Multiplying the decimal fractions
Learning objectives
You will discover the method of multiplying the decimal fractions.
Learning effect
You do the mental multiplication of the decimal fractions.
You multiply the decimal fractions by using the written method.
You use English to describe the method of multiplication of the decimal fractions.
Bring the calculator for the lesson. Revise the written methods of multiplying the natural numbers and multiplying the decimal fractionsdecimal fractions by the natural number.
Today you are going to multiply the decimal fractions.
Draw the table with four rows and four columns on the sheet of paper. Write step by step the following numbers in the first column: 2; 0,2; 0,02; 0,002, and the following numbers in the first row: 3; 0,3; 0,03; 0,003. Complete the table, by using the calculator to calculate the operations.
Consider:
What are the differences between the results in the same row of the table?
What are the differences between the results in the same column of the table?
What does the number of the digits after the decimal point depend on?
What method can be used to calculate the productproduct of the decimal fractions?
Note, that:
The results of the row (column) of the table differ only in the number of the digits after the decimal point.
The number of the digits after the decimal point depends on the number of the decimal digits of the both factors.
To multiply the decimal fractionsdecimal fractions we multiply these numbers first, ignoring the decimal points. Next, we place the decimal point in the productproduct to get the same number of the decimal digits as the sum of number of decimal digits in the decimal fractionsdecimal fractions which are multiplied.
Using the gained information multiply the decimal fractions.
Calculate mentally:
a) 467,21 · 0,14
b) 5,3 · 231,7
c) 9001,5 · 0,548
Use the written multiplicationwritten multiplication to calculate:
7809 · 3; 5042 · 3; 5042 · 4011.
Next, use a calculator to calculate:
78,09 · 0,3; 5,042 · 2,5; 0,065 · 401,1.
Consider:
What is the difference between the products of 7809 · 3 and 78,09 · 0,3? And between the products 5042 · 25 and 5,042 · 2,5 or the products of 65 · 4011 and 0,065 · 401,1?
What does the number of the digits after the decimal point depend on? What written method should we use to calculate the multiplication of the decimal fractionsdecimal fractions?
Note, that:
The results of the products differ only in the number of the digits after the decimal point.
The number of the digits after the decimal point depends on the number of digits in the decimal fraction which is multiplied.
To multiply the decimal fractionsdecimal fractions we multiply these numbers first, ignoring the decimal points. Next, we place the decimal point in the productproduct to get the same number of the decimal digits as the sum of number of decimal digits in the decimal fractions which are multiplied.
Using the gained information multiply the decimal fractions.
Calculate using the written method of multiplication:
a) 467,21 · 0,14
b) 5,3 · 231,7
c) 9001,5 · 0,548
Marcin took part in the boat race. On the first day he sailed 22,6 of the nautical mile, on the second day the 18.9 of the nautical mile and on the third day 20,1. How many kilometres did Marcin sail during these days if one nautical mile equals approximately 1,852 km?
Watch the slideshow to do the following task.
Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/D1Aj9u5Tj
a) How much are we going to pay for 2,4 kg of pears?
b) How much are we going to pay for 1,8 kg of apples and 2,1 kg of oranges?
c) How much less should we pay for 1,5 kg of plums than per 2,7 kg of bananas?
An extra task:
Calculate:
Remember:
To multiply the decimal fraction by the natural number we multiply these numbers first, ignoring the decimal point.
Next, we place the decimal point in the productproduct to get the same number of the decimal digits both in the product and the decimal fraction.
Do the summarising tasks.
Exercises
Determine which sentences are true.
- If 7 ∙ 8 ∙ 9 = 504 then 0,7 ∙ 0,08 ∙ 0,009 = 0,00504.
- If 4,21 ∙ 20,3 = 85,463 then 42,1 ∙ 0,203 = 8,5463.
- The product of the numbers 1,2 and 0,04 is less than 0,05.
A group of scouts decided to make a journey of 64,2 km within 3 days. On the first day they did the 0,37 of the route, on the second day 0,31 of the route and on the third day the remaining part. How many kilometres did the scouts travel on the last day?
Use the written method to calculate:
a) 0,5 of the number 876,34.
b) the product of the number 709,3 and the number 2,3.
c) the number 1,5 larger than the number 90,17.
Describe the written method of multiplication of the decimal fractions in English.
Indicate which pairs of expressions or words are translated correctly.
- ułamki dziesiętne - decimal fractions
- iloczyn - product
- mnożenie w pamięci - mental multiplication
- mnożenie pisemne - written multiplication
- czynnik - price
- liczba większa - smaller number
- czynnik
- product
- decimal fractions
- product
- ułamki dziesiętne
- mnożenie sposobem pisemnym
- factor
- written multiplication
- mental multiplication
- iloczyn
Glossary
ułamki dziesiętne
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: decimal fraction
iloczyn
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: product
mnożenie w pamięci
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: mental multiplication
mnożenie sposobem pisemnym
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: written multiplication
czynnik
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: factor
cena
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: price
liczba większa
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: greater number
liczba mniejsza
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: smaller number
Keywords
decimal fractionsdecimal fractions
productproduct
mental multiplicationmental multiplication
written multiplicationwritten multiplication
factorfactor