# 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:

### 5/7 + 2/3 = 29/21 = 1 8/21 ≅ 1.3809524

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

- Add: 5/7 + 2/3 = 5 · 3/7 · 3 + 2 · 7/3 · 7 = 15/21 + 14/21 = 15 + 14/21 = 29/21

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 3) = 21. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 3 = 21. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - five sevenths plus two thirds = twenty-nine twenty-firsts.

#### 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:

- Larry 2

Larry spends half of his workday teaching piano lessons. If he sees 6 students, each for the same amount of time, what fraction of his workday is spent with each student? - Unknown number

I think the number - its sixth is 3 smaller than its third. - Cakes

1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes? - Two divided

Two divided by nine-tenths. - Original number

Joe divided a number by 2 1/4 to get 2/3. What was the original number? - I have

I have 1/5 of an ounce of water left. I separate the water equally into two cups. How many ounces of water are in each cup? - Brick

Isosceles scale has on one side all brick and second weight 1 kg and 1/4 of brick. The balance is in equilibrium. What is the weight of a brick? - Athletic race

Before a race, you start 4 5/8 feet behind your friend. At the halfway point, you are 3 2/3 feet ahead of your friend. What is the change in distance between you and your friend from the beginning of the race? - Farmer Peter

Farmer Peter paints 12 chicken coop. He started painting this day morning. Now he only has 1/4 of the chicken coop left to paint this afternoon. How many chicken coops did farmer Peter paint this morning? - Sales tax

A sales tax on a Php 10,800 appliance is Php.1,620. What is the rate of sales tax? - Diamonds

If simva had 8 diamond and cuts them each into 1/3 pieces, then how many pieces does she have? - Wood 11

Father has 12 1/5 meters long wood. Then I cut the wood into two pieces. One part is 7 3/5 meters long. Calculate the length of the other wood? - A man

A man spends 5/9 of his money on rent, and 5/16 of the remainder on electricity. If the final balance remaining is 550 find how much was spent on rent

next math problems »