BGS - 02. Fractions, Decimals and Ratios Flashcards
Fractions
Number of top of the line is known as what
2/8
1
NUMERATOR
Fractions
Number on the bottom of the line is known as what
2/8
1
DEONOMINATOR
Fractions
How do you find ⅜ of 24?
Method 1
1
Find ⅛ of 24
⋉
24 / 8 = 3
Multiple this by the original numerator
⋉
3 x 3 = 9
ANSWER
⅜ of 24 = 9
Fractions
How do you find ⅜ of 24?
Method 2
1
Multiple the fraction ⅜ by the whole number, in this case 24
REMEMBER when you express a whole number, there is always an invisible 1 beneath it
i.e. 24 / 1.
Therefore to express a fraction multipled by a whole number we write it as so;
⅜ x 24
= 3/8 x 24/1
= 3 x 24 / 8 x 1
= 72/8 = 9
Where in the fraction we do 3 x 24 to find the top line and we do 8 x 1 to find the bottom line
3 x 24 = 72
1 x 8 = 8
⋉
72 / 8
Equivilant Fractions
Fractions can be written in different ways but represent the same value i.e.
2/3 = 4/6
2
Simplifying Fractions
When you can no longer divide the top and bottom number by the same number you have found the simplest fraction.
The simplest form is reached when either the denominator or numerator are a prime number
3
12/16
Both 12 and 16 can be divided by 4
12/4 = 3
16/4 = 4
Simplest fraction is therefore;
12/16 = 3/4
Simplifying Fractions
A prime number is a natural number greater than 1 that has no positive divisors other than 1 itself
3
3 is an example.
3 can only be divided by 1 or by itself
4 in contrast can be divided by 1, itself, and 2, all of which give a whole number
Addition of Fractions
Where the denominator is the same, you simply add the numerators together to arrive at your answer
4
2/9 + 1/9 + 4/9
All the denominators are the same. Add the numerators together and keep the same denominator;
2 + 1 + 4 = 7
2/9 + 1/9 + 4/9 = 7/9
Addition of Fractions
It is possible to simplify a fraction addition when adding together
4
3/8 + 1/8
Use the additioan technique where you add the numerator, leave the denominator;
3 + 1 = 4
3/8 + 1/8 = 4/8
However, we can see 4 and 8 are not prime numbers so we have not reached the simplest fraction.
Both numbers are divisible by 4
4/4 = 1
8/4 = 2
Simplest Fraction = 1/2
Addition of Fractions
Where denominators are not the same, you can use equivilant fractions to make them have the same denomintor so that you can then add the fractions together more easily.
4
2/3 + 1/4
In this example, we want to find the common denominator. What is the first number both 3 and 4 go into. This is 12.
A simple technique is to multiple by the denominator of each fraction i.e;
2/3 multipled by the denominator of 1/4 (which is 4)
1/4 multipled by the denominator of 2/3 (which is 3)
2x4 = 8
3 x 4 = 12
= 8/12
And;
1x3 = 3
4x3 = 12
= 3/12
We now have the same denominator on each side;
8/12 + 3/12 and we can use the additioan technique of adding the numerator and leaving the denomintor;
8+3 = 11 ⋉ 11/12
2/3 + 1/4 ⋉ 8/12 + 3/12 = 11/12
Subtraction of Fractions
For subtracting fractions, use the same technique for adding fractions i.e. multiple by the denominator of each fraction
4
5/8 - 1/5
5x5 = 25 and 8x5 = 40
1x8 = 8 and 5x8 = 40
⋉
25/40 - 8/40
Deduct numerators from each other, leave denominator;
25 - 8 = 17
17/40
5/8 - 1/5 = 17/40
Decimals
When adding or subtracting decimals, especially from whole numbers, ensure to align the decimal in the same place and add zeros where required
5
7 - 0.19
Becomes..
7.00
-0.19
= 6.81
Division of Decimals
When dividing by decimals, you need to determine the equivilant fractions. This is achieved by multiplying the numerator and denominator by the same decimal value i.e. 10, 100, 1000 etc..
