Exit to T O C MAT 086 Prealgebra
Exit to T O C MAT 086 Prealgebra Class 8 Unit A © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Preview Class 8 Unit A When you finish this unit, you will be able to: • Add and subtract fractions with the same denominator • Add and subtract signed numbers with the same denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Preview Class 8 Unit A When you finish this unit, you will be able to: • Add and subtract rational expressions with the same denominator • Add and subtract fractions with different denominators © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A how ? . 25’s = 100 many © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator 10¢ + 10 ¢ = 20 ¢ © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator Whole 6 slices 2 + + 3 = 5 = © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator Whole 5 pieces 3 + = 1 + = © Pima Community College 2000 4
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator D pieces add numerators keep deno min ator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator 5 total + = © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator 7 total + = © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator how ? . 25’s = 100 many © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator 7 pieces - © Pima Community College 2000 =
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator le p m a An ex Jack gas gauge reads 7/8 of a tank at the beginning of the day. At 5 PM the gauge reads 1/8 full. . How much of a tank-full of gas he used that day? If he gets 240 miles on a full tank, , how far has he tank driven? © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator Given: 7/8 full - start 1/8 full - end 240 miles - full tank Full 240 mi Asked: how much of a tank-full? how far has he driven? © Pima Community College 2000 7 8 1 8
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator Asking for the difference between beginning and the end of the day. Subtract tank used Gas used is ¾ of 240 mi - © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator Check: Is 180 gal ¾ of 240 gal? OK © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Same Denominator Rule: subtract numerators keep deno min ator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A how ? . 25’s = 100 many © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Signed Numbers Class 8 Unit A A flash from the past © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Signed Numbers © Pima Community College 2000 Class 8 Unit A
Exit to T O C MAT 086 Prealgebra Signed Numbers Class 8 Unit A All operations of integer math apply! © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Signed Numbers © Pima Community College 2000 Class 8 Unit A
Exit to T O C MAT 086 Prealgebra Signed Numbers © Pima Community College 2000 Class 8 Unit A
Exit to T O C MAT 086 Prealgebra Signed Numbers © Pima Community College 2000 Class 8 Unit A
Exit to T O C MAT 086 Prealgebra Class 8 Unit A 4 x 2 – x + 1 x– 3 4 4 4 x 2 – x + 1 – x + 3 4 6 x 2 - 1 x + 9 = 4 © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Rational Expressions/Same Denominator Rational Number: Number expressed as a ratio of integers Like Terms: having the same variables, raised to the same powers. 5 x 2 + 2 x 2 = 7 x 2 … 5 x 3 + 2 x 2 = ? © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Rational Expressions/Same Denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Rational Expressions/Same Denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Rational Expressions/Same Denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Rational Expressions/Same Denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A . 05 +. 10 =. 15 = 15 3 100 = 20 © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator + quarter dollar = half dollar + © Pima Community College 2000 =
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator + quarter dollar = half dollar + © Pima Community College 2000 =
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator + one quarter dollar = two quarter dollars + © Pima Community College 2000 =
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator + = © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator • Upscale fractions without changing value so that they all have the same denominator. • Do the math © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator At the end of the day, Chuck’s Diner has 2 pieces of an apple pie cut into 6 slices and one piece of an equal sized blueberry pie cut into 4 slices left over. How much pie remains? © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator Given: 2 pieces of 6 slices 1 piece of 4 slices Slices are different sizes for each pie Asked: How much pie remains? © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator 2 pieces of 6 slices 1 piece of 4 slices + Need to represent 6 th and 4 th as same denominator. © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator + Need to represent 6 ths and 4 ths with same (common) denominator. 12 pieces © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator 12 pieces + + = + © Pima Community College 2000 = =
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator Finding a common denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator The easiest way… 6 8 8 8 6 6 To get a common denominator: Multiply numerator and denominator of each term by the denominator of the other(s). © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator The easiest way… 6 8 8 8 © Pima Community College 2000 6 6
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator Example: © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator Example: © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Class 8 Unit A Fractions/Different Denominator Example: © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Review Class 8 Unit A We have seen how to: • Add fractions with the same denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Review Class 8 Unit A We have seen how to: • Add subtract with the same denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Review Class 8 Unit A We have seen how to: • Add fractions with the same denominator using signed numbers. © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Review Class 8 Unit A We have seen how to: • Add rational expressions with the same denominator © Pima Community College 2000
Exit to T O C MAT 086 Prealgebra Review Class 8 Unit A We have seen how to: • Add fractions with different denominators © Pima Community College 2000
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