# 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:

### 10 5/7 - 5 2/3 = 106/21 = 5 1/21 ≅ 5.047619

Spelled result in words is one hundred six twenty-firsts (or five and one twenty-first).### How do you solve fractions step by step?

- Conversion a mixed number 10 5/7 to a improper fraction: 10 5/7 = 10 5/7 = 10 · 7 + 5/7 = 70 + 5/7 = 75/7

To find a new numerator:

a) Multiply the whole number 10 by the denominator 7. Whole number 10 equally 10 * 7/7 = 70/7

b) Add the answer from previous step 70 to the numerator 5. New numerator is 70 + 5 = 75

c) Write a previous answer (new numerator 75) over the denominator 7.

Ten and five sevenths is seventy-five sevenths - Conversion a mixed number 5 2/3 to a improper fraction: 5 2/3 = 5 2/3 = 5 · 3 + 2/3 = 15 + 2/3 = 17/3

To find a new numerator:

a) Multiply the whole number 5 by the denominator 3. Whole number 5 equally 5 * 3/3 = 15/3

b) Add the answer from previous step 15 to the numerator 2. New numerator is 15 + 2 = 17

c) Write a previous answer (new numerator 17) over the denominator 3.

Five and two thirds is seventeen thirds - Subtract: 75/7 - 17/3 = 75 · 3/7 · 3 - 17 · 7/3 · 7 = 225/21 - 119/21 = 225 - 119/21 = 106/21

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 - seventy-five sevenths minus seventeen thirds = one hundred six 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:

- Square metal sheet

We cut out four squares of 300 mm side from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet. - Sundar

Sundar has 50 chocolates. He gave 2/5 of these chocolates to Ram and he ate 1/5 of them. How many chocolates are left with Sundar? - Equation with mixed 2

A number, X, is subtracted from 8 1/4. The result is 12 3/5. What is the value of X? - Translate 2

Translate the given phrases to mathematical phrases. Thrice the sum of three fifths and two thirds less one half is what number? - From a 2

From a rope that is 11 m long, two pieces of lengths 13/5 m and 33/10 m are cut off. What is the length of the remaining rope? - Mrs. Susan

Mrs. Susan bought 1/8 m of curtain cloth. She used 3/5 m to make a curtain for the living room window. How many meters of cloth were not used? - Leo hiked

Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometer. Who covered a longer distance? How much longer? - Jose studied

Jose studied for 4 and 1/2 hours on Saturday and another 6 and 1/4 hours on Sunday. How many subjects did he study if he has alloted 1 and 1/2 hours per subject on Saturday and 1 and 1/4 hours per subject on Sunday? - Half of halves

Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part? - Pounds

Three pounds subtract 1/3 of a pound. - Sixth graders

About 6/9 of the sixth- grade pupils will be going to the parents' seminar. If 1/6 of the participants are girls, what part of the portion of sixth graders are boys? - Hotel 4

A 360 room hotel has 1/3 of its rooms occupied at present. How many rooms are empty? - Product and sum

What is the product of two fourths and the sum of three halves and four?

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