Mastering Ratios and Proportions for Math Success
Dive into the world of ratio and proportion with this comprehensive guide. Learn the basics, solve real-world scenarios, and master the skills needed for success in math. Perfect for students seeking clarity on this fundamental mathematical concept.
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Presentation Transcript
Unit 3: Ratio and Proportion
Ratios - Review Recall: a ratio is a comparison of two or more quantities Ratios, like fractions, should always be reduced to lowest terms Ratios can be written in three different ways: 1 to 2 1:2
Ratios Review A class of apprentices consists of 12 women and 36 men. What is the ratio of women to men? 12:36 = 1:3 What is the ratio of women to the class total? 12:48 = 1:4 What is the ratio of men to the class total? 36:48 = 3:4
Ratios A roof has a rise of 7 feet and a run of 14 feet. Express the rise over run in simplest terms Express 16 qt to 5 gal as a ratio in simplest terms (1 gal = 4 qt)
Ratios Simplify the ratio 2 ft 8 in to 6 ft 8 in A line 15 in long on a blueprint represents a length of 40 feet on a house. To what scale was the blueprint drawn?
Ratios A concrete mix uses a mixture of cement, sand, and crushed stone in the ratio of 1 : 2 : 5 by weight. How much of each component is necessary if 4000 lb of concrete mix is needed for a job?
Ratios Find the slope of a roof (rise/run) if the rise is 5 ft and the run is 15 ft
Proportion - Review When two ratios are set equal to each other, the equation formed is called a proportion To solve a proportion where one of the quantities is missing, cross multiplication is used
Proportions Review Solve 4 ? 15 Solve ? 5 15 5= 12= 4 15 = ? 5 ? 15 = 5 12 60 = 5? 15? = 60 60 5=5? 15? 15=60 5 15 12 = ? ? = 4
Proportion Solve the proportion ? 24=7 3 Solve the proportion 14.87 3.91=5.12 ?
Proportion To solve a proportion, set up two fractions properly so that they are in the correct position. This may be done in more than one way. In Blueprints we may have: ??????? ????? 1 ?????? ????? 1= ??????? ????? 2 ?????? ????? 2 Proportions are used when one of the parts (either a numerator or denominator) is missing 1 ?? 12 ????= 3 ?? ? ???? For example:
Proportion ABC Construction Company can build four identical ranch houses in 9 weeks. How many weeks would it take to build 18 houses?
Proportion Two pulleys are belted together. The larger pulley has a diameter of 24 inches and the smaller pulley has a 9 inch diameter. If the smaller pulley is rotating at 3600 rpm, how fast is the larger pulley rotating? (think: is the larger pulley rotating faster or slower?)
Proportion A blueprint has a scale of in = 1 ft. If the length of a house on a blueprint is 7 inches, what is the actual length of the house?
Proportion A blueprint has a scale of in = 1 ft. If the length of a pipe is 25 feet, how long will it be drawn on the blueprint?
