Subtraction of decimal fractions
Odejmowanie ułamków dziesiętnych
Learning objectives
You will learn to subtract the decimals.
Learning effect
You subtract decimals both mentally and in a written algorithm.
Introduction. Review the rules and methods of adding decimal fractionsdecimal fractions. In which situations do we most often encounter the subtraction of decimal fractionsdecimal fractions?
Prices of sample commodities before and after price reduction
Notebook | Pencil case | Pen | Pencil | |
Before price reduction | 15,60 zł | 34,99 zł | 5,60 zł | 1,60 zł |
After price reduction | 9,40 zł | 32,55 zł | 4,20 zł | 0,90 zł |
On the basis of the table, answer the questions
How much less does a notebook cost after price reduction?
How much has the price of the notebook been reduced?
How much has the price of the pen been reduced?
Formulate the principle of the mental subtraction of decimal fractionsdecimal fractions and compare with the following expressionBy subtracting two decimal fractionsdecimal fractions, we subtract the whole from the whole, and the fractional parts from the fractional parts, e.g.
![Na rysunku przedstawione są przykłady odejmowania liczb dziesiętnych. Pierwsze działanie: 33,99 - 32,55 = 2,44. Drugie działanie: 15,6 - 6,2 = 9,4. Trzecie działanie: 8,108 - 4,043 = 4,065. Za pomocą koloru zielonego zaznaczone są całości liczb, natomiast części dziesiętne tych liczb zaznaczone są w kolorze niebieskim.](https://static.zpe.gov.pl/portal/f/res-minimized/R18egy2tUst0h/1/KQA9Gb1l10nJPXHrXJnY2ZJLRi7ExIfn.png)
Calculate in memory.
a) 4,758 - 2,452
b) 12,52 - 4,20
c) 14,6 - 5,2
d) 0,825 - 0,520
Think how to subtract decimals, in which the number of digits after the decimal point is not the same. Perform calculations.
a) 3,56 - 2,5
b) 5,2 - 3,15
c) 12,54 - 2,125
Conclusion:
To subtract fractions with a different number of digits, first expand or simplify the fractions so that the number of digits after the decimal point matches. Then perform the subtraction.
Open the slideshow and observe how we subtract the decimal fractionsdecimal fractions in written algorithms.
After completing the task, present the results of your observations.
![](https://static.zpe.gov.pl/portal/f/res-minimized/R1EH9fOfbs9Xi/1/1PmTcWqFYIGyOtMcwFkAGHGO6V6tANzk.png)
Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/DN1tzIQra
Conclusions:
Subtracting decimal fractions in a written algorithmSubtracting decimal fractions in a written algorithm is performed in a similar way as in a written algorithm of subtraction of natural numbers.
The numbers should be written in such a way that the commas in both numbers are lined one after the other vertically.
We subtract the whole from the whole, the tenths from the tenths, the hundredths from the hundredths, etc.
Perfom subtraction in a written algorithm.
a) 31,46 - 12,32
b) 16,70 - 9,74
c) 42,8 - 36,49
d) 19,4‑6,728
e) 127,28 - 14,56
Solve word problems below. Perform a written subtraction algorithm and check its correctness by adding.
The box together with the fruit weighs 11.5 kg. How much does the fruit weigh if the empty box weighs 0.96 kg?
The Elbląg Canal is 62.5 km long, and the Augustowski Canal is 80 km. How many kilometers is the Elbląg Canal shorter than the Augustowski Canal?
In the morning there were 350,5 kg of sweets in the store, and 275,75 kg in the evening. How many kilos of candies were sold?
An extra task
Calculate, with the order of operations in mind.
a) 325,32 + 25,32 - 201,25
b) 215,65 - 26,35 + 45,32
c) 215,65 - (23,35 + 45,32)
Remember:
By subtracting decimal fractionsdecimal fractions, we subtract the whole from the whole, the tens from the tens, the hundreds from the hundreds, etc.
Subtracting decimal fractions in a written algorithmSubtracting decimal fractions in a written algorithm is performed in a similar way as a written subtraction of natural numbers.
The numbers should be written in such a way that the commas in both numbers are lined one after the other vertically. Then we subtract the whole from the whole, the tenthstenths from the tenthstenths, the hundredths from the hundredths, etc.
If there is a different number of digits after the decimal point, we extend or simplify the fractions, so that the number of digits after the decimal point matches.
We check the subtraction result by adding.
Do revision exercises.
Exercises
Which difference is the smallest?
- 325,61 - 128,7
- 325,61 - 110,96
- 325,61 - 128,96
- 325,61 - 111,61
Perform the subtraction with a written algorithm. Check the correctness of the operations using the addition.
a) 489,58 - 254,36
b) 264,39 - 159,58
c) 159,68 - 45,365
Henryk Sienkiewicz (1846 - 1916) received The Nobel Prize in 1905.
a) Write who Henryk Sienkiewicz was and what he received the Nobel Prize for.
b) Calculate how old he lived.
c) Calculate how old he was when he received the Nobel Prize.
Give your answers in English.
Indicate which pairs of expressions or words are translated correctly.
- odejmowanie ułamków dziesiętnych sposobem pisemnym - subtraction of decimal fractions in a written algorithm
- odejmowanie w pamięci ułamków dziesiętnych - subtraction of decimal fractions in memory / also mental subtraction of decimal fractions
- ułamki dziesiętne - decimal fractions
- całości - wholes
- części dziesiąte - hundredths
- części setne - thousandths
- subtraction of decimal fractions in memory
- części setne
- tenths
- części tysięczne
- odejmowanie ułamków dziesiętnych sposobem pisemnym
- thousandths
- subtraction of decimal fractions in a written algorithm
- odejmowanie w pamięci ułamków dziesiętnych
- części dziesiąte
- hundredths
Glossary
odejmowanie ułamków dziesiętnych sposobem pisemnym
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: subtraction of decimal fractions in a written algorithm
odejmowanie w pamięci ułamków dziesiętnych
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: subtraction of decimal fractions in memory / also mental subtraction of decimal fractions
ułamki dziesiętne
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: decimal fraction
całości
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: wholes
części dziesiąte
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: tenths
części setne
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: hundreths
części tysięczne
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: thousandths
Keywords
hundrethshundreths
subtraction of decimal fractions in a written algorithmsubtraction of decimal fractions in a written algorithm - we do it similarly to the written subtraction of natural numbers. The numbers should be written in such a way that the commas in both numbers are placed one below the other. We subtract the whole from the whole, tenths form the tenths, the hundredths from the hundredths, etc.
subtraction of decimal fractions in memorysubtraction of decimal fractions in memory - we subtract the whole from the whole, the tenths from the tenths, the hundredths from the hundredths, etc.
tenthstenths
thousandthsthousandths