 10) At a local bakery, Young Jae decorated 8 cakes at a time. Marta decorated 7 at a time. If they ended up decorating the same number of cakes by the end of the day, what is the smallest number of cakes that each must have decorated cakes Answer:_______________ |
| 1) Anand has two pieces of yarn, one 12 feet long and the other 9 feet long. For a craft project, he wants to cut them up to produce many pieces of yarn that are all of the same length, with no yarn left over. What is the greatest length, in feet, that he can make them Answer: 3 feets SOLUTION 1 : Remember: The greatest common factor is the greatest whole number that is a factor of each of two or more numbers. Solve: Write the prime factorisation for each number. 12 = 2 × 2 × 3 9 = 3 × 3 Next, find the common factors shared by both of the numbers. 12 = 2 × 2 × 3 9 = 3 × 3 The only common factor of 12 and 9 is 3, so the greatest common factor is 3. That means that the longest possible length is 3 feet, because 12 feet of yarn could be cut into 4 pieces that are 3 feet long and 9 feet of yarn could be cut into 3 pieces that are 3 feet long. The greatest length the cloth can be cut to is 3 feet. |
| 2) At a party, the cheese pizza is cut into 15 slices and the veggie pizza is cut into 5 slices. If the host wants to serve identical platters that contain the same combination of cheese and veggie slices, with no slices left over, what is the greatest number of platters the host can prepare Answer: 5 platters SOLUTION 1 : Remember: The greatest common factor is the greatest whole number that is a factor of each of two or more numbers. Solve: Write the prime factorisation for each number. 5 is a prime number. You do not need to factorise 5. 15 = 3 × 5 5 Next, find the common factors shared by both of the numbers. 15 = 3 × 5 5 = 5 The only common factor of 15 and 5 is 5, so the greatest common factor is 5. That means that the greatest possible number of platters is 5, because 15 slices of cheese pizza could be put onto 5 platters with 3 slices of cheese pizza each and 5 slices of veggie pizza could be put onto 5 platters with 1 slice of veggie pizza each. The greatest number of platters the host can prepare is 5. |
| 3) Stanley is thinking of a number that is divisible by both 7 and 10. What is the smallest possible number that Stanley could be thinking of {short;ans} SOLUTION 1 : Remember: The least common multiple is the least whole number that is a multiple of each of two or more numbers. Solve: You need to find the smallest number that is a multiple of both 7 and 10. This is the least common multiple. Write the prime factorisation for each number. 7 is a prime number. You do not need to factorise 7. 7 Repeat each prime factor the greatest number of times it appears in any of the prime factorisations above. 2 × 5 × 7 = 70 The least common multiple of 7 and 10 is 70. That means that the smallest possible number is 70, because 10 times 7 is 70 and 7 times 10 is 70. The smallest possible number that Stanley could be thinking of is 70. |
| 4) Savithri has pieces of construction paper that are 12 centimetres long and 5 centimetres wide. For an art project, she wants to create the smallest possible square, without cutting or overlapping any of the paper. How long will each side of the square be Answer: 60 centimetre SOLUTION 1 : Remember: The least common multiple is the least whole number that is a multiple of each of two or more numbers. Solve: You need to find the smallest number that is a multiple of both 12 and 5. This is the least common multiple. Write the prime factorisation for each number. 5 is a prime number. You do not need to factorise 5. 12 = 2 × 2 × 3 Repeat each prime factor the greatest number of times it appears in any of the prime factorisations above. 2 × 2 × 3 × 5 = 60 The least common multiple of 12 and 5 is 60. That means that the smallest possible square has 60-centimetre sides. The length could be made of 5 pieces that are 12 centimetres tall and the width could be made of 12 pieces that are 5 centimetres wide. Each side of the square will be 60 centimetres long. |
| 5) Mrs. Kalai, the maths teacher, has 10 logic puzzles and 18 visual puzzles that she wants to group into sets for students who finish their tests early. Mrs. Kalai wants each set to be identical, containing the same combination of logic puzzles and visual puzzles, with no puzzles left over. What is the greatest number of sets she can create Answer: 2 sets SOLUTION 1 : Remember: The greatest common factor is the greatest whole number that is a factor of each of two or more numbers. Solve: Write the prime factorisation for each number. 10 = 2 × 5 18 = 2 × 3 × 3
