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:

82/3 - 35/7 = 104/21 = 4 20/21 ≅ 4.952381

Spelled result in words is one hundred four twenty-firsts (or four and twenty twenty-firsts).

How do you solve fractions step by step?

1. Conversion a mixed number 8 2/3 to a improper fraction: 8 2/3 = 8 2/3 = 8 · 3 + 2/3 = 24 + 2/3 = 26/3

To find new numerator:
a) Multiply the whole number 8 by the denominator 3. Whole number 8 equally 8 * 3/3 = 24/3
b) Add the answer from previous step 24 to the numerator 2. New numerator is 24 + 2 = 26
c) Write a previous answer (new numerator 26) over the denominator 3.

Eight and two thirds is twenty-six thirds
2. Conversion a mixed number 3 5/7 to a improper fraction: 3 5/7 = 3 5/7 = 3 · 7 + 5/7 = 21 + 5/7 = 26/7

To find new numerator:
a) Multiply the whole number 3 by the denominator 7. Whole number 3 equally 3 * 7/7 = 21/7
b) Add the answer from previous step 21 to the numerator 5. New numerator is 21 + 5 = 26
c) Write a previous answer (new numerator 26) over the denominator 7.

Three and five sevenths is twenty-six sevenths
3. Subtract: 26/3 - 26/7 = 26 · 7/3 · 7 - 26 · 3/7 · 3 = 182/21 - 78/21 = 182 - 78/21 = 104/21
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(3, 7) = 21. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 7 = 21. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - twenty-six thirds minus twenty-six sevenths = one hundred four 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:

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:

• Bucket 4
Bucket has 5/8 gallon of water. The bucket tips over, and 7/12 gallon of water pours out. How much water is left in the bucket, in gallons, written as a fraction?
• Leo hiked
Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometer. Who covered a longer distance? How much longer?
• Savings
Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?
• Colored blocks
Tucker and his classmates placed colored blocks on a scale during a science lab. The brown block weighed 8.94 pounds, and the red block weighed 1.87 pounds. How much more did the brown block weigh than the red block?
• 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?
Mike buys flowers to plant around his trees. 3/8 of the flowers are red. 1/3 of the flowers are pink. The rest of the flowers are white. Find the fraction of flowers that are white.
• Two ribbons
The total length of the two ribbons is 13 meters. If one ribbon is 7 and 5/8 meters long, what is the length of the other ribbon?
• Cups of punch
Cyka made 6 19/20 cups of punch punch at two different types of juice in it. If the punch had 4 1/5 cups of one type of juice how many cups of the other type of juice did it have?
• Wood 11
Father has 12 1/5 meters long wood. Then I cut the wood into two pieces. One part is 7 3/5 meters long. Calculate the length of the other wood?
• 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?
• The pet
Ananya has a bunny. She bought 4 7/8 pounds of carrots. She fed her bunny 1 1/4 pounds of carrots the first week. She fed her bunny 5/6 pounds of carrots the second week. All together, how many pounds of carrots did she feed her bunny? 1. Draw a tape diag
• Shirts
In a classroom,1/6 of the students are wearing blue shirts, and 2/3 are wearing white shirts. There are 18 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts?