## Fraction calculator

This calculator divides fractions. The first step makes the reciprocal value of the second fraction – exchange numerator and denominator of 2nd fraction. Then multiply both numerators and place the result over the product of both denominators. Then simplify the result to the lowest terms or a mixed number.

## The result:

### 3/5÷2/3 = 9 / 10 =0.9

Spelled result in words is nine tenths.

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

1. Divide:

3
/
5

:

2
/
3

=

3
/
5

·

3
/
2

=

3 · 3
/
5 · 2

=

9
/
10

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of

2
/
3

is

3
/
2
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words – three fifths divided by two thirds is nine tenths.

#### 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.

Read:   Which Expression is Represented by the Model

### 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)

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:

• A class IV.A In a class, there are 15 girls and 30 boys.  What fraction of the class represents the boys?
• A company A company has 860 employees, of which 500 are female. Write a fraction to represent the female employees in the company.
• 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.
• Evaluate expression Calculate the value of the expression z/3 – 2 z/9 + 1/6, for z = 2
• Lowest terms 2 We can write the expression 4/12 in its lowest term as 1/3. What is 3/15 expressed in its lowest term?
• 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?
• 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.
• The parsley Milka’s grandmother planted 12 rows of vegetables. 1/6 of the rows are carrots. The rest is parsley. How many rows are planted with parsley?
• Children 9 There are 11 children in a room. Six of the children are girls. What fraction of the children are girls?
• One Saturday One Saturday evening there are 40 girls, 25 boys, 18 women and 17 men at a cinema. What fraction are girls?
• Mathew Mathew has eight pencils. Three of them do not have erasers on end. What fraction of the pencils do not have erasers on end?
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