how to use percentage - rate - base (prb) and translation in solving math problems

How to Use PRB & Translation in Solving Math Word Problems

Kristine Tanfor Pinoy Math Forum

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Dear Reader,

This presentation aims to show you how to use two techniques, Percentage – Rate – Base and Translation, in solving math word problems.

I will give you some sample exercises, and we will solve each one step by step.

Percentage-Rate-Base

Review of PRB

P Percentage (portion, part, or share), always without a percent sign

RRate or percent, usually with a percent sign, it is the Percentage IN RELATION to the Base

B Base, the original amount, usually the whole

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Identify the P, R, and B in the sentence below:

Answers:

Percentage: Rate:Base:

.1

20 is of 1005

201/5100

All the 3 quantities Percentage, Rate, and Base, are GIVEN already. You are just being asked to IDENTIFY which is which.

20 20 20 20 20

The sentence means that if you cut 100 into 5 equal parts, then each of the 5 parts, or 1/5, is equal to 20.

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.1

20 is of 1005

As seen from the previous slide,

.1

shows how 20 is RELATED TO to 1005

.

either in fraction form or % form,

The rate shows the relationship,

of the percentage to the base

R

P B

We can say that,

P R B

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Let’s use P-R-B in everyday math.

In the following situations, identify the P, R, and the B.

Identify the Percentage, Rate, and the Base.1. Jessy ate 4 out of the 5 parts of her chocolate bar. This means she ate 80% of the chocolate bar.

ANSWERPercentage Rate Base

4 80% 5

2. The interest rate for savings in a bank is 1% per year. When Anton deposited P1,000 in the bank, his money earned an interest of P10 in one year.

ANSWERPercentage Rate Base

P10 1% P1,000www.yeinstein.com www.pinoymathforum.com

In the previous slide, all 3 quantities were given.

Given in the problem You need to find

Percentage & Rate Base

Percentage & Base Rate

Rate & Base Percentage

A typical PRB word problem is different. It will provide you with any 2 of the 3 quantities, and you will need to solve for the 3rd quantity.

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Typical P-R-B Word Problem:What part of 30 is 6?

The Rate.

Base Percentage

What is missing?

• Identify which 2 of the 3 quantities are given.

The trick is to use the PRB triangle.Since the rate R is missing, we cover R.

We see that P is “over” B.

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PB

"over" Rate P B

630

15

:

16 is of 30.

5

Answer

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PRB Application: Discount

A PRB Application: DiscountDuring a sale with all items marked 20% off, Manuel bought a t-shirt at Php 200.00. What was the original price of the t-shirt? What are given in the problem?What does Php 200.00 represent? Percentage. (Or part of the

original price)What does 20% represent? The common misconception is that the given

% quantity in the problem is the rate, but this is not always the case.

The correct rate is (100% -20%) = 80%.Therefore, the given are:

Php 200.00 = 80%

PercentageRate

Which means we have to FIND the Base.

What do we need to find?

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Php 200.00 = 80%

PercentageRate

"over" Base P RPR

.

%

200 0080

.

.

200 000 80

. .0 80 200 00

25080 20000

160 400 400 0

Answer:The original price is Php 250.00.

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Now, let’s try answering some PRB problems using Translation.

Translation of the English Sentence into a Mathematical Equation

Using the same word problem:What part of 30 is 6?

We will translate the sentence into a mathematical equation.

As you can see, in translating sentences to math equations,

N 30 6

“of” becomes multiplication“is” becomes the equal sign

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30 6N To answer N:What should N be, so that if you multiply it to 30, you get 6?

:

1 must be .

5

Answer

N

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Let’s try another problem.

20% of 25 is what part of 160?

Step 1: Find 20% of 25.

“20% of 25” = 0.20 x 25 = 5

Step 2: Find the answer to “5 is what part of 160?”.

Percentage PP

RB

Base BIn Step 2 now, we are looking for the rate R. 5

160

132

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Your turn:

Forty is 0.25% of what number?• Identify: what do 40 and 0.25% represent?• Answer: 40 represents the Percentage P.• 0.25% is the Rate R, where, in this problem, the

number 40 is worth 0.25% of some number.• The number we are looking for is the Base B.

PB

R

. %

400 25

.

400 0025

Warning: 0.25% is NOT the same as 0.25. Take note of the “%” symbol!

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.16000

25 400000

-25 150 -150 0

Move the decimal point 4 places to the right, in both divisor and dividend. (Because we need to make the divisor 0.0025 a whole number).

.0 0025 40.

400 0025

is the same as:

Answer: 40 is 0.25% of 16000.

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