Mnożenie ułamków dziesiętnych przez liczby naturalne

Learning objectives

You will discover the method of multiplication of the decimals by the natural numbers.

Learning effect

• You do the mental multiplication of the decimal fraction by the natural numbers.

• You multiply the decimal fractions by the natural numbers using written method.

• You use English to describe the method of multiplication the decimals by the natural numbers.

Prepare for the lesson:

• a set of 10 cards, one of the following numbers is written on each of them: 2 ; 3 ; 4 ; 5 ; 10 ; 60 ; 100 ; 700 ; 1000 ; 8000;

• a set of 10 cards, one of the following numbers is written on each of them:  0,004 ; 0,013 ; 0,01 ; 0,09 ; 0,12 ; 0,2 ; 0,5 ; 1,1 ; 1,5 ; 2,2;

• a calculator.

Revise the written method of multiplying the natural numbersnatural numbersnatural numbers.

Consider:

• What are the differences between the results in the same row of the table?

• What does the numbernumbernumber of the digits after the decimal point depend on?

• What method can be used to calculate the productproductproduct of the decimal fraction and the natural numbernumbernumber?

Note, that:

• The results of the row of the table differ only in the numbernumbernumber of the digits after the decimal point.

• The number of the digits after the decimal point depends on the numbernumbernumber of the decimal digits of the decimal fraction that is multiplied.

• 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 productproductproduct to get the same numbernumbernumber of the decimal digits both in the productproductproduct and the decimal fraction

  .

Using the gained information multiply the decimal fractionsdecimal fractionsdecimal fractions by the natural numbersnatural numbersnatural numbers.

Consider:

• What is the difference between the products of 354 ∙ 7 and 35,4 ∙ 7?

• And between the products 2004 ∙ 63 and 2,004 ∙ 63 or the products of 78 ∙ 1123 and 78 ∙ 11,23?

• What does the numbernumbernumber of the digits after the decimal point depend on?

• What written method should we use to calculate the multiplication of the decimal fraction and the natural numbernumbernumber?

Note, that:

• The results of the products differ only in the numbernumbernumber of the digits after the decimal point.

• The number of the digit after the decimal point depends on the numbernumbernumber of digits in the decimal fraction which is multiplied.

• 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 productproductproduct to get the same numbernumbernumber of the decimal digits both in the productproductproduct and the decimal fraction.

Using the gained information multiply the decimal fractionsdecimal fractionsdecimal fractions by the natural numbersnatural numbersnatural numbers. Use calculator to check the results.

Remember:

• To multiply the decimal fraction by the natural numbernumbernumber we multiply these numbers first ignoring the decimal point. Next, we place the decimal point in the productproductproduct to get the same numbernumbernumber of the decimal digits both in the productproductproduct and the decimal fraction.

Do the summarising tasks.

Exercises

Glossary

Keywords

decimal fractionsdecimal fractionsdecimal fractions

mental multiplicationmental multiplicationmental multiplication

natural numbersnatural numbersnatural numbers

productproductproduct

written multiplicationwritten multiplicationwritten multiplication