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IMA 101 Basic Mathematics

IMA 101 Basic Mathematics. Lecture 6. Lecture Outline. Proportions Unit conversions Descriptive Statistics. Proportions. Section 6.2 of Tussy and Gustafson. Equations: an introduction. Definition: an equation is a statement that two quantities are equal.

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IMA 101 Basic Mathematics

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  1. IMA 101 Basic Mathematics Lecture 6

  2. Lecture Outline Proportions Unit conversions Descriptive Statistics IMA101 1/2010

  3. Proportions Section 6.2 of Tussy and Gustafson IMA101 1/2010

  4. Equations: an introduction Definition: an equation is a statement that two quantities are equal. We use the “=“ sign to signify that the quantities to the left and to the right are the same Examples 4+4 = 8 0.5 * 6 = 3 4*3 = 2*6 IMA101 1/2010

  5. Percents revisited percent*base = amount is an equation. We can use equations to solve for an unknown, however we need to make sure to maintain the equality This means any operation we do to the left side, we have to do to the right side as well. Examples: Divide both sides by “percent” Divide both sides by “base” IMA101 1/2010

  6. Proportion Definition: a statement that two ratios are equal Two ratios are proportional if they are equal Examples IMA101 1/2010

  7. Proportion: checking equality Sometimes ratios are not visibly equivalent We can quickly check an equality by using the cross-product Recall: ratios are just fractions We can multiply both sides of the equation by the left denominator, and the right denominator Then check if the resulting numbers are equal IMA101 1/2010

  8. Proportion: finding the cross-product Practicing the cross-product technique IMA101 1/2010

  9. Proportion: solving problems generally If we know that the ratio of apples to oranges is 3:4 We have 19 oranges, so how many apples will we get? This time we want to solve for the number of apples such that the equality of our proportion will hold Ultimately, we want something of the form x=# Use cross products and then divide both sides by whatever is multiplying x IMA101 1/2010

  10. Proportions: solving problems generally As long as we have 3 of the 4 numbers, we can solve for the unknown value IMA101 1/2010

  11. Proportions: solving word problems Proportions are very useful when you want to scale up or scale down anything Examples: 1. You are throwing a party and you estimate that 3 pizzas can be eaten by 7 people. How many pizzas do you need if you expect 215 people to arrive? 2. You are making a refreshing drink of mint lemonade for your friends. Each drink requires 4 leaves of mint for every glass of lemonade. If you have 17 leaves of mint, how many glasses can you make? IMA101 1/2010

  12. Proportions: solving word problems 3. You have a cookie recipe that calls for 2 ½ cups of flour for ever 1 ¼ cup of sugar. What is this ratio? How many cups of sugar do you need if you want to use up all your 4 ½ cups of flour? IMA101 1/2010

  13. Unit Conversions IMA101 1/2010

  14. Unit Conversions: Metric The Metric system is the most widely used system around the world. (Thailand in included) Why? How many centimeters are in 1.45 m? WARNING: do NOT do unit conversions in your head IMA101 1/2010

  15. Unit Conversion: Time Recall: a unit rate is just a ration of the number of units in the numerator to 1 unit of the denominator Examples: How many seconds are in this 2 hour class? IMA101 1/2010

  16. Student examples If class includes a 10 minute break and ends 5 minutes early, how many seconds are in class? How many meters per second is 13 km/hr ? IMA101 1/2010

  17. Units of Conversion: Currency If you are used to one form of currency then you will often need to convert between currencies. Thai Baht to Lao Kip Thai Baht to Vietnamese Dong Thai Baht to Singapore Dollar Thai Baht to Myanmar Kyat IMA101 1/2010

  18. Unit Conversion: Currency Round to the nearest whole number You arrive in Vientiane, Laos with 1,546 baht in your pocket. If you convert it all, how many kip will you have? You have spent 199,904 kip, and have now arrived in Ha Noi, Vietnam. How many dong will you have once you convert? After spending 1,275 dong you arrive in Singapore. How many Singapore Dollars will you have? Your last stop is Mandalay, Mayanmar. If you only spent 30 Singapore dollars, how many kyat will you have? What can you by with this? IMA101 1/2010

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