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Calculating a number based on its percent

Source: licencja: CC 0.

Obliczanie liczby na podstawie danego jej procentu

Learning objectives

  • You will learnt to calculate a number based on its percent and apply percentage calculations to do text exercises.

Learning effect

  • You calculate a number based on its percent and apply percentage calculations to do text exercises.

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Introduction:

Think what number this is?

  • 50% of this number is equal to 30.

  • 25% of this number is equal to 30.

  • 10% of this number is equal to 30.

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Did you find a way to calculate these numbers?
Are your conclusions about solving this task the same as the following ones?

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Conclusions:

To find the searched number we need to:
- multiply times 2, if we have 50% of the number;
- multiply times 4, if we have 25% of the number;
- multiply times 10, if we have 10% of the number.

Task 1
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Open the interactive illustration that shows one of the method of calculating a number based on its percent.

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Ilustracja interaktywna przedstawia sposób obliczania liczby, której 14% wynosi 322. Napis 14% of the searched number is 322. Strzałki w dół opisane podzielić na 14. Napis 1% of the searched number is 23. Strzałki w dół opisane pomnożyć przez 100. Napis 100% of the searched number is 2300. Na ilustracji widoczne są numery, a na nich podpisy. 1. We calculate how much is 1% of the searched number. {audio}, 2. We calculate how much is 100% of the searched number. {audio}.
Calculating a number based on its percent
Source: GroMar, licencja: CC BY 3.0.
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Did you notice that:
- To find a number based on its percent we need to:
- calculate how much is 1% of the searched number;
- calculate how much is 100% of the searched number.

Task 2
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Find the number whose:

a) 30% is 150,

b) 450% is 6000,

c) 45% is 900,

d) 240% is 192.

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Do the exercise using the formula.

Example 1

Formula:
Find the number whose 12% is 42.

We marked:
x – searched number

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Equation
Source: GroMar, licencja: CC BY 3.0.
Exercise 1
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Find the number whose:

a) 60% is 180,
b) 220% is 462,
c) 1427% is 634.

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Do the exercise using the formula.

Example 2

Formula:
A TV costs 4930 PLN after 15% discount. How much did the TV cost before the discount?

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TV
Source: GroMar, licencja: CC BY 3.0.
Exercise 2
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After lowering the price of a jacket by 10%, it cost 630 PLN. How much did it cost before lowering the price?

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Do the exercise using the formula.

Example 3

Formula:
An avocado costs 4,34 after 24% raise of the price.
How much did it cost before the raise?

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Avocado
Source: GroMar, licencja: CC BY 3.0.
Exercise 3
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After raising prices of tram tickets by 10%, Miss Kasia had to pay 3,85 PLN. How much did this ticket costs before the raise?

Task 3
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An extra task:

Karol got 1350 PLN of a bonus, that is 30% of his salary. How much does he make a month?

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Remember:

To find the searched number we need to:

  • multiply times 2, if we have 50% of the number,

  • multiply times 4, if we have 25% of the number,

  • multiply times 10, if we have 10% of the number,

  • calculate how much is 1% of the searched number and multiply it times 100,

  • solve a proper equation.

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Do the revision exercises.

Exercises

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Exercise 4
Wersja alternatywna ćwiczenia: The number 70 is 20% of the number Możliwe odpowiedzi: 1. 140, 2. 1400, 3. 350, 4. 35
zadanie
Source: GroMar, licencja: CC BY 3.0.
Exercise 5

Find the number x whose 40% is equal to the number a if

a=(301915):0,3

Exercise 6

5,76 kg of apples were obtained after drying them. How many apples were dried if we know that they lose about 84% of its mass after drying? Write the solution and the answer in English.

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Exercise 7
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. znalezienie liczby, gdy dany jest jej procent - finding a number when we have a percent given, 2. obliczenie, ile wynosi 1% danej liczby - calculating how much is 1% of the given number, 3. znalezienie liczby, gdy dane jest 50% liczby - finding a number when we have 50% of this number , 4. znalezienie liczby, gdy dane jest 25% liczby - finding a number when we have 25% of this number , 5. znalezienie liczby, gdy dane jest 25% liczby - finding a number when we have 50% of this number , 6. znalezienie liczby, gdy dane jest 50% liczby - finding a number when we have 10% of this number
zadanie
Source: GroMar, licencja: CC BY 3.0.
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Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

calculating how much is 1% of the given number
calculating how much is 1% of the given number

obliczenie, ile wynosi 1% danej liczby

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wymowa w języku angielskim: calculating how much is 1% of the given number
finding a number when we have a percent given
finding a number when we have a percent given

znalezienie liczby, gdy dany jest jej procent

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wymowa w języku angielskim: finding a number when we have a percent given
finding a number when we have 50% of this number
finding a number when we have 50% of this number

znalezienie liczby, gdy dane jest 50% liczby

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wymowa w języku angielskim: finding a number when we have 50% of this number
finding a number when we have 25% of this number
finding a number when we have 25% of this number

znalezienie liczby, gdy dane jest 25% liczby

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wymowa w języku angielskim: finding a number when we have 25% of this number
finding a number when we have 10% of this number
finding a number when we have 10% of this number

znalezienie liczby, gdy dane jest 10% liczby

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wymowa w języku angielskim: finding a number when we have 10% of this number
solving appropriate equation
solving appropriate equation

rozwiązanie odpowiedniego równania

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wymowa w języku angielskim: solving appropriate equation

Keywords

finding a number when we have a percent givenfinding a number when we have a percent givenfinding a number when we have a percent given – calculating how much is 1% of the searched number and multiply the result times 100

finding a number when we have 50% of this numberfinding a number when we have 50% of this numberfinding a number when we have 50% of this number – we multiply times 2

finding a number when we have 25% of this numberfinding a number when we have 25% of this numberfinding a number when we have 25% of this number – we multiply times 4

finding a number when we have 10% of this numberfinding a number when we have 10% of this numberfinding a number when we have 10% of this number – we multiply times 10