# 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:

### 1/3 - 2/5 = -1/15 ≅ -0.06666667

Spelled result in words is minus one fifteenth.### How do you solve fractions step by step?

- Subtract: 1/3 - 2/5 = 1 · 5/3 · 5 - 2 · 3/5 · 3 = 5/15 - 6/15 = 5 - 6/15 = -1/15

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(3, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - one third minus two fifths = minus one fifteenth.

#### 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:

- Lowest terms 2

The expression 4/12 can be expressed in its lowest term as 1/3. What is 3/15 expressed in its lowest term? - 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. - Number

I think the number. If I add to its third seven I get same as when to its quarter add 8. Which is the number? - Report 2

A School reports students to teacher ratio of 6:1. If there are 45 teachers in the School, how many students are there? - Golf balls

Of the 28 golf balls, 1/7 are yellow. How many golf balls are yellow? Use the model to help you. Enter your answer in the box. - DIY press

Under socialism regime was in some socialist countries to own a typewriter requires special permission. That has hindered the spread of DIY literature (manually transcribed through carbon copy paper for typewriters). Calculate how many typewriters today c - Seed germination

Seed germination is 80%. 8% of the germinated plants subsequently die. How many seeds does a gardener have to sow in order to grow 2,000 plants? - The rope 2

The rope in the school gym is 10 ½ feet long. To make it easier to climb, Coach Hill tied a knot in the rope every ¾ foot. How many knots are in the rope? - All tasks - taskman

Skilled workshop master washes client car 1/5 hour, cleaned the client's car in 5/4 hour, and painted small defects on car 1 1/3 hour. How long did it take him to do all the necessary work tasks? - Chester

Chester has a piece of wood measuring 1 2/3 cm. He needs to cut it to pieces measuring 3/4 cm long. How many pieces of wood did Chester cut? - Tina has

Tina has 10 packages of yarn to knit a scarf. She uses 1/3 of package of yarn for each inch of length she adds to the scarf. If Tina uses all the yarn, how long will her scarf be? - Mushrooms

Grandfather gathered fresh mushrooms. The fifth was wormwood, and we threw it away. The other dried up. He obtained 720 grams of dried mushrooms. How many kilograms did the grandfather collect, and by drying the mushrooms, they lost 75% of their weight? - Four pupils

Four pupils divided $ 1485 so that the second received 50% less than the first, the third 1/2 less than a fourth, and fourth $ 154 less than the first. How much money had each of them?

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