# 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:

### 21/6 - 12/7 = 37/42 ≅ 0.8809524

Spelled result in words is thirty-seven forty-seconds.

### How do you solve fractions step by step?

1. Conversion a mixed number 2 1/6 to a improper fraction: 2 1/6 = 2 1/6 = 2 · 6 + 1/6 = 12 + 1/6 = 13/6

To find new numerator:
a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6
b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 6.

Two and one sixth is thirteen sixths
2. 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 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
3. Subtract: 13/6 - 9/7 = 13 · 7/6 · 7 - 9 · 6/7 · 6 = 91/42 - 54/42 = 91 - 54/42 = 37/42
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(6, 7) = 42. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 7 = 42. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - thirteen sixths minus nine sevenths = thirty-seven forty-seconds.

#### 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:

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:

• Michael
Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
• Empty and full
An empty can has a mass of 1/6 lb. When it is filled with sand, it has a mass of 7/12 lb. Find the mass of the sand in the can?
• Animal species
Of 100 types of animals, 9/100 were discovered in ancient times, and 2/100 were discovered in the Middle Ages. Another 3/10 were discovered in the 1800s. What fraction of the 100 types of animals was discovered after the 1800s? Explain.
• 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?
• Sarah
Sarah has a photography blog. 3/7 of her photos are of nature, 1/4 of the rest are of her friends. What fraction of all of Sarah's photos is of her friends?
• 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
• Mr. Peter
Mr. Peter mowed 2/7 of his lawn. His son mowed 1/4 of it. Who mowed the most? How much of the lawn still need to be mowed?
• On the floor 2
The floor area of a living room is 9 7/9 m2. A carpet with an area of 5 5/8 m2 is placed on the floor. Find the area of the room that is not covered with carpet.
• 5 2/5
5 2/5 hours a week  mathematics,  3 3/4 hours a week   Natural sciences, 4 3/8 hours a week  Technology . how many hours does  he spend on social sciences if he spend 17 1/2 hours a week for the four subject?
• 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?
• Larry
Larry received 1/3 pound of candy from his grandmother and 2/5 pound of candy from his best friend. Larry's sister ate 1/2 pound of Larry's candy. How many pounds of candy does Larry have left?
• Grandmother
Stella's family traveled 5/8 of the distance to her grandmother’s house on Saturday. They traveled 2/3 of the remaining distance on Sunday. What fraction of the total distance to her grandmother’s house was traveled on Sunday?
• Curtain
Mrs. Lazo bought 9 1/8 m curtain cloth. She used 3 5/6 m to make a curtain for their bedroom. How many meters of cloth were not used?