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:

53/4 - 35/6 = 23/12 = 1 11/12 ≅ 1.9166667

Spelled result in words is twenty-three twelfths (or one and eleven twelfths).

How do you solve fractions step by step?

1. Conversion a mixed number 5 3/4 to a improper fraction: 5 3/4 = 5 3/4 = 5 · 4 + 3/4 = 20 + 3/4 = 23/4

To find new numerator:
a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/4 = 20/4
b) Add the answer from previous step 20 to the numerator 3. New numerator is 20 + 3 = 23
c) Write a previous answer (new numerator 23) over the denominator 4.

Five and three quarters is twenty-three quarters
2. Conversion a mixed number 3 5/6 to a improper fraction: 3 5/6 = 3 5/6 = 3 · 6 + 5/6 = 18 + 5/6 = 23/6

To find new numerator:
a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6
b) Add the answer from previous step 18 to the numerator 5. New numerator is 18 + 5 = 23
c) Write a previous answer (new numerator 23) over the denominator 6.

Three and five sixths is twenty-three sixths
3. Subtract: 23/4 - 23/6 = 23 · 3/4 · 3 - 23 · 2/6 · 2 = 69/12 - 46/12 = 69 - 46/12 = 23/12
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(4, 6) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 6 = 24. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - twenty-three quarters minus twenty-three sixths = twenty-three twelfths.

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:

• Cupcakes
In a bowl was some cupcakes. Janka ate one third and Danka ate one quarter of cupcakes. a) How many of cookies ate together? b) How many cookies remain in a bowl? Write the results as a decimal number and in notepad also as a fraction.
• Algebra problem
This is algebra. Let n represent an unknown number. 1. Eight more than the number n 2. Three times the number n 3. The product of the number n and eight 4. Three less than the number n 5. Three decreased by the number n
• Toilets
Federal law requires that all residential toilets sold in the United States use no more than 1 3/5 gallons of water per flush. Before this legislation, conventional toilets used 3 2/5 gallons of water per flush. Find the amount of water saved in one year
• 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?
• Square metal sheet
We cut out four squares of 300 mm side from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
• Difference of two fractions
What is the difference between 1/2 and 1/6? (Write the answer as a fraction in lowest terms. )
• Package
The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
• Michael
Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
• You leave
You leave school and the end of the day and walk 3/8 of a mile away before realizing that you left your backpack and immediately turn around you then walk 1/6 of a mile back towards school at this point assuming you walked in a straight line how many mile
• Akpan
Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week?