Dodawanie ułamków o różnych mianownikach

Learning objectives

You will discover the adding the fractions and the mixed numbers whose fractions have different denominators.

Learning effect

• You describe the method of adding the fractions and the mixed numbers whose fractions have different denominators.

• You reduce and expand the common fractions.

• You convert the common fractions to common denominator.

• You use English to describe the method of adding the fractions and the mixed numbers whose fractions have different denominators.

Today you are going to find out the method of adding the fractions and mixed numbers with different denominatorsdifferent denominatorsdifferent denominators.

Put the board of the game made of the A4 size of paper in front of you. Prepare the card with numbers from 2 to 9.

Draw two cards and put them in the empty places of the board to get two fractions. Give the number which can be the common denominator of these two fractions. Consider if you can think of any smaller common denominator. Then draw the other cards, make subsequent fractions and repeat the activity.

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Prezentacja multimedialna prezentuje dodawanie ułamków zwykłych o różnych mianownikach. Instrukcja obsługi z poziomu klawiatury: 1. Uruchomienie aplikacji - ENTER, 2. Na każdym ze slajdów czytany jest automatycznie tekst alternatywny po polsku, 3. Przy pierwszym uruchomieniu na pierwszym slajdzie, czytanie tekstu po angielsku - TAB, 4. Przejście między slajdami: do następnego slajdu - TAB, do poprzedniego slajdu - TAB + SHIFT, 5. Przejście do czytania napisu po angielsku - strzałka w górę + strzałka w dół (czyta tekst po angielsku widoczny na slajdzie).

Prezentacja multimedialna prezentuje dodawanie ułamków zwykłych o różnych mianownikach. Instrukcja obsługi z poziomu klawiatury: 1. Uruchomienie aplikacji - ENTER, 2. Na każdym ze slajdów czytany jest automatycznie tekst alternatywny po polsku, 3. Przy pierwszym uruchomieniu na pierwszym slajdzie, czytanie tekstu po angielsku - TAB, 4. Przejście między slajdami: do następnego slajdu - TAB, do poprzedniego slajdu - TAB + SHIFT, 5. Przejście do czytania napisu po angielsku - strzałka w górę + strzałka w dół (czyta tekst po angielsku widoczny na slajdzie).

Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/DfNmgQigc

Watch the slideshow to discover the method of adding the common fractions with different denominatorsdifferent denominatorsdifferent denominators.

Look carefully at the example: $\frac{1}{4}+\frac{1}{3}$. Illustrate the addition to the drawing. Consider if we can present the fractions $\frac{1}{4}$ and $$$\frac{1}{3}$ in a different way?

The fractions can be converted to the same denominator for example 12. Analyse the following example:

Conclusion:

When we add the fractions with different denominatorsdifferent denominatorsdifferent denominators we have to convert them to the same denominatorssame denominatorssame denominators first by reducing or expanding the fraction. Next, we should add them in the same way as the fractions with the same denominators.

Notice, that:

One of the ways of looking for the same denominator is writing down the subsequent multiple of the bigger denominator. We can always expand the first fraction by the denominator of second fraction and the second one by the denominator of the first one. The smallest common denominator makes the calculation easier. 

Conclusion:

When we add the mixed numbers whose fraction parts have different denominators we should convert the fractions to the same denominator first. Then we calculate the sum of the integers and the sum of the fractions We should remember to write the result in the simplest form after excluding the  integers and reducing the fraction.

Remember:

• When we add the fractions with different denominators we have to convert them to the same denominatorssame denominatorssame denominators first by reducing or expanding the fraction. Next, we should add them in the same way as the fractions with the same denominators.

• When we add the mixed numbers whose fraction parts have different denominators we should convert the fractions to the same denominator first. Then we calculate the sum of the integers and the sum of the fractions We should remember to write the result in the simplest form after excluding the integers and reducing the fraction.

Check what you have learned by doing the following tasks.

Exercises

Glossary

Keywords

irreducible fractionirreducible fractionirreducible fraction

common fractioncommon fractioncommon fraction

mixed numbermixed numbermixed number

different denominatorsdifferent denominatorsdifferent denominators

addition of the fractionsaddition of the fractionsaddition of the fractions