## Fraction calculator

This calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 1/2 *2/3 = 1 / 3 ≅0.3333333

Spelled result in words is one third.

### How do we solve fractions step by step?

1. Multiple:

1
/
2

*

2
/
3

=

1 · 2
/
2 · 3

=

2
/
6

=

1 · 2
/
3 · 2

=

1
/
3

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(2, 6) = 2. In the following intermediate step, cancel by a common factor of 2 gives

1
/
3
.

In other words – one half multiplied by two thirds is one third.

#### Rules for expressions with fractions:

Fractions
– use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter
5/100. If you use mixed numbers, leave a space between the whole and fraction parts.

Mixed numerals
(mixed numbers or fractions) keep one space between the integer and
fraction and use a forward slash to input fractions i.e.,
1 2/3
. An example of a negative mixed fraction:
-5 1/2.
Because slash is both signs for fraction line and division, use a colon (:) as the operator of division fractions i.e.,
1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point
.
and they are automatically converted to fractions – i.e.
1.45.

### Math Symbols

Symbol Symbol name Symbol Meaning Example
+ plus sign addition 1/2 + 1/3
minus sign subtraction 1 1/2 – 2/3
* asterisk multiplication 2/3 * 3/4
× times sign multiplication 2/3 × 5/6
: division sign division 1/2 : 3
/ division slash division 1/3 / 5
: colon complex fraction 1/2 : 1/3
^ caret exponentiation / power 1/4^3
() parentheses calculate expression inside first -3/5 – (-1/4)
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The calculator follows well-known rules for
the order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS
– Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS
– Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS
– Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS
– Grouping Symbols – brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS
– Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do
multiplication and division
before
addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

## Fractions in word problems:

• Zdeněk

Zdeněk picked up 15 l of water from a 100-liter full-water barrel. Write a fraction of what part of Zdeněk’s water he picked.
• A class IV.A

In a class, there are 15 girls and 30 boys.  What fraction of the class represents the boys?
• Evaluate expression

Calculate the value of the expression z/3 – 2 z/9 + 1/6, for z = 2
• Children 9

There are 11 children in a room. 6 of the children are girls. What fraction of the children are girls?
• Babies

There are two adults, two children, and four babies on a bus. What fraction of the people are babies?
• In fractions

An ant climbs 2/5 of the pole in the first hour and climbs 1/4 of the pole in the next hour. What part of the pole does the ant climb in two hours?
• In the cafeteria

There are 18 students in Jacob’s homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In the simplest form, what fraction of students eat lunch in the cafeteria?
• Marry

Marry had 1 1/2 dozen eggs in the refrigerator. She used 1/3 of the eggs. What part of the eggs was used?
• Andy gets

Andy gets five out of 15 questions wrong in his math test. What fraction of the question does andy answer correctly?
• Value of Z

For x = -9, what is the value of Z, where Z equals fraction numerator x minus 17 over denominator 6.5 end fraction Give your answer to 2 decimal places.
• Max has 2

Max has 13 pairs of socks. From this, six pairs are blue, three pairs are brown, two are black, and two are white. What fraction of Max’s socks are either brown or black?
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