10 = 2 × 5 18 = 2 × 3 × 3
The greatest number of sets Mrs. Kalai can create is 2. |
| 6) Haritha has 15 commemorative plates and 10 commemorative spoons. She wants to display them in groups throughout her house, each with the same combination of plates and spoons, with none left over. What is the greatest number of groups Haritha can display Answer: 5 groups SOLUTION 1 : Remember: The greatest common factor is the greatest whole number that is a factor of each of two or more numbers. Solve: Write the prime factorisation for each number. 15 = 3 × 5 10 = 2 × 5
15 = 3 × 5 10 = 2 × 5
The greatest number of groups Haritha can display is 5. |
| 7) Kumar and his friends made dinner reservations at two local restaurants on two different days. While the first restaurant sat all the friends in groups of 7, the second restaurant sat all the friends in groups of 6. What is the smallest number of people that could be in the group Answer: 42 groups SOLUTION 1 : Remember: The least common multiple is the least whole number that is a multiple of each of two or more numbers. Solve: You need to find the smallest number that is a multiple of both 7 and 6. This is the least common multiple. Write the prime factorisation for each number. 7 is a prime number. You do not need to factorise 7. 7 Repeat each prime factor the greatest number of times it appears in any of the prime factorisations above. 2 × 3 × 7 = 42 The least common multiple of 7 and 6 is 42. That means that the smallest possible number of people in the group is 42, because 6 tables of 7 friends is 42 people in total and 7 tables of 6 friends is 42 people in total. The smallest number of people that could be in the group is 42. |
| 8) Prem has two pieces of twine, one 18 feet long and the other 9 feet long. If he wants to cut them up to produce many pieces of twine that are all of the same length, with no twine left over, what is the greatest length, in feet, that he can make them Answer: 9 feets SOLUTION 1 : Remember: The greatest common factor is the greatest whole number that is a factor of each of two or more numbers. Solve: Write the prime factorisation for each number. 18 = 2 × 3 × 3 9 = 3 × 3 Next, find the common factors shared by both of the numbers. 18 = 2 × 3 × 3 9 = 3 × 3 Finally, multiply the common factors to find the greatest common factor. 3 × 3 = 9 The greatest common factor of 18 and 9 is 9. That means that the longest possible piece of cut twine is 9 feet long, because the 18-foot piece of twine could be cut into 2 pieces that are 9 feet long and the 9-foot piece of twine could remain 9 feet long. The greatest length the twine can be cut to is 9 feet. |
| 9) With flu season coming up, Charmaine decides to make get-well-soon kits. She has 9 cans of chicken soup and 15 boxes of tissue, which she wants to use to make identical kits with no materials left over. What is the greatest number of get-well-soon kits Charmaine can make Answer: 3 kits SOLUTION 1 : Remember: The greatest common factor is the greatest whole number that is a factor of each of two or more numbers. Solve; Write the prime factorisation for each number. 9 = 3 × 3 15 = 3 × 5 Next, find the common factors shared by both of the numbers. 9 = 3 × 3 15 = 3 × 5 The only common factor of 9 and 15 is 3, so the greatest common factor is 3. That means that the greatest possible number of kits is 3, because 9 cans of chicken soup could be put into 3 kits with 3 cans of soup each and 15 boxes of tissue could be put into 3 kits with 5 boxes of tissue each. The greatest number of kits Charmaine can make is 3. |
| 10) At a local bakery, Young Jae decorated 8 cakes at a time. Marta decorated 7 at a time. If they ended up decorating the same number of cakes by the end of the day, what is the smallest number of cakes that each must have decorated Answer: 56 cakes SOLUTION 1 : Remember: The least common multiple is the least whole number that is a multiple of each of two or more numbers. Solve: You need to find the smallest number that is a multiple of both 8 and 7. This is the least common multiple. Write the prime factorisation for each number. 7 is a prime number. You do not need to factorise 7. 8 = 2 × 2 × 2 Repeat each prime factor the greatest number of times it appears in any of the prime factorisations above. 2 × 2 × 2 × 7 = 56 The least common multiple of 8 and 7 is 56. That means that the smallest number of cakes that each must have decorated is 56, because 7 groups of 8 cakes decorated by Young Jae is 56 cakes in total and 8 groups 7 cakes decorated by Marta is 56 cakes in total. The smallest number of cakes that each must have decorated is 56. |