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Evaluate each of the following questions without using a calculator.

Explore various mathematical problem scenarios involving fractions, arithmetic operations, and logical thinking without using a calculator. Understand concepts such as LCM, fractions, total amounts, and initial amounts through practical examples.

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Evaluate each of the following questions without using a calculator.

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  1. 1. Evaluate each of the following questions without using a calculator. (ii) (i) LCM = 21 LCM = 9

  2. 1. Evaluate each of the following questions without using a calculator. (iv) (iii) LCM = 20

  3. 1. Evaluate each of the following questions without using a calculator. (vi) (v) LCM = 14

  4. 1. Evaluate each of the following questions without using a calculator. (viii) (vii)

  5. 1. Evaluate each of the following questions without using a calculator. (x) (ix) LCM = 21

  6. 1. Evaluate each of the following questions without using a calculator. (xi)

  7. Evaluate each of the following questions without using a calculator. 1. (xii) LCM = 18

  8. 2. There are 96 children in a library. of them are girls. How many of the children are boys? Method 1: of the 96 children are girls. To find the number of girls: To find the number of boys: 96 – 60 = 36 boys

  9. 2. There are 96 children in a library. of them are girls. How many of the children are boys? Method 2: If of the children are girls then of the children are boys. To find the number of boys:

  10. 3. David had €40. He spent of the money on a book and on a calculator. How much did he spend altogether? Money spent on the book: Money spent on the calculator: Total spent: 8 + 12 = €20

  11. 4. Scott had some eggs. He sold of them. If he sold 300 eggs, how many eggs did he have to begin with? To find : 300 ÷5 = 60 To find : 60 × 8 = 480 Total,

  12. 5. On a certain day, of the students in a school walked to school, of the students came to school by bus and the remaining 68 students came by car. (i) What fraction of the students came by car? We must first find the fraction of students that didn’t come by car. This is the fraction that walked and came by bus. LCM = 10 Wenowfind the fraction that came by car. came by car.

  13. 5. On a certain day, of the students in a school walked to school, of the students came to school by bus and the remaining 68 students came by car. (ii) How many students came to school by bus? of the students came by car and the number who came by car is 68. To find the total numbers of students : The total numbers of students 680.

  14. 5. On a certain day, of the students in a school walked to school, of the students came to school by bus and the remaining 68 students came by car. (ii) How many students came to school by bus? of the students came by bus. To find the number of students who came by bus: = 272 came by bus.

  15. 6. Alex, Betty, and Chris are trading marbles. First, Alex gives Betty of his marbles. Then Betty gives Chris of her marbles. Finally, Chris gives Alex two marbles. If everyone ends up with 12 marbles, how many marbles did each person start with? Alex 12 – 2 = 10 [Got 2 from Chris] Alex’s marbles [Gave to Betty] Alex originally had 20 marbles.

  16. 6. Alex, Betty, and Chris are trading marbles. First, Alex gives Betty of his marbles. Then Betty gives Chris of her marbles. Finally, Chris gives Alex two marbles. If everyone ends up with 12 marbles, how many marbles did each person start with? Betty To find the total : 6 3 Gave of her marbles to Chris. Got of Alex’smarbles (10) . To find : 12 ÷ 2 18 – 10 = 8 Betty originally had 8 marbles.

  17. 6. Alex, Betty, and Chris are trading marbles. First, Alex gives Betty of his marbles. Then Betty gives Chris of her marbles. Finally, Chris gives Alex two marbles. If everyone ends up with 12 marbles, how many marbles did each person start with? Chris Betty gave of 18 marbles to Chris = 6 Chris gave 2 to Alex: 6 – 2 = 4 4 + = 12 4 + 8 = 12 Chris originally had 8 marbles.

  18. 7. Emma started with a certain amount of money. She spent of her money. She earned €5 the next day. Later, she lost of her money, but she still had €20 left. How much did she start with? She lost of her money, so she has left. To find : 20 ÷ 4 = 5 To find : 5 × 7

  19. 7. Emma started with a certain amount of money. She spent of her money. She earned €5 the next day. Later, she lost of her money, but she still had €20 left. How much did she start with? The previous day she had earned €5 so we need to subtract this from €35. 35 − 5 = 30 She had spent of her money so she had left. To find : 30 ÷ 3

  20. 7. Emma started with a certain amount of money. She spent of her money. She earned €5 the next day. Later, she lost of her money, but she still had €20 left. How much did she start with? To find : 10 × 5 Shestarted with €50.

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