# Fractions Calculator

The calculator will find (with steps shown) the sum, difference, product and result of the division of fractions or mixed numbers. It will also convert the fraction into decimal number and into improper fraction (if possible).

• In general, you can skip the multiplication sign, so 5x is equivalent to 5*x.
• In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x).
• Also, be careful when you write fractions: 1/x^2 ln(x) is 1/x^2 ln(x), and 1/(x^2 ln(x)) is 1/(x^2 ln(x)).
• If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. write sin x (or even better sin(x)) instead of sinx.
• Sometimes I see expressions like tan^2xsec^3x: this will be parsed as tan^(2*3)(x sec(x)). To get tan^2(x)sec^3(x), use parentheses: tan^2(x)sec^3(x).
• Similarly, tanxsec^3x will be parsed as tan(xsec^3(x)). To get tan(x)sec^3(x), use parentheses: tan(x)sec^3(x).
• From the table below, you can notice that sech is not supported, but you can still enter it using the identity sech(x)=1/cosh(x).
• If you get an error, double check your expression, add parentheses and multiplication signs where needed, and consult the table below.
• All suggestions and improvements are welcome. Please leave them in comments.
The following table contains the supported operations and functions:
 Type Get Constants e e pi pi i i (imaginary unit) Operations a+b a+b a-b a-b a*b a*b a^b, a**b a^b sqrt(x), x^(1/2) sqrt(x) cbrt(x), x^(1/3) root(3)(x) root(x,n), x^(1/n) root(n)(x) x^(a/b) x^(a/b) abs(x) |x| Functions e^x e^x ln(x), log(x) ln(x) ln(x)/ln(a) log_a(x) Trigonometric Functions sin(x) sin(x) cos(x) cos(x) tan(x) tan(x), tg(x) cot(x) cot(x), ctg(x) sec(x) sec(x) csc(x) csc(x), cosec(x) Inverse Trigonometric Functions asin(x), arcsin(x), sin^-1(x) asin(x) acos(x), arccos(x), cos^-1(x) acos(x) atan(x), arctan(x), tan^-1(x) atan(x) acot(x), arccot(x), cot^-1(x) acot(x) asec(x), arcsec(x), sec^-1(x) asec(x) acsc(x), arccsc(x), csc^-1(x) acsc(x) Hyperbolic Functions sinh(x) sinh(x) cosh(x) cosh(x) tanh(x) tanh(x) coth(x) coth(x) 1/cosh(x) sech(x) 1/sinh(x) csch(x) Inverse Hyperbolic Functions asinh(x), arcsinh(x), sinh^-1(x) asinh(x) acosh(x), arccosh(x), cosh^-1(x) acosh(x) atanh(x), arctanh(x), tanh^-1(x) atanh(x) acoth(x), arccoth(x), cot^-1(x) acoth(x) acosh(1/x) asech(x) asinh(1/x) acsch(x)

Enter fractions or

First fraction:

Second fraction:

The second fraction is needed for addition, subtraction, multiplication, division; but not for converting to decimal
If you don't need a mixed number, leave the left cell empty
If you need negative fraction, write the minus sign in the left cell

Write all suggestions in comments below.

## Solution

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

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

Convert $$2\frac{3}{7}$$$into improper fraction. Rewrite $$2$$$ as $$\frac{14}{7}$$$Add 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, $$2\frac{3}{7}=\frac{17}{7}$$$## Fractions addition 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 fractions: $$\frac{153}{63}+\frac{35}{63}=\frac{188}{63}$$$ (we just add the numerators, since the denominators are equal).

Convert to mixed number.

Rewrite $$188$$$as $$2\cdot63+62$$$: $$\frac{188}{63}=\frac{2\cdot63+62}{63}=2\frac{62}{63}$$$So, $$\frac{188}{63}=2\frac{62}{63}$$$

## Fractions subtraction

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 numerators, since denominators are equal). Convert to mixed number. Rewrite $$118$$$ as $$1\cdot63+55$$$: $$\frac{118}{63}=\frac{1\cdot63+55}{63}=1\frac{55}{63}$$$

So, $$\frac{118}{63}=1\frac{55}{63}$$$## Fractions multiplication Multiple the numerators and denominators: $$\frac{17}{7} \cdot \frac{5}{9}=\frac{85}{63}$$$

Convert to mixed number.

Rewrite $$85$$$as $$1\cdot63+22$$$: $$\frac{85}{63}=\frac{1\cdot63+22}{63}=1\frac{22}{63}$$$So, $$\frac{85}{63}=1\frac{22}{63}$$$

## Fractions division

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 to mixed number. Rewrite $$153$$$ as $$4\cdot35+13$$$: $$\frac{153}{35}=\frac{4\cdot35+13}{35}=4\frac{13}{35}$$$

So, $$\frac{153}{35}=4\frac{13}{35}$$$## Decimal representation Decimal representaion of $$\frac{17}{7}$$$ is $$2.42857142857143$$$Decimal representaion of $$\frac{5}{9}$$$ is $$0.555555555555556$$$Answer: $$2\frac{3}{7}+ \left( \frac{5}{9} \right)=\frac{188}{63}=2\frac{62}{63}$$$

$$2\frac{3}{7}- \left( \frac{5}{9} \right)=\frac{118}{63}=1\frac{55}{63}$$$$$2\frac{3}{7} \cdot \left( \frac{5}{9} \right)=\frac{85}{63}=1\frac{22}{63}$$$

$$2\frac{3}{7} \div \left( \frac{5}{9} \right)=\frac{153}{35}=4\frac{13}{35}$$$Decimal representaion of $$2\frac{3}{7}$$$ is $$2.42857142857143$$$Decimal representaion of $$\frac{5}{9}$$$ is $$0.555555555555556$$\$