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BITS AND PIECES III

Explore whether the product of 1.25 and 0.5 should be greater or less than 1. Understand how the product of 125 and 5 relates to the product of 1.25 and 0.5. Solve multiplication problems involving decimals and whole numbers.

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BITS AND PIECES III

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  1. BITS AND PIECES III • Investigation 2.2 Missing Factors

  2. Should the product of 1.25 and 0.5 be greater or less than 1? Why?

  3. Should the product of 1.25 and 0.5 be greater or less than 1? Why? The product should be less than 1 because the product of 2 and 0.5 would be exactly 1 and 1.25 is less than 2.

  4. Should the product of 1.25 and 0.5 be greater or less than 1/2? Why?

  5. Should the product of 1.25 and 0.5 be greater or less than 1/2? Why? Greater because 1.25 is greater than 1 and the product of 1 and 0.5 would be exactly 1/2.

  6. How does the product of 125 and 5 relate to the product of 1.25 and 0.5?

  7. How does the product of 125 and 5 relate to the product of 1.25 and 0.5? The product of 125 and 5 is greater than the product of 1.25 and 0.5, but it has the same digits. Whether you are multiplying whole numbers or decimals, you start by multiplying 125 by 5.

  8. A. Use what you know about fraction multiplication and place value. 1. What number times 6 gives the product 0.36?

  9. 1. What number times 6 gives the product 0.36? This is the same as saying N x 6 = 0.36

  10. 1. What number times 6 gives the product 0.36? What whole number problem will help us think about this?

  11. 1. What number times 6 gives the product 0.36? The whole number problem is 6 x 6 = 36.

  12. 1. What number times 6 gives the product 0.36? N x 6 = 0.36 Is the value of N greater or less than 1?

  13. Is the value of N greater or less than 1? N x 6 = 0.36 • Its less than because one of the factors (6) is greater than 1 and the product is less than 1. • What is the answer to the problem?

  14. N x 6 = 0.36 N = 0.06 because there is two place values in 0.36 and zero in 6.

  15. What number times 0.9 gives the product 2.7? What would the whole number problem be?

  16. What would the whole number problem be? The whole number problem would be 9 x 3 = 27. What is the answer to 0.9 x N = 27?

  17. What is the answer to 0.9 x N = 27? The answer is 30 because there is one place value in 0.9 and there is no place values in 27. In order to multiply 0.9 by a factor to get 27 we must put a zero on the end of 3 to make 30. Remember: Zeroes at the end of a factor such as 30 moves the decimal point to the right in the product, decimals in the factors move the decimal point to the left in the product. If there is a decimal as one factor (0.9) and a zero on the end of another factor (30)than the product must be a whole number (27).

  18. Let’s look at the number 1,560. Give me a number that is a factor of 1,560. Hint: Use factor trees or rainbow method.

  19. Let’s look at the number 1,560. Give me a number that is a factor of 1,560. Hint: Use factor trees or rainbow method. Some possibilities: 156, 10, 2, 5, 20.

  20. Some factors of 1,560 are 156, 10, 2, 5, 20. Now that you have some factors give me two numbers whose product is 1,560.

  21. Now that you have some factors give me two numbers whose product is 1,560. Since we know some factors now we can divide them by 1560. For example 156 x 10, 78 x 20, 39 x 40, and 13 x 20.

  22. Let’s look at the number 1,344. Give me some numbers that are a factor of 1,344. Hint: Use factor trees or rainbow method.

  23. Let’s look at the number 1,344. Give me a number that is a factor of 1,344. Hint: Use factor trees or rainbow method. Some possibilities: 4, 24, 32, 42, 56, 336.

  24. Some factors of 1,344 are 4, 24, 32, 42, 56, 336. Now that you have some factors give me two numbers whose product is 1,344.

  25. Let’s look at the number 134.4. Give me some numbers that are factors of 134.4.

  26. Since the factors of 1,344 are 42, 32, 24, 56, 4, and 366, than the factors of 134.4 must be 4.2, 3.2, 2.4, 5.6, 0.4, and 36.6. Now that you know factors what are two numbers that can be multiplied together to get 134.4?

  27. What are two numbers that can be multiplied together to get 134.4 when you have the factors 0.4, 4.2, 32, 5.6, 24 etc. Since 4 x 336 = 1,344, than 0.4 x 336 = 134.4 and since 24 x 56 = 1,344, than 24 x 5.6 or 2.4 x 56 = 134.4. Remember: Since there is a decimal in the product there must be at least one decimal in one of the factors.

  28. ARE THERE ANY QUESTIONS? Work on problems (7-16) on page 28 for homework.

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