[Music] oh [Music] we have ratio and proportion a ratio is a quotient that compared to quantities we have four fifths in a fractional form four to five and four is to five where the colon sign is in the middle but these are all the same a proportion is an equation of two equal ratios let's say 40 miles per 6 gallons is equal to 20 miles per 3 gallons when we cross multiply 40 miles times 3 gallons is equal to 100 miles per gallons and 20 miles for six gallons is the same as 120 miles per gallon with these examples the proportion three-sixths is equal to four-eighths which is also equal to 5 10 all reduced to one half so proportion is true if fractions are equal when it is in lowest terms the extremes the means we have here a is to b is equal to c is to d so let's find out the extremes here are a and d and the means are b and c let's have example when we have three fourths is equal to nine twelves the extremes there are three and twelve and the means are nine and four the product of the means equals the product of this extremes so cross products are equal we have here when we have multiplied 3 and 12 we have 36 and so when we also multiply 9 and 4 we also have 36 meaning 36 is equal to itself they are actually proportion proportional the products are equal to each other let's have the first example to solve for proportions so find n the given there is 15 over 45 is equal to 1 over n let's clearly identify 15 when we multiply it by n so we have 15 n then do the same with 1 and 45 remember we are applying the cross multiplication so 1 times 45 that's 45 so in order to find the value of n just simply divide 45 by 15 and that ends with the result of three meaning we have the value of n which is three [Music] let's have another [Music] example solve for w we have seven fourths is equal to w over five times five thousand minus w so of course we're going to apply the distributive property meaning after applying the cross multiplication where 7 should be paired or to be multiplied by 5000 minus w then w times 4 so we are done distributing seven times five thousand that is thirty five thousand then seven times negative w that's negative seven w is equal to four w now combine the like terms meaning just leave the 35 000 at the left because it is a constant then transpose negative 7 w to the right and now it will become positive 7 w then combine them for w plus 7w we have 11 w so we have 35 000 equals 11 w they're not yet done let's proceed multiply i mean divide both sides by 11 in order to get the value of w then [Music] cancel the 11 when being divided by itself then divide 35 000 by 11 and now we have the value of w which is 3181.82 let's have the third example solving for n we solve for n we have 4 x to 7 is equal to n is to 8 of course align that first i mean convert that first into fractional form so that we can apply the cross multiplication so we have four sevenths is equal to n over eight so applying the cross multiplication of course four times eight that is 32 as the product and then seven times and that's seven or seven n then divide both sides left and right by 7 in order to get the value of n so we have 32 divided by 7 and 7 divided by itself so we have the value of n now which is 4.57 how about this one solving for a b or solved for a b let's say we have this small and big the 2 11 and 4 over a b so applying the same thing the cross multiplication the same process just like what we did previously so we have two a b or two times a b equals to a b and then four times eleven equals forty four so in order to get the value of a b just simply divide both sides by two so two divide by itself and then 44 divide by two so we have the value now which is 22 as the value of 80. lastly how about this solve for x six over eight is equal to x over five let's do the same process six times five that is thirty then eight times x that is eight x so for us to know the value of x just simply divide both sides left and right by eight so meaning divide eight by itself then divide thirty by eight so of course cancel and the variable x remains and we have now the value when we divide 30 by eight and we ended up with 3.75 lastly i would like to share this life coat the only true measure of success is the ratio between what we might have done and what we might have been on the one the one hand and the thing we have made and the things we have made of ourselves on the other by h.g wells thank you so much [Music] you