# 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:

### 2 1/2 - 1 2/7 = 17/14 = 1 3/14 ≅ 1.2142857

Spelled result in words is seventeen fourteenths (or one and three fourteenths).### How do you solve fractions step by step?

- Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2

b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs - Conversion a mixed number 1 2/7 to a improper fraction: 1 2/7 = 1 2/7 = 1 · 7 + 2/7 = 7 + 2/7 = 9/7

To find a new numerator:

a) Multiply the whole number 1 by the denominator 7. Whole number 1 equally 1 * 7/7 = 7/7

b) Add the answer from previous step 7 to the numerator 2. New numerator is 7 + 2 = 9

c) Write a previous answer (new numerator 9) over the denominator 7.

One and two sevenths is nine sevenths - Subtract: 5/2 - 9/7 = 5 · 7/2 · 7 - 9 · 2/7 · 2 = 35/14 - 18/14 = 35 - 18/14 = 17/14

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(2, 7) = 14. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 7 = 14. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - five halfs minus nine sevenths = seventeen fourteenths.

#### 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? - 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? - Cherries 2

If a farmer reaped 636 cherries and he sold one third to a shop keeper, how many did he retain? - 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? - 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? - Mother 7

Mother bought 18 fruits. 1/3 were pineapple and the rest were mangoes . how many were mangoes - There 17

There is 3/4 of a cake on a plate in Maria's kitchen. Silvia sees the cake and eats 1/5 of the cake. Then Franca takes 1/3 of what was there and shares half of her portion with Antonella. What fraction of the cake is left? - 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? - Ali bought 2

Ali bought 5/6 litre of milk. He drank 1/2 litre and his brother drank 1/6 litre. How much litre of milk left? - Hotel 4

A 360 room hotel has 1/3 of its rooms occupied at present. How many rooms are empty? - A basket 2

A basket contains three types of fruits weighing 87/4 kg in all. If 23/4 kilograms of these are oranges, 48/7 kg are mangoes, and the rest are apples. What is the weight of the apples in the basket? - Translate 2

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

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

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