Ratio+and+Proportion

A ratio may be written as A:B or A/B or by the phrase "A to B".**
 * Ratio and Proportion **:
 * Ratios tell how one number is related to another number.
 * A ratio of 1:5 says that the second number is five times as large as the first.**
 * The following steps will allow determination of a number when one number and the ratio between the numbers is given.**
 * Example: Determine the value of B if A=6 and the ratio of A:B = 2:5**
 * **Determine how many times the number A is divisible by the corresponding portion of the ratio. (6/2=3)**
 * **Multiply this number by the portion of the ratio representing B (3*5=15)**
 * **Therefore if the ratio of A:B is 2:5 and A=6 then B=15**

** How to Determine a Ratio **
 * Ratios represent how one quantity is related to another quantity.**
 * A ratio may be written as A:B or A/B or by the phrase "A to B".**
 * A ratio of 1:5 says that the second quantity is five times as large as the first.**
 * The following steps will allow a ratio to be determination if two numbers are known.**
 * Example: Determine the ratio of 24 to 40.**
 * **Divide both terms of the ratio by the greatest common factor (24/8 = 3, 40/8=5)**
 * **State the ratio. (The ratio of 24 to 40 is 3:5)**

** Cross multiplication to solve proportions ** code 21     3    --  =  --    70     10
 * A proportion is an equation which states that two ratios are equal.**
 * When the terms of a proportion are cross multiplied, the cross products are equal.**
 * Cross multiplication is the multiplication of the numerator of the first ratio by the denominator of the second ratio and the multiplication of the denominator of the first ratio by the numerator of the second ratio.**

21 x 10 = 70 x 3

210 = 210

code code x     3 -- =  --    70     10
 * If one term of a proportion is not known, cross multiplication can be used to find the value of that term.**

x. 10 = 70 . 3

10x = 210

10x  210 --- = ---   10    10

x = 21 code

** Unit Rates **
 * A rate is a ratio that is used to compare different kinds of quantities.**
 * A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.**
 * Some common unit rates are miles (or kilometers) per hour, cost per item, earnings per week, etc. In each case the first quantity is related to 1 unit of the second quantity.**


 * Automotive Engine Compression Ratio Work Sheet **

**1. A 364 C.I.D (cubic inch displacement) engine has a cylinder volume (piston displacement) of 649.5 cc and a combustion chamber volume of 60 cc. What is the compression ratio**?


 * 2. A 375 CID engine has a piston displacement of 687.9 and a chamber volume of 50 cc.**


 * b. If the piston displacement is increased to 702.4, what is the new compression ratio?**


 * 3. If the chamber volume is increased to 70 cc while the piston displacement remains at 687.9, what is the new compression ratio?**


 * 4. Looking at our original formula:**


 * a.When we increase PD, does the CR increase, decrease, or stay the same**?


 * b. When we increase the CV, does the CR increase, decrease, or stay the same?**


 * 4. Look at this formula:** **PD + CV**
 * CR = **** CV **
 * a. As the distance (d) increases, what happens to hp? Is this direct or indirect variation?**


 * b. As the weight (w) increases, what happens to hp? Is this direct or indirect variation?**


 * 5. Given the equation, circle the word that makes each statement correct:**


 * a. C varies (directly, indirectly) with A **


 * b. C varies (directly, indirectly) with T **

**Automotive Engine Compression Ratios Worksheet KEY **  Piston Displacement + Chamber Volume CR = - Chamber Volume
 * 1.**

Use the formula above for CR 649.5 + 60 CR = - = **__11.825 cc__** 60


 * 2.**

a. What is the compression ratio? 687.9 + 50 CR = - = **__14.758 cc__** 50 b. If the piston displacement is increased to 702.4, what is the new compression ratio?

702.4 + 50 CR = - = **__15.048 cc__** 50


 * 3.**

If the chamber volume is increased to 70 cc while the piston displacement remains at 687.9, what is the new compression ratio? 687.9 + 70 CR = - = **__10.827 cc__** 70
 * 4.**

CR = -- CV a. When we increase PD, does the CR increase, decrease, or stay the same? b. When we increase the CV, does the CR increase, decrease, or stay the same? c. Look at this formula d x w Hp = --- 33,000
 * Looking at our original formula PD + CV**
 * __increases __**
 * __decreases __**

As the distance (d) increases, what happens to hp? Is this direct or indirect variation? **__Increases, direct __**  As the weight (w) increases, what happens to hp? Is this direct or indirect variation? **__Increase, direct __** **5.**


 * Given the equation, circle the word that makes each statement correct:**

a. C varies (directly, indirectly) with A  b. C varies (directly, indirectly) with T
 * __<span style="font-family: 'Arial','sans-serif';">directly __**
 * __<span style="font-family: 'Arial','sans-serif';">indirectly __**