2. The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns. These are called the natural numbers, or sometimes the counting numbers. Introduction
3. Natural Numbers NATURAL NUMBERS 1, 2, 3, 4, 5, . . . The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever.
4. At some point, the idea of “zero” came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers. WHOLE NUMBERS Natural Numbers together with “zero” 0, 1, 2, 3, 4, 5, . . . Whole Numbers
5. Hopefully you remember these from grade 8! INTEGERS Whole numbers plus negatives . . . –4, –3, –2, –1, 0, 1, 2, 3, 4, . . . Number lines are useful for representing integers Integers
6. n Numerator d Denominator Rational Numbers A rational numberis any number that can be written as a fraction, d≠0. Decimals that terminate or repeat are rational numbers. Terminate means come to an end
8. Work With a Partner Turn to the person next to you and work together to find a solution An ice cream parlor has 6 flavors of ice cream. A dish with two scoops can have any two flavors, including the same flavor twice. How many different double-scoop combinations are possible? 21
9. The Goal for all Rational Numbers is… The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1. The goal is to have the fraction in its smallest possible form!
16. Write the decimal as a fraction in simplest form. 2 GCF = ? –0.8 Tenths
17. Write the decimal as a fraction in simplest form. 1 GCF = ? 5.37 5 and 37 are relatively prime!! Hundredths
18. Write the decimal as a fraction in simplest form. 0.622 2 GCF = ? Thousandeths
19. Write the decimal as a fraction in simplest form. 8.75 25 GCF = ? Hundredths
20. Write the fraction as a decimal. 11 9 = 1.2 1.222222…, a repeating decimal
21. Write the fraction as a decimal. 7 20 = 0.35 0.35, a terminating decimal
22. Write the fraction as a decimal. 15 11 = 1.36 1.363636…, a repeating decimal
23. 3 7 5 7 5 8 27 100 – Practice Simplify. 15 21 18 42 2. 1. Write each decimal as a fraction in simplest form. 4. –0.625 3. 0.27 5. Write as a decimal 13 6 2.16
24. What Does it All Mean? Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.) 0.325
25. Homework Part 1 (More Practice) Convert the following decimals into fractions 0.3 0.2 0.01 5.22 -3.25 0.34 -1 -4.24 44.4 12.964
26. Convert the fractions into decimals (don’t forget to indicate when a decimal is repeating) 34 58 214 −312 −263 35 -323 −64 67 −1315 Homework Part 2(more practice)
