# 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:

### 7 2/5 - 5 2/3 = 26/15 = 1 11/15 ≅ 1.7333333

Spelled result in words is twenty-six fifteenths (or one and eleven fifteenths).### How do you solve fractions step by step?

- Conversion a mixed number 7 2/5 to a improper fraction: 7 2/5 = 7 2/5 = 7 · 5 + 2/5 = 35 + 2/5 = 37/5

To find new numerator:

a) Multiply the whole number 7 by the denominator 5. Whole number 7 equally 7 * 5/5 = 35/5

b) Add the answer from previous step 35 to the numerator 2. New numerator is 35 + 2 = 37

c) Write a previous answer (new numerator 37) over the denominator 5.

Seven and two fifths is thirty-seven fifths - 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 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: 37/5 - 17/3 = 37 · 3/5 · 3 - 17 · 5/3 · 5 = 111/15 - 85/15 = 111 - 85/15 = 26/15

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

In words - thirty-seven fifths minus seventeen thirds = twenty-six fifteenths.

#### 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? - Two cakes

Two cakes were each cut into 8 slices. Maria ate 1/8 of the chocolate cake and 1 slice of carrot cake. Julia ate 1/2 of the carrot cake. Mark ate 1 slice of each. Thomas ate 3 slices of chocolate cake. How many slices were left? - Difference mixed fractions

What is the difference between 4 2/3 and 3 1/6? - School

There are 150 pupils in grade 5 . 2/3 of them are female. By what fractions are the males? - Carrie

Carrie picked 2/5 of the raspberries from the garden, and Robin picked some too. When they were finished, 1/3 of the raspberries still needed to be picked. What fraction of the raspberries did Robin pick? Use pictures, numbers or words and write your fi - Hussein

Hussein owns 450000 crowns (local currency). He spent at the bookstore 2 over 9 to buy some books and tales. He paid 3 over 5 of his money to buy his math book. a. Calculate the remaining amount of money with Hussein? b. Hussein lost 3 over 4 of the remai - Two pizzas

Jacobs mom bought two whole pizzas. He ate 2/10 of the pizza and his dad ate 1 1/5. How much is left. - Stock market 2

For the week of July 22, the following day to day changes in the stock market was recorded a certain stock: -2 on Monday; +4 Tuesday; -8 Wednesday; + 2 1/2 Thursday; - 3 1/4 Friday. The stock began the week at 78 points. How many points did it finish with - Honey

Ila collected the honey from 3 of her beehives. From the first hive, she collected 2/3 gallons of honey. The last two hives yielded 1/4 gallon each. After using some of the honey she collected for baking, Lila found that she only had 3/4 gallon of honey l - Complicated sum minus product

What must be subtracted from the sum of 3/8 and 5/16 to get difference equal to the product of 5/8 and 3/16? - On the floor 2

The floor area of a living room is 9 7/9 m^{2}. A carpet with an area of 5 5/8 m^{2}is placed on the floor. Find the area of the room that is not covered with carpet. - Shirts

In a classroom, 1/6 of the students are wearing blue shirts and 2/3 are wearing white shirts. There are 36 students in the class. How many students are wearing a shirt other than blue or white? - Simplify 3

Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.

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