(7) Lesson 3.5 - Divide Integers
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This document contains a mathematics lesson on multiplying and dividing integers. It includes examples of multiplying and dividing integers with the same and different signs. The answers are provided for multiplying integers. Rules are stated that the quotient of integers with different signs is negative, while the quotient of integers with the same sign is positive. Step-by-step examples demonstrate dividing integers in various contexts. The document also contains standards and explanations of concepts covered in the lesson.
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This document provides examples for writing numbers using negative exponents. It begins with examples of writing expressions like 6-3 and 4-4 using positive exponents. It then provides step-by-step examples of writing fractions with negative exponents other than -1, like writing 5-2. Further examples show simplifying expressions using the properties of exponents, like 53 • 5-5 = 53 + (-5). In the examples, writing numbers with negative exponents allows writing very small or large numbers without fractions and makes multiplying or dividing numbers with the same base easier.
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1. This document provides examples and explanations for simplifying expressions using exponents. It discusses the laws for taking the power of a power and the power of a product.
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Here are the steps to write a number between 0 and 1 in scientific notation with an example:
1. Write the number in decimal form. For example, 0.000375.
2. Count the number of decimal places in the number. In this example there are 4 decimal places.
3. Move the decimal point to the left by that number of places. This gives 3.75.
4. Write the number as a coefficient and exponent of 10. Since we moved the decimal point 4 places to the left, the exponent is -4.
So, 0.000375 written in scientific notation is 3.75 × 10-4.
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1) The document provides examples of writing expressions using exponents and evaluating those expressions. It gives the expressions 2c8, 85, and m5n3p3 as examples and evaluates the expressions 512, 216, and m5n3p3.
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1. This document provides examples and explanations for simplifying expressions using exponents. It discusses the laws for taking the power of a power and the power of a product.
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Here are the steps to write a number between 0 and 1 in scientific notation with an example:
1. Write the number in decimal form. For example, 0.000375.
2. Count the number of decimal places in the number. In this example there are 4 decimal places.
3. Move the decimal point to the left by that number of places. This gives 3.75.
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(7) Lesson 3.5 - Divide Integers
- 1. Course 2, Lesson 3-5 Multiply. 1. 21(−5) 2. −7(−4) 3. (−9)2 4. (−5)(−2)(−3) 5. (−3)(−2)(7) 6. What is −3(8g) simplified?
- 2. Course 2, Lesson 3-5 ANSWERS 1. −105 2. 28 3. 81 4. −30 5. 42 6. –24g
- 3. WHAT happens when you add, subtract, multiply, and divide integers? The Number System Course 2, Lesson 3-5
- 4. Course 2, Lesson 3-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. The Number System • 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. • 7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real- world contexts. • 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
- 5. The Number System • 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 5 Use appropriate tools strategically. 7 Look for and make use of structure. Course 2, Lesson 3-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
- 6. • To divide integers with different signs • To divide integers with the same sign Course 2, Lesson 3-5 The Number System
- 7. Course 2, Lesson 3-5 The Number System Words The quotient of two integers with different signs is negative. Examples 33 ÷ (–11) = –3 –64 ÷ 8 = –8
- 8. 1 Need Another Example? Step-by-Step Example 1. Find 80 ÷ (–10). The integers have different signs. 80 ÷ (–10) = –8 The quotient is negative.
- 9. Answer Need Another Example? Find 51 ÷ (–3). –17
- 10. 1 Need Another Example? Step-by-Step Example 2. Find . The integers have different signs. = –5 The quotient is negative.
- 12. Need Another Example? Step-by-Step Example 3. Use the table to find the constant rate of change in centimeters per hour. 1 2 3 The height of the candle decreases by 2 centimeters each hour. So, the constant rate of change is –2 centimeters per hour.
- 13. Answer Need Another Example? Use the table to find the constant rate of change in inches per month. 1 in. per month
- 14. Course 2, Lesson 3-5 The Number System Words The quotient of two integers with the same sign is positive. Examples 15 ÷ 5 = 3 –64 ÷ (–8) = 8
- 15. 1 Need Another Example? Step-by-Step Example 4. Find –14 ÷ (–7). –14 ÷ (–7) = 2 The integers have the same sign. The quotient is positive.
- 16. Answer Need Another Example? Find –12 ÷ (–2). 6
- 17. 1 Need Another Example? Step-by-Step Example 5. Find . = 9 The integers have the same sign. The quotient is positive.
- 19. 1 Need Another Example? Step-by-Step Example 6. Evaluate –16 ÷ x if x = –4. –16 ÷ x = –16 ÷ (–4) Replace x with –4. 2 = 4 Divide. The quotient is positive.
- 20. Answer Need Another Example? Evaluate –18 ÷ x if x = –2. 9
- 21. 1 Need Another Example? 2 3 Step-by-Step Example 7. One year, the estimated Australian koala population was 1,000,000. After 10 years, there were about 100,000 koalas. Find the Average change in the koala population per year. Then explain its meaning. N is the new population, 100,000. P is the previous population, 1,000,000. = or –90,000 Divide. The koala population has changed by –90,000 per year.
- 22. Answer Need Another Example? An October newspaper headline read that the total value of stocks held by Japanese financial institutions dropped from $987 billion to $900 billion in 6 weeks. What was the average change in value per week? –$14.5 billion
- 23. How did what you learned today help you answer the WHAT happens when you add, subtract, multiply, and divide integers? Course 2, Lesson 3-5 The Number System
- 24. How did what you learned today help you answer the WHAT happens when you add, subtract, multiply, and divide integers? Course 2, Lesson 3-5 The Number System Sample answers: • The quotient of two integers with different signs is negative. • The quotient of two integers with the same sign is positive.
- 25. Find . Ratios and Proportional RelationshipsThe Number System -14 2 Course 2, Lesson 3-5