Percentage calculations

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Obliczenia procentowe

Learning objectives

You will learn to do percentage calculations and apply them to do text exercises.

Learning effect

You do percentage calculations and apply them to do text exercises.

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nagranie abstraktu

Revise ways of doing tasks with percents.

Prepare a poster with sentences that start with phrases.

To calculate p% of the given numberp% of the given numberp% of the given number a, we need to …
To calculate a number based on its percentpercentpercent, we need to …
To calculate what percentpercentpercent of the given number b is number a, we need to …

Compare sentences from your poster with following conclusions.

Conclusions:

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nagranie abstraktu

To calculate p% of the given a number, we need to convert this percentpercentpercent into fractionfractionfraction and multiply it by the number a.
To calculate number a based on its percentpercentpercent, we need to convert percent into fraction and divide the given number a by this fractionfractionfraction.
To calculate what fraction of the given number b is number a, we need to calculate what fractionfractionfraction of number b is number a first. Then, we need to convert obtained fraction into percentpercentpercent.

Task 1

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nagranie abstraktu

Open the interactive illustration, that explains the idea of percentpercentpercent points and watch it carefully.

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nagranie abstraktu

In elections for the president of the fishing club there were two candidates. 100 people voted and results are presented in posters.

Analyse information presented in the illustration. Write down conclusions.

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Percent points

Source: GroMar, licencja: CC BY 3.0.

Conclusion:

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nagranie abstraktu

PercentpercentPercent points is a unit of difference between two values of one quantity expressed in percents.

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nagranie abstraktu

Do exercises, using any of the methods you know.

Task 2

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nagranie abstraktu

Write solutions of exercises and answers to them. The number obtain as a result indicates number of the next task to do.


Number of the task	Exercise to do
50	In 32‑people class 25% of students play basketball and 50% - football. How many more percent point of students play football rather than basketball?
25	An art‑tools sets for kid costs 48,50 PLN. How much willi t cost after 15% discount?
41,30	There were 200 people at a tent field. After the first week, 15% of people left, and in the next one 20% of those who stayed also left. How many people stayed at the tent field if no one new came at this time?
136	In 32‑people class, 25% of students play basketball and 50% - football. How many more percent more students play football than basketball?
32	A bike cost 1500 PLN. Its price was raised twice: first by 10% and then by 6%. How much does it cost now?
1749	A group went for a trip to Venice. Men were 36% of all participants and women 42%. Apart from them, there were 11 kids of the trip. How many participants were there?

Task 3

An extra task:

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nagranie abstraktu

There is a certain two‑digit number in which the digit of tens is $33 \frac{1}{3} %$ smaller than the digit of ones. What is this number?

Remember:

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nagranie abstraktu

To calculate $p$ % of the given $a$ number, we need to convert this percentpercentpercent into fractionfractionfraction and multiply it by the number $a$ .
$p$ % of number $a$ is $\frac{P}{100} \cdot a$
To calculate number $a$ based on its percentpercentpercent, we need to convert percent into fractionfractionfraction and divide the given number $a$ by this fraction.
To calculate what fraction of the given number $b$ is number $a$ , we need to calculate what fractionfractionfraction of number $b$ is number $a$ first. Then, we need to convert obtained fraction into percentpercentpercent.
PercentpercentPercent points is a unit of difference between two values of one quantity expressed in percents.

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nagranie abstraktu

Do the revision exercises.

Exercises

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Exercise 1

A tent cost 320 zł and its price was decreased by 40 zł. How many percent was the decrease?

8%
25%
12,5%
80%

zadanie

Source: GroMar, licencja: CC BY 3.0.

Exercise 2

30 dag of salt was poured into 250 g of water. Calculate the percentage concentration of this solution.

Exercise 3

See the system of evaluation of a certain school.


Grade from the test	Percent of points obtained on the test
excellent	100%
very good	from 91% to 99%
good	from 75% to 90%
satisfactory	from 60% to 74%
poor	from 42% to 59%
unsatisfactory	from 0% to 41%

It was possible to obtain 50 points at the last maths test. Kasia got 25 points, Maciek 46 points and Tomek 15 points. What grades did they get?

Write the answer and solution in English.

Exercise 4

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Indicate which pairs of expressions or words are translated correctly.

p% danej liczby - p% of the given number
procent - percent
punkt procentowy - percent point
dany procent liczby - given percent of number
cena końcowa - initial price
cena początkowa - final price

zadanie

Source: GroMar, licencja: CC BY 3.0.

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Match Polish terms with their English equivalents.

percent point
cena początkowa
fraction
cena końcowa
initial price
percent
final price
procent
punkt procentowy
ułamek

Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

converting fraction into percent

zamiana ułamka na procenty

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wymowa w języku angielskim: converting fraction into percent

final price

cena końcowa

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wymowa w języku angielskim: final price

fraction

ułamek

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wymowa w języku angielskim: fraction

given percent of number

dany procent liczby

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wymowa w języku angielskim: given percent of number

initial price

cena początkowa

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wymowa w języku angielskim: initial price

p% of the given number

p% danej liczby

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wymowa w języku angielskim: p% of the given number

percent

procent

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wymowa w języku angielskim: percent

percent point

punkt procentowy

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wymowa w języku angielskim: percent point

Keywords

percent pointpercent pointpercent point - jednostka różnicy między dwiema wartościami jednej wielkości wyrażonymi w procentach

converting fraction into percentconverting fraction into percentconverting fraction into percent

given percent of numbergiven percent of numbergiven percent of number

$p$ % of the given numberp% of the given number $p$ % of the given number - $p$ % danej liczby $a$ , to $\frac{P}{100}$ liczby $a$

Scenariusz

Exercises

Glossary

Keywords