Ratio and Proportion

Like fractions, ratio and proportion has already been studied in our earlier days. And it is just as important to the real world.  

A ratio is a relationship between two numbers of the same kind like a:b
A proportion is an equation a:b = c:d stating that two ratios are equivalent.

Sample problems:

15ft to 45 ft
Solution:in this problem, get the lowest term of the two numbers which is 15
                =15 is 1 and 45 is 3 so
                =15/45 = 1/3

30 minutes to 2 hours
Solution: convert first the hours into minutes which is 1 hour = 60 minutes
               = 2*60 = 120
               = 30 minutes and 120 minutes, get the lowest term which 30
               = 30 is 1 and 120 is 4
               = 30/60 = 1/4

If 2 ballpen cost 20 php. How many ballpens will she have if he has 320php
Solution: make a proportion formula and represent the second ballpen with x
                 = 2 ballpen                x ballpen
                   -------------     =     --------------
                    20 pesos                 320 pesos
                 = cross multiply
                      2*320 = 640 and 20* x = 20x
                 = 640 = 20x divide the number by 20 (to make the x an individual number)
               
                 = 640    20x   = 32 = x
                    -----   ------
                     20      20
                 = she will have 32 pencils

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Prof. Cris Paner

Fraction

fractions are a common term in elementary days but it is as common to the real world. Although it may not seem to be that used, it is important to relearn this lessons the addition, subtraction, multiplication and division of fractions.

Sample problems:

At a wedding, the girls ate  3 1/2 slices of cake and the boys ate 6 1/2 of sliced cake. How many cakes were eaten at the wedding?
Solution: 3 1/2 + 6 1/2
                  turn the mixed number into improper 2*3+1 = 7/2 and 2*6+1 = 13/2
                  since both are the same denominator just add them
                  ==== 10 slices of cake


Rizza bought 2 1/2 gallons of water and gave 2/4 of the water to the neighbor. How much water is left?
Solution: 2 1/2 - 2/4
                 turn the mixed number into improper 2*2+1 = 5/2
                 find their lcd which is 4, then 4/2*5 = 10/4
                                                                    4/4*2 = 2/4
                 subtract the two number
                 ==== 2 gallons

Ms. Go has a lemonade stand. She used 4/5 bags of lemonade on friday and on saturday, she used 1/2 as many lemonades on friday. How many bags of lemonade did she use on saturday?
Solution: 4/5*1/2
                 in multiplication, just multiply it like normal... 4*1 and 5*2
                  ==== 4/10, simplify then 2/5

1/8 of the original cake is left on the refrigerator. If there are 4 siblings that will share on it. How much cake per sibling will have?
Solution: 1/2 / 4
                 in division it's like multiplication but you will invert the 2nd number so 1/8 * 1/4
                 ====  1/8 cake per sibling

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Prof. Cris Paner

Borrowing and Lending Money

Everyone has supposedly experienced borrowing or lending money, to friends and you yourself borrowed to them. And as you lend them money you sometimes joke to them "hey there's an interest when you give it back to me". Well as a continuation to that it's time to understand how interest really works.

The first thing to do about interest is learning a couple of formulas:
1. I=Prt
2. t=I/Pr
3. r=1/Pt
4. F=P+1
5. F=P+Prt
6. F=P(1+rt)
7. P=F/(1+rt)
8. t+1/r(F/P-1)

where:
I = interest
t = time (expressed in years unless if stated months in the problem)
r = interest rate
P = principal amount
F = final amount

*to change the time from years to months just multiply it by 12 (since there are 12 months) and from months to years is divide it by 12.

Next time someone borrows money from you try to compute the interest as a practice, it might come in handy. The most important thing to remember are the formulas and designating the right number to the right term. 

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sample problem: Find the time in months investing P30,000 at the rate of 12% if the person earns an interest of P459?

SOLUTION
    P = 30,000
    r = 12% = 0.12
    I = 459
    t = ?

    t=I/Pr = 459/30,000(0.12)
           = 459/3600
           = 0.1275 yrs
           = 0.1275 (12)
           = 1.53 months

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Prof. Cris Paner