# Fraction calculator

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

## Result:

### 5/8÷4/10 = 25/16 = 1 9/16 = 1.5625

Spelled result in words is twenty-five sixteenths (or one and nine sixteenths).### How do you solve fractions step by step?

- Divide: 5/8 : 4/10 = 5/8 · 10/4 = 5 · 10/8 · 4 = 50/32 = 2 · 25 /2 · 16 = 25/16

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 4/10 is 10/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 2 gives 25/16.

In words - five eighths divided by four tenths = twenty-five sixteenths.

#### Rules for expressions with fractions:

**Fractions**- use the slash “/” between the numerator and denominator, i.e., for five-hundredths, enter

**5/100**. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.

The slash separates the numerator (number above a fraction line) and denominator (number below).

**Mixed numerals**(mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e.,

**1 2/3**(having the same sign). An example of a negative mixed fraction:

**-5 1/2**.

Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e.,

**1/2 : 3**.

Decimals (decimal numbers) enter with a decimal point

**.**and they are automatically converted to fractions - i.e.

**1.45**.

The colon

**:**and slash

**/**is the symbol of division. Can be used to divide mixed numbers

**1 2/3 : 4 3/8**or can be used for write complex fractions i.e.

**1/2 : 1/3**.

An asterisk

*****or

**×**is the symbol for multiplication.

Plus

**+**is addition, minus sign

**-**is subtraction and

**()[]**is mathematical parentheses.

The exponentiation/power symbol is

**^**- for example:

**(7/8-4/5)^2**= (7/8-4/5)

^{2}

#### Examples:

• adding fractions: 2/4 + 3/4• subtracting fractions: 2/3 - 1/2

• multiplying fractions: 7/8 * 3/9

• dividing Fractions: 1/2 : 3/4

• exponentiation of fraction: 3/5^3

• fractional exponents: 16 ^ 1/2

• adding fractions and mixed numbers: 8/5 + 6 2/7

• dividing integer and fraction: 5 ÷ 1/2

• complex fractions: 5/8 : 2 2/3

• decimal to fraction: 0.625

• Fraction to Decimal: 1/4

• Fraction to Percent: 1/8 %

• comparing fractions: 1/4 2/3

• multiplying a fraction by a whole number: 6 * 3/4

• square root of a fraction: sqrt(1/16)

• reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22

• expression with brackets: 1/3 * (1/2 - 3 3/8)

• compound fraction: 3/4 of 5/7

• fractions multiple: 2/3 of 3/5

• divide to find the quotient: 3/5 ÷ 2/3

The calculator follows well-known rules for

**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.

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:

- The recipe

The recipe they are following requires 7/8 cups of milk, Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe? - Rolls

Mom bought 13 rolls. Dad ate 3.5 rolls. How many rolls left when Peter yet put two at dinner? - New bridge

Thanks to the new bridge, the road between A and B has been cut to one third and is now 10km long. How much did the road between A and B measure before? - Fruits

Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all? - Ricky

Ricky painted 3/5 of the side of the garage. When he repainted ½ of this part, what part of the side of the garage did he painted twice? - Homework

In the crate are 18 plums, 27 apricot and 36 nuts. How many pieces of fruit left in the crate when Peter took 8 ninth: 1. nuts 2. apricots 3. fruit 4. drupe - Difference mixed fractions

What is the difference between 4 2/3 and 3 1/6? - Third of an hour

How many minutes is a third of an hour? Do you know to determine a third of the lesson hour (45min)? - Reciprocals

Which among the given reciprocal is correct a. 3/15x1/3= 1 b. 3/20x20/3=1 c. 7/14x7/7=1 d. 34/3x34/34=1 - Equation with x

Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9 - Mrs Perry

Mrs Perry shares out 25 biscuits between Gemma and Zak in the ratio 1:4. How many biscuits has each? - Cancel fractions

Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)! - Evaluate expr with 2 vars

If a=6 and x=2, find the value of (2ax + 7x- 10) /(4ax-3a-2)

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