Breukenrekenmachine

Your input: find the sum, difference, and product of two fractions, the result of the division; convert them into decimal.

The fractions are: $$$2\frac{3}{7}$$$, $$$\frac{5}{9}$$$

Convert $$$2\frac{3}{7}$$$ into an improper fraction.

Rewrite $$$2$$$ as $$$\frac{14}{7}$$$

Add the fractions: $$$2\frac{3}{7}=\frac{14}{7}+\frac{3}{7}=\frac{17}{7}$$$ (we just add the numerators, since the denominators are equal).

So, $$$2\frac{3}{7}=\frac{17}{7}$$$

Multiply the numerator and the denominator of the first fraction by $$$9$$$: $$$\frac{17}{7}=\frac{153}{63}$$$

Multiply the numerator and the denominator of the second fraction by $$$7$$$: $$$\frac{5}{9}=\frac{35}{63}$$$

Add the fractions: $$$\frac{153}{63}+\frac{35}{63}=\frac{188}{63}$$$ (we just add the numerators, since the denominators are equal).

Convert into a mixed number.

Rewrite $$$188$$$ as $$$2 \cdot 63+62$$$: $$$\frac{188}{63}=\frac{2 \cdot 63+62}{63}=2\frac{62}{63}$$$

So, $$$\frac{188}{63}=2\frac{62}{63}$$$

Multiply the numerator and the denominator of the first fraction by $$$9$$$: $$$\frac{17}{7}=\frac{153}{63}$$$

Multiple the numerator and the denominator of the second fraction by $$$7$$$: $$$\frac{5}{9}=\frac{35}{63}$$$

Subtract fractions: $$$\frac{153}{63}-\frac{35}{63}=\frac{118}{63}$$$ (we just subtract the numerators, since the denominators are equal).

Convert into a mixed number.

Rewrite $$$118$$$ as $$$1 \cdot 63+55$$$: $$$\frac{118}{63}=\frac{1 \cdot 63+55}{63}=1\frac{55}{63}$$$

So, $$$\frac{118}{63}=1\frac{55}{63}$$$

Multiple the numerators and denominators: $$$\frac{17}{7} \cdot \frac{5}{9}=\frac{85}{63}$$$

Convert into a mixed number.

Rewrite $$$85$$$ as $$$1 \cdot 63+22$$$: $$$\frac{85}{63}=\frac{1 \cdot 63+22}{63}=1\frac{22}{63}$$$

So, $$$\frac{85}{63}=1\frac{22}{63}$$$

Multiple the first fraction by inverted second fraction: $$$\frac{17}{7} \div \frac{5}{9}=\frac{17}{7} \cdot \frac{9}{5}=\frac{153}{35}$$$

Convert into a mixed number.

Rewrite $$$153$$$ as $$$4 \cdot 35+13$$$: $$$\frac{153}{35}=\frac{4 \cdot 35+13}{35}=4\frac{13}{35}$$$

So, $$$\frac{153}{35}=4\frac{13}{35}$$$

The decimal representation of $$$\frac{17}{7}$$$ is $$$2.42857142857143$$$

The decimal representation of $$$\frac{5}{9}$$$ is $$$0.555555555555556$$$

Answer:

$$$2\frac{3}{7}+ \left( \frac{5}{9} \right)=\frac{188}{63}=2\frac{62}{63}$$$

$$$2\frac{3}{7}- \left( \frac{5}{9} \right)=\frac{118}{63}=1\frac{55}{63}$$$

$$$2\frac{3}{7} \cdot \left( \frac{5}{9} \right)=\frac{85}{63}=1\frac{22}{63}$$$

$$$2\frac{3}{7} \div \left( \frac{5}{9} \right)=\frac{153}{35}=4\frac{13}{35}$$$

The decimal representation of $$$2\frac{3}{7}$$$ is $$$2.42857142857143$$$

The decimal representation of $$$\frac{5}{9}$$$ is $$$0.555555555555556$$$