Operations on common and decimal fractions

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Działania na ułamkach zwykłych i dziesiętnych

Learning objectives

You will discover the operations on the common and decimal fractions at the same time.

Learning effect

You add, subtract, multiply and divide the common and decimal fractions.
You use the correct order of operations.
You use English to describe the correct order of operations on common and decimal fractions.

Prepare for the lesson:

the sheet of paper with the table of six rows and two columns;
in the first row write step by step in each field one of the following operations:
$0,04 : \frac{2}{10}$ ; $0,75 + \frac{1}{5}$ ; $\frac{4}{5} \cdot 1,2$ ; $40 \frac{1}{5} - 39,9$ ; $2 \frac{1}{2} : 1,25$ ; $0,24 + \frac{3}{5}$ ;
in the second row write step by step one of the following operation:
$\frac{5}{9} \cdot 1,1$ ; $\frac{25}{17} \cdot 0,34$ ; $\frac{36}{56} : 0,5$ ; $6,125 - 4 \frac{1}{4}$ ; $1 \frac{1}{5} \cdot 1,2$ ; $\frac{2}{5} \cdot 0,4 .$ ;

a set of 12 cards, place one of the following writing on each card: $0,84$ ; $2 A$ ; $0,29 F$ ; $\frac{96}{100} E$ ; $0,95 T$ ; $\frac{2}{10} S$ ; $\frac{4}{25} H$ ; $1,44 C$ ; $1 \frac{7}{8} A$ ; $1 \frac{2}{7} N$ ; $\frac{1}{2} A$ ; $\frac{11}{18} B$ ;

twelve‑faced dice.

Revise the addition, the subtraction the multiplication and the division of common and decimal fractionsdecimal fractionsdecimal fractions and the order of operationsorder of operationsorder of operations.

Today you are going to do the operations on the common and decimal fractionsdecimal fractionsdecimal fractions at the same time.

Task 1

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nagranie abstraktu

Analyse the slideshow concerning the operations on the common and decimal fractionsdecimal fractionsdecimal fractions at the same time.

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Operations on common and decimal fractions

Consider:

How can we do the operations on the common and decimal fractionsdecimal fractionsdecimal fractions at the same time?
Does the order of operation on the common and decimal fractionsdecimal fractionsdecimal fractions differ from the order of the operation on the natural numbers?

Conclusions:

Doing the operations on the common and decimal fractions at the same time:

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nagranie abstraktu

we convert the decimal fraction in the common fractionscommon fractionscommon fractions or if it is possible the common fraction in the finite decimal fraction,
the order of the operations remains the same as the order on the natural numbers.

Exercise 1

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nagranie abstraktu

Use the set prepared by the teacher: the paper with the table, 12 cards and the dice. Do the operation presented in the table. Next, find the cards with the appropriate result and place it in the field of the table. The letters read step by step will make the key word: the name of the Polish scientist.

Do the operations on the common and decimal fractionsdecimal fractionsdecimal fractions at the same time.

Task 2

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nagranie abstraktu

Calculate:

$(\frac{3}{4} - \frac{1}{5}) \cdot 4,2$
$5,1 \cdot \frac{10}{17} + 1,5$
$(\frac{2}{3})^{2} + 3,65$
$2,5 \cdot \frac{2}{5} : 0,7$

Task 3

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Source: GroMar, licencja: CC BY 3.0.

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nagranie abstraktu

Write the task in the form of the arithmetic expression and calculate its value.

a) Increase the number of $\frac{2}{3}$ by the productproductproduct of the numbers $\frac{1}{4}$ and $3,5$ .
b) Multiply the differencedifferencedifference of the numbers $2,5$ and $\frac{2}{5}$ by $\frac{3}{4}$ .
c) Reduce the quotationquotationquotation of the numbers $1 \frac{1}{10}$ by $0,25$ by the differencedifferencedifference of the numbers $5 \frac{1}{10}$ and $4,5$ .

