Transcript 2-1
2-1 Rational Numbers Preview Evaluating Algebraic Expressions Warm Up Lesson Presentation 2-1 Rational Numbers Warm Up Evaluating Algebraic Expressions Divide. 1. 36 3 3. 68 17 12 4 5. 1024 64 16 2. 144 6 4. 345 115 24 3 2-1 Rational Numbers Warm Up Evaluating Algebraic Expressions Patricia works twice as many days as Laura works each month. Laura works 3 more days than Jaime. If Jaime works 10 days each month, how many days does Patricia work? 2-1 Rational Numbers Evaluating Algebraic Expressions Vocabulary rational number terminating decimal repeating decimal 2-1 Rational Numbers Evaluating Algebraic Expressions A rational number is any number that can n be written as a fraction , where n d and d are integers and d 0. Any fraction can be written as a decimal by dividing the numerator by the denominator. If the division ends or terminates, because the remainder is zero, then the decimal is a terminating decimal. 2-1 Rational Numbers Evaluating Algebraic Expressions If the division leads to a repeating block of one or more digits (where all digits are not zeros) after the decimal point, then the decimal is a repeating decimal. A repeating decimal can be written with a bar over the digits that repeat. So 0.13333… = 0.13 (bar notation) 2-1 Rational Numbers Additional Example 1A: Writing Fractions as Decimals Evaluating Algebraic Expressions Write the fraction as a decimal. 11 9 1 .2 9 11 .0 –9 20 –1 8 2 The fraction The pattern repeats. This is a repeating decimal. 11 is equivalent to the decimal 1.2 9 2-1 Rational Numbers Additional Example 1B: Writing Fractions as Decimals Evaluating Algebraic Expressions Write the fraction as a decimal. 7 20 0.3 5 This is a terminating decimal. 20 7.0 0 –0 70 –6 0 1 00 –1 0 0 0 The remainder is 0. 7 The fraction is equivalent to the decimal 0.35 20 2-1 Rational Numbers Partner Share! Example 1A Write the fraction as a decimal. Check your Evaluating Algebraic Expressions answer with a calculator. 15 9 1 .6 9 15 .0 –9 60 –5 4 6 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 15 The fraction is equivalent to the decimal 1.6. 9 2-1 Rational Numbers Partner Share! Example 1B Write the fraction as a decimal. Check your Evaluating Algebraic Expressions answer with a calculator. 9 40 0.2 2 5 This is a terminating 40 9.0 0 0 decimal. –0 90 –8 0 1 00 – 80 200 – 2 00 0 The remainder is 0. 9 The fraction is equivalent to the decimal 0.225. 40 2-1 Rational Numbers Evaluating Algebraic Expressions 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. 2-1 Rational Numbers Additional Example 2: Writing Terminating Decimals as Fractions WriteEvaluating each decimal Algebraic as a fraction Expressions in simplest form. A. 5.37 37 7 is in the hundredths place, so 5.37 = 5 100 write hundredths as the denominator. B. 0.622 2 is in the thousandths place, so 622 0.622 = write thousandths as the 1000 denominator. 311 = 500 Simplify by dividing by the greatest common divisor. 2-1 Rational Numbers Evaluating Algebraic Expressions Remember! A fraction is in reduced, or simplest, form when the numerator and the denominator have no common divisor other than 1. 2-1 Rational Numbers Partner Share! Example 2 Write each decimal as a fraction in simplest form. Evaluating Algebraic Expressions A. 8.75 5 is in the hundredths place, 75 so write hundredths as the 8.75 = 8 100 denominator. 3 Simplify by dividing by the = 8 4 greatest common divisor. B. 0.2625 5 is in the 2625 0.2625 = 10,000 ten-thousandths place. Simplify by dividing by the 21 = greatest common divisor. 80 2-1 Rational Numbers Additional Example 3: Writing Repeating Decimals as Fractions _ Algebraic Expressions WriteEvaluating 0.4 as a fraction in simplest form. x = 0.44444… 10x = 10(0.44444…) 10x = 4.444444… -x = -0.44444… 9x = 4 9x = 4 9 9 4 x= 9 Let x represent the number. Multiply both sides by 10 because 1 digit repeats. Subtract x from both sides to eliminate the repeating part. Since x = 0.44444…, use 0.44444… for x on the right side of the equation. Since x is multiplied by 9, divide both sides by 9. 2-1 Rational Numbers __ Partner Share! Example 3 Write 0.36 as a fraction in simplest form. Evaluating Algebraic Expressions x = 0.363636… 100x = 100(0.363636…) 100x = 36.363636… -x = -0.363636… 99x = 36 99x = 36 99 99 x = 36 = 4 99 11 Let x represent the number. Multiply both sides by 100 because 2 digits repeat. Subtract x from both sides to eliminate the repeating part. Since x = 0.363636…, use 0.363636… for x on the right side of the equation. Since x is multiplied by 99, divide both sides by 99. Write in simplest form. 2-1 Rational Numbers Lesson Review! Write each decimal as a fraction in Evaluating Algebraic Expressions simplest form. 3 7 1. 0.35 2. 0.600 5 20 13 3. Write as a decimal. 2.16 6 4. 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