7
2.42 / 0.2
To make 0.2 a whole number multiple by 10. Do the same to the numerator i.e. move decimal place 1 space to the right
2.42 / 0.2 ⋉ 24.2 / 2
This is a simplier fraction to work out.
24.2 / 2 = 12.1
Dvision of Decimials
When dividing by decimals, you need to determine the equivilant fractions. This is achieved by multiplying the numerator and denominator by the same decimal value i.e. 10, 100, 1000 etc..
In some examples, this can leave us in a position where we can use long division to then derive the answer required
3.715 / 0.005
To make 0.005 a whole number, multiple by 1000 i.e. move decimal place right by 3 spaces and do the same to the top number.
3.715 / 0.005 ⋉ 3715/5
Now use long division to reach answer
743
Percentage
To work out a percentage of a number, write it as a fraction so that you can multiple the numerator by the quantity.
As a percentage is always out of 100, this is then divided by 100
30% of 150 seats
30% x 150
⋉
(30x150)/100
30x150
(remove zeros)
3x15 = 45
(add zeros back - we removed 2)
4500
⋉
4500/100
(remove zeros)
⋉
45/1
30% of 150 seats = 45
Reoccuring Decimal to Fraction
Multiple the decimal by 10 and subtract the original decimal from the answer. This means you now know what 9x the original decimal will be
10
If you multiple 0.5555 by 10 (move decimal 1 to the right) you have 5.555
If you subtract 0.5555 from 5.5555, you have 5
Therefore you now know that 9 x 0.5555 = 5
0.5555 as a fraction = 5/9
Repeating Decimal to Fraction
Multiple the decimal by 100 and subtract the original decimal from the answer. This means you know what 99x the oringinal decimal will be
10
If you multiple 0.353535 by 100 (move decimal to the right twice) you have 35.353535
If you subtract 0.353535 from 35.353535 you have 35.
Therefore know what 99x 0.353535 is
0.353535 as a fraction = 35/99
Ratios
Ratios can be simplified
Find a number that is common to both sides
What is the simplied ratio of 78 crews to 12 aeroplanes
78 crews to 12 aeroplanes written as a ratio
78:12
Both sides are divisible by 6 where;
6 goes into 78 13 times
6 goes into 12 2 times
13:2
Simplied raito = 13:2
HOWEVER, it is common to express ratios as 1:n or n:1 i.e. down to 1 part. Therefore, now we have our simplied ratio of 13:2, simply divide each side by 2 to get to 1 part.
13/2 - 6.5
2/1 = 1
6.5:1 - there are 6.5 crews to 1 areoplane
Ratios
Ratios can be expressed with more than 2 elements. This means to determine 1 part, you need the sum of all the parts and divide the total by the answer.
180 oranges are shared between 3 people in ratio of
1:2:6
What is the largest volume of oranges someone will possess
12
180 oranges are shared between 3 people in ratio of
1:2:6
Add each of the parts together to get the sum of all parts
1+2+6 = 9
Divide the total number of oranges by the sum of all parts
180/9 = 20
Answer is:
20:40:120
Largest volume = 120
Proportions
Aircrafts aspect ratio is mean chord to span where mean chord is the average distance from front to back
If one aircraft has a chord of 0.65m anda span of 14.3m, this is stated as a ratio
0.65:14.3
If the chord of another aircraft is 0.72m with the same aspect ratio, what is the span of the second aircraft and what is the aspect ratio
Aircraft 1 we know has an aspect ratio of 0.65:14.3
Simplify by multiply both sides by 10;
6.5:143
We want this as 1 part so divide both sides by 6.5
6.5/6.5 = 1
143/6.5 = 22
Aspect ratio 0.65:14.3 ∝ 1:22
Aircraft 2 has same aspect ratio. Therefore to reverse the workings to get the chord and span, multiple both sides by the given chord;
1:22 ∝ 1x0.72:22x0.77
∝ 0.72:15.84
Aspect Ratio : 22
Aircraft 2 span: 15.84m
