Ch. 3 Math (Important Ch notes) Flashcards
Adding Fractions:
To add fractions, the denominator must be the same same number. (This goes back to having a common denominator)
EX: Adding 1/7 + 4/7
What’s a Ratio:
A ratio is a fraction comparing 2 numbers.
EX. A ratio is 2:4 or 2 to 4 or 2/4
What’s a proportion:
A proportion is the statement that compares 2 ratios & expresses that they’re equal.
EX: 10/15 = 2/3
(so these ratios are a proportion because if you multiply 15x2=30 & 10x3=30, so it’s equal. OR find a common number to divide by to get the same ratio it equals.)
EX 2: 10/5, both mumbers divided by 5 equal 2/3.
Subtracting Fractions:
To subtract fractions they must have a common denominator as well.
Multiplying Fractions:
Multiplying fravtions doesn’t require a common denominator. To multiply you first multiply the numerators…then multiply the denominators.
EX: 3/5 x 7/8 x 1/2
=3 x 7 x 1 = 21
= 5 x 8 x 2 = 80
=21/80
Dividing Fractions:
Dividing fractions doesn’t require a common denominator either. To divide you first change the division symbol to multiplication. Next, you invert the 2nd fraction & then multiply the fractions.
EX: 7/8 divided by 4/3
=7/8 x 3/4
= 21/32
Adding Mixed Numbers:
To add the mixed numbers, add the whole numbers together & then add the fractions together by finding a common denominator. Then add the sum of the whole numbers to the sum of the fractions for the final answer.
EX: 9/7/8 + 8/3/4
=9/7/8 + 8/6/8
= 17/13/8
= 18/5/8
( 8 goes into 13 once so then you add 1 to 17 and that leaves you with a remainder of 5)
Subtraction of mixed numbers:
To subtract mixed numbers, find a common denominator. May be necessary to borrow from the larger whole number when subtracting.
Bolt Dimensions:
|———Shank———|
______|—-Grip—–|—TP—|
| |___________ /\/\/\/\/\
| ___________ | |
|_____| \/\/\/\/\/
|———Overall Length——|
TP= Threaded Portion
Bolt Dimensions:
|———Shank———|
______|—-Grip—–|—TP—|
| |___________ /\/\/\/\/\
| ___________ | |
|_____| \/\/\/\/\/
|———Overall Length——|
TP= Threaded Portion
Aviation Application Typical Ratios:
EX 1: Compression Ratio on a reciprocating engine would be 10:1 or 10 to 1
EX 2: Aspect Ratio of the lengh(or span) of an Airfoil to its width (cord) would be 7:1 or 7 to 1
EX 3: Air fuel ratio of the weight of the air to the weight of fuel would be 14.3:1 or 14.3 to 1
EX 4: Glide ratio of the forward distance travelled to the vertical distamce descended when an aircraft is operating without power could be in example, 10,560:1,000 or 10,560 to 1,000
EX 5: Gear ratio is the number of teeth each gear represents when 2 gears are used in an aircraft component which could be 8:28 or 8 to 28
EX 6: Speed ratio is when 2 gears are used in an aircraft component and could be 2:9 as their gear ratio but 9:2 as their speed ratio
2 types lf gears:
- Pinion Gear: The smaller one
- Spur Gear: The bigger one
Teeth in Pinion Gear Speed of Spur Gear _____________________=____________________
Teeth in Spur Gear Speed of Pinion Gear
Example of solving for speed of Pinion Gear:
10Teeth 160rpm
__________=____________________
40Teeth Sp(Speed of pinion gear)
=40 x 160 / 10
=640rpm
Special Powers:
Power of Zero: Anything to the power of zero equals 1, even if its negative or positive number
Negative Powers:
When a number is to a negative power you multiply the mumber that many times over 1.
EX: 2 to the negative 3 power
= 1 = 1/8
________
2x2x2
