2 Problem of the DayAn 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
3 TB PLearn to write rational numbers in equivalent forms.
5 and d are integers and d 0. A rational number is any number that can be written as a fraction , where nand d are integers and d 0.nd
6 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.
7 The same total area is shaded. You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3.12154512 of the 15 boxes are shaded.4 of the 5 boxes are shaded.=121545The same total area is shaded.
8 Additional Example 1A: Simplifying Fractions 16 8016 = 1 • = 5 • 16;16 is a common factor.=16 ÷ 1680 ÷ 16Divide the numerator and denominator by 16.16801 5== 0 for a ≠ = 1 for a ≠ 0= = –Remember!0aaa–7 87 –87 8
9 Additional Example 1B: Simplifying Fractions –182918 = 2 • 929 = 1 • 29;There are no common factors.–1829=–1829–18 and 29 are relatively prime.
10 Decimals that terminate or repeat are rational numbers. To write a terminating decimal as a fraction, identify the place value of the digit farthest to the right. Then write all of the digits after the decimal point as the numerator with the place value as the denominator.
11 Rational NumberDescriptionWritten as a Fraction–3.2Terminating decimal0.16Repeating decimal–32___101__6
12 Additional Example 2: Writing Decimals as Fractions Write each decimal as a fraction in simplest form.A. 5.3737 100= 55.377 is in the hundredths place.B=2 is in the thousandths place.0.622Simplify by dividing by the common factor 2.=
13 numerator denominator denominator numerator To write a fraction as a decimal, divide the numerator by the denominator. You can use long division.numeratordenominatordenominatornumerator
14 Additional Example 3A: Writing Fractions as Decimals Write the fraction as a decimal.11 91.29 11.0The pattern repeats.–92–18A repeating decimal can be written with a bar over the digits that repeat. So … = 1.2.Writing Math_2The fraction is equivalent to the decimal 1.2.11 9
15 Additional Example 3B: Writing Fractions as Decimals Write the fraction as a decimal.7 20.35This is a terminating decimal.20 7.0–07–6 01 0–1 0The remainder is 0.The fraction is equivalent to the decimal 0.35.7 20
16 1. 2. – 3. 0.27 4. –0.625 5. Write as a decimal Simplify. 18 42 3 7 Lesson Quiz: Part 1Simplify.18 423 715 215 71.2.Write each decimal as a fraction in simplest form.27 100–5 84. –0.62513 65. Write as a decimal2.16
17 Lesson Quiz: Part 26.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