Multiplying and dividing rational numbers Student Activity Sheet 1; use with Exploring Multiplying rational numbers
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1 1. What is Tyler s yearly growth if he grows inch each month? Multiply. 2. REINFORCE Tyler tracked his changes in weight, as well as his height. This table shows how many pounds Tyler gained from year to year. Tyler s age Weight increase (in pounds) 9 years old 10 years old 11 years old 12 years old 13 years old 14 years old List the changes in weight in order from least to greatest. 3. REINFORCE Find the product and record your answer in simplest form. Use a mixed number when needed. a. = b. = c. 7 = d. = Page 1 of 17
2 4. What is the product of? 5. Fill in the blanks to summarize the process of finding this product: In the example above, the product of the whole number multiplied by the fraction is a. The numerator of the answer is the of the whole number times the the of the original fraction. of the fraction. The denominator of the answer is 6. Complete each sentence. Think about the patterns in the sentences. of 4 is of 2 is of 2 is of 2 is Page 2 of 17
3 7. REINFORCE To keep the grass alive during the hot summer months, Justin programs his water sprinkler so that his lawn receives ¾-inch of water per week. Assuming there is no rain, how many inches of water will Justin s lawn receive in six weeks? a. Show how to solve this problem using a model. b. Show how to solve this problem numerically (using computation). Page 3 of 17
4 8. REINFORCE Find the product and record your answer in simplest form. Use a mixed number when needed. a. = b. = c. = d. = 9. Draw an area model of. Page 4 of 17
5 10. Identify the correct fraction problem and product for the given area model. Problem Area model Product 11. REINFORCE Find the product and record your answer in simplest form. a. = b. = c. = d. = Page 5 of 17
6 12. Draw the area model for. Then show the partial products of the result. Page 6 of 17
7 13. Complete the puzzle by filling in a reason for each step. Simplify common factors. Rewrite product as a whole number or a mixed number. Rewrite each factor as an improper fraction. Multiply numerators and denominators. Page 7 of 17
8 14. Calculate the area of a rectangular portion of the upstairs hallway that measures. Page 8 of 17
9 15. Consider different products of the number six. Investigate the table below to decide when the product is less than six, equal to six, or greater than six Order the products from your table from least to greatest by placing them on the number line. 17. What are some general statements can you make about the products that result when you multiply a number by a fraction? Page 9 of 17
10 18. REINFORCE Answer each question below and explain your reasoning. a. Is 1 greater than or less than 1? b. Is greater than or less than? c. Is greater than or less than? d. Is greater than or less than? Page 10 of 17
11 19. REINFORCE For each situation below, write a number sentence and show the resulting product. a. The product of and a number so that the product is greater than. b. The product of 3 and a number so that that product is less than 1. c. The product of and a number so that the product is a whole number greater than 5. d. The product of and a number so that the product is less than. Page 11 of 17
12 20. Explain how to multiply two decimals using a grid. Page 12 of 17
13 21. Complete the table. Then summarize the patterns for multiplying rational numbers. Problem Answer Page 13 of 17
14 22. How are the answers to these three problems similar? How are they different? Why are they different? What is an example of a multiplication problem that would have an answer of ? Why does your answer make sense? Page 14 of 17
15 For questions 24-28, use appropriate tool(s) to determine each product. Then write a question that would be answered by performing the indicated multiplication. 24. REINFORCE 25. REINFORCE Page 15 of 17
16 26. REINFORCE 27. REINFORCE Page 16 of 17
17 28. REINFORCE Page 17 of 17
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