# 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:

### 6 1/5 - 4 1/4 = 39/20 = 1 19/20 = 1.95

Spelled result in words is thirty-nine twentieths (or one and nineteen twentieths).### How do you solve fractions step by step?

- Conversion a mixed number 6 1/5 to a improper fraction: 6 1/5 = 6 1/5 = 6 · 5 + 1/5 = 30 + 1/5 = 31/5

To find new numerator:

a) Multiply the whole number 6 by the denominator 5. Whole number 6 equally 6 * 5/5 = 30/5

b) Add the answer from previous step 30 to the numerator 1. New numerator is 30 + 1 = 31

c) Write a previous answer (new numerator 31) over the denominator 5.

Six and one fifth is thirty-one fifths - Conversion a mixed number 4 1/4 to a improper fraction: 4 1/4 = 4 1/4 = 4 · 4 + 1/4 = 16 + 1/4 = 17/4

To find new numerator:

a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/4 = 16/4

b) Add the answer from previous step 16 to the numerator 1. New numerator is 16 + 1 = 17

c) Write a previous answer (new numerator 17) over the denominator 4.

Four and one quarter is seventeen quarters - Subtract: 31/5 - 17/4 = 31 · 4/5 · 4 - 17 · 5/4 · 5 = 124/20 - 85/20 = 124 - 85/20 = 39/20

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, 4) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 4 = 20. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - thirty-one fifths minus seventeen quarters = thirty-nine twentieths.

#### 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:

- Circular garden

Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante - Visit to grandfather

Shane's family traveled 3/10 of the distance to his grandfather’s house on Saturday. They traveled 4/7 of the remaining distance on Sunday. What fraction of the total distance to his grandfather’s house was traveled on Sunday? - Lunch time

In a cafeteria, 3/10 of the students are eating salads, and 3/5 are eating sandwiches. There are 30 students in the cafeteria. How many students are eating lunches other than salads or sandwiches? - The boy

The boy scouts spent 10/12 hour doing their daily exercises. They only used 1/4 hour in hiking. How much time did they use for other body exercises? - Cereals

Ari and Joey share a 30-ounce box of cereal. By the end of the week, Ari has eaten 3/10 of the box, and Joey has eaten 3/5 of the box of cereal. How many ounces are left in the box? - Fractions mul add sum

To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get? - Gingerbread house

Janka and Marienka calculated that there are 210 gingerbreads on the gingerbread house. Janko ate one-seventh of all gingerbreads, and Marienka ate a third less than Janko. How many gingerbreads remained in the gingerbread house? - Claire and book

After Claire has read the first 5/8 of the book, there are 120 pages left to read. What is the total number of pages of the book? - Pizza fractions

Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left? - Flower garden

In the mr elliots garden 1/8 of the flowers are red 1/4 of them are purple and 1/4 of the remaning flowers are pink. If there is 128 flowers how many of them are pink? - A turtle

A turtle is 20 5/6 inches below the surface of a pond. It dives to a depth of 32 1/4 inches. What is the change in the turtle’s position? Write your answer as a mixed number. - The frame

Rodney has a board that is 5/6 yards long. He cuts 1/5 yard off the board and uses the rest of the board to make a frame. How much of the board is used to make the frame? - Fractions and mixed numerals

(a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate following ex

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