Number 4 :
Given :
20/32 and 12/20
Tell whether the two ratios form a proportion and explain why :
Okay remember the Definition or a proportion
there two ratio that equal each other So let see if 20/32 = 12 /20
two ways to do this
1) reduce both fraction down to lowest common fractions
2) cross multiply it and divide it out
I will do this by # 2
20/32 = 12 /20
Cross multiply it like so
20 *20 = 12 *32
400 = 384
Oh boy we have a problem here they do not equal each other ( unlike 9/24 = 15/40 which is 9*40 = 15*24 which is 360 = 360 in the above problem )
let do it by # 1 :
20/32 = 12 /20 - Given equation
(20/4)/ (32/4) = (12/4)/ (20/4) - reducing the fraction down to lowest common fraction by dividing 4 to each part of the fraction
5/8 = 4/5 - Division
sorry! This Does Not Compute!, This Does Not Compute!, This Does Not Compute!,
So this not a proportion due the Definition of a proportion which those two ratio don't equal each other
Number 5
x – 2 1/3 = - 4 4/15
Slove for x
x – 2 1/3 + 2 1/3 = - 4 4/15+ 2 1/3
x = -4 4/15 + 2 5/15
x = -3 19/15 + 2 5/15 - Borrowing 1 and turning it to 15/15 and adding it 4/15 to get 19/15 for it
x = - 1 14/15 - Subtraction
Number 6 :
Given :
3 6/7x = 2 1/4 - original equation
solve for x
Step 1 :
3 6/7x = 2 1/4 - original equation
27/7 x = 9/4 - changing 3 6/7 and 2 1/4 to vulgar or improper fractions
7/27* 27/7 x = 9 / 4 * 7/27 - Multiplying the reciprocal of a coefficient to both sides of the equation to solve for d
x = 63/108 - multiplication
x = 7/12 - division or reducing the fraction down to lowest common fraction
Proof or check:
3 6/7x = 2 1/4 - original equation
27/7 x = 9/4 - changing 3 6/7 and 2 1/4 to vulgar or improper fractions