1 1.7 Problem Solving. 2 A ratio derived from the equality between two different units that can be used to convert from one unit to another Conversion.

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Presentation transcript:

1 1.7 Problem Solving

2 A ratio derived from the equality between two different units that can be used to convert from one unit to another Conversion Factors

3 Conversion factors always equal 1. Conversion factors always equal 1. The numerator is equal to the denominator. The numerator is equal to the denominator. Conversion Factors 4 quarters 1 dollar = 1 12 inches 1 foot = 1 1 kilogram 1000 grams = 1

4 Conversion Factors Animation

5 A mathematical technique that allows you to use units to solve a problem involving measurements Dimensional Analysis

6 # given unit x wanted unit given unit = # wanted unit Put in numbers to make the numerator equal to the denominator

7 Dimensional Analysis xxxx= Arrange the units so that all cancel out except the last one, which should be the one you want.

8 Using Conversion Factors Image p. 40*

9 Dimensional Analysis How many seconds in one week? How many seconds in one week?

10 Dimensional Analysis 1. Express a length of m in centimeters and in kilometers. 2. Express a mass of mg in grams. p cm and km g

11 10um x 1m x 39.37inches = in 10um x 1m x 39.37inches = in 1,000,000um 1m 1,000,000um 1m

12 Practice Problems 250.cm to inches 250.cm to inches ? gal in 39L ? gal in 39L ? cm in 16in ? cm in 16in ? seconds in 5 days ? seconds in 5 days ? ft in 86cm ? ft in 86cm ? cm3 in 2.3gal ? cm3 in 2.3gal ? m in 3.5mi ? m in 3.5mi

13 Direct Proportions Two quantities are directly proportional to each other if dividing on by the other gives a constant value Two quantities are directly proportional to each other if dividing on by the other gives a constant value As Y increases; X increases As Y increases; X increases Y X = k Y = k X The equation for a line! k is the slope.

14 Directly Proportional Graph p. 55 The line must go through the origin to be directly proportional

15 Inverse Proportions Two quantities are inversely proportional to each other if their product is constant. Two quantities are inversely proportional to each other if their product is constant. As X increases; Y decreases As X increases; Y decreases X Y = k X Y = k produces a curve – a hyperbola

16 Inversely Proportional Graph p. 57

17 Directly Proportional & Inversely Proportional Graph Animation