Task 4

An extra task:

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nagranie abstraktu

Put the bracketsbracketsbrackets in such a way you will get the correct result:

$2 \frac{2}{5} \cdot 2 + 1 \frac{4}{5} : 0,2 - 0,3 = 3$

Remember:

Doing the operations on the common and decimal numbers at the same time:

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nagranie abstraktu

we convert the decimal fraction in the common fractions or if it is possible the common fraction in the finite decimal fraction,
the order of the operations remains the same as the order on the natural numbers.

Do the summarising tasks.

Exercises

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Exercise 3

Determine which sentences are true.

$8, 7 - 3 \frac{3}{4} = 4 \frac{19}{20}$
$\frac{8}{11} \cdot 0, 33 = 0, 24$
$5 \frac{2}{3} + 2, 75 = 8, 42$
$(1 \frac{1}{7})^{2} = 1 \frac{15}{49}$
$\frac{3}{4} : 1, 6 = 1 \frac{1}{5}$

zadanie

Source: GroMar, licencja: CC BY 3.0.

Exercise 4

The squaresquaresquare of the sum of the numbers $\frac{1}{4}$ i $2,15$ divide by $0,3$ .

$(\frac{1}{4} + 2,15)^{2} : 0,3 = (0,25 + 2,15)^{2} : 0,3 =$

$= {(2, 4)}^{2} : 0, 3 = 5, 76 : 0, 3 = 19, 2$

Exercise 5

Calculate:

$3,2 : (6 \frac{1}{9} - 1 \frac{2}{3}) + 17,09$

Describe in English step by step the operations you have done.

$3,2 : (6 \frac{1}{9} - 1 \frac{2}{3}) + 17,09 =$

$= 3,2 : (6 \frac{1}{9} - 1 \frac{6}{9}) + 17,09 =$

$= 3, 2 : 4 \frac{4}{9} + 17, 09 =$

$= 3 \frac{2}{10} : 4 \frac{4}{9} + 17,09 =$

$= \frac{32}{10} : \frac{40}{9} + 17,09 =$

$= \frac{32}{10} \cdot \frac{9}{40} + 17,09 =$

$= \frac{8}{10} \cdot \frac{9}{10} + 17,09 =$

$= \frac{72}{100} + 17,09 = 17,81$

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Exercise 6

Indicate which pairs of expressions or words are translated correctly.

dodawanie ułamków - addition of the fractions
odejmowanie ułamków - subtraction of the fractions
mnożenie ułamków - multiplication of the fractions
dzielenie ułamków - division of the fractions
odwrotność liczby - reducible fraction
liczba mieszana - order of operations

zadanie

Source: GroMar, licencja: CC BY 3.0.

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Match Polish terms with their English equivalents.

ułamki zwykłe
common fractions
ułamki dziesiętne
nawiasy
decimal fractions
square
brackets
kwadrat
order of operations
kolejność wykonywania działań

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

Glossary

brackets

nawiasy

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wymowa w języku angielskim: brackets

common fractions

ułamki zwykłe

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wymowa w języku angielskim: common fractions

decimal fractions

ułamki dziesiętne

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wymowa w języku angielskim: decimal fraction

difference

różnica – wynik odejmowania

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wymowa w języku angielskim: difference

order of operations

kolejność wykonywania działań

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wymowa w języku angielskim: the order of operations

product

iloczyn – wynik mnożenia

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wymowa w języku angielskim: product

quotation

iloraz – wynik dzielenia

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wymowa w języku angielskim: quotation

square

kwadrat

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wymowa w języku angielskim: square

sum

suma – wynik dodawania

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wymowa w języku angielskim: sum

Keywords

bracketsbracketsbrackets

common fractionscommon fractionscommon fractions

decimal fractionsdecimal fractionsdecimal fractions

order of operationsorder of operationsorder of operations

squaresquaresquare

Scenariusz

Exercises

Glossary

Keywords