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:

1/4 * 1/4 = 1/16 = 0.0625

Spelled result in words is one sixteenth.

How do you solve fractions step by step?

1. Multiple: 1/4 * 1/4 = 1 · 1/4 · 4 = 1/16
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(1, 16) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - one quarter multiplied by one quarter = one sixteenth.

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:

• Slices of pizza
Maria ate 1/4 of a pizza. If there were 20 slices of pizza, how many slices did Maria eat?
• One-third 2
One-third of the people in a barangay petitioned the council to allow them to plant in vacant lots, and another 1/5 of the people petitioned to have a regular garbage collection. What FRACTION of the barangay population made the petition?
• There 12
There are 42 students in the class and 2/3 of them are girls. How may girls are there in the class?
• Paper clips
Mrs. Bright is organizing her office supplies. There are 5 open boxes of paper clips in her desk drawer. Each box has 1/2 of the paper clips remaining. How many boxes of paper clips are left?
• A store
A store received a shipment of 240 skateboards. In three weeks, it sold 1/3 of those skateboards. How many skateboards did the store sell?
• Scouts 4
4/7 of the students in a school are boys. If 3/8 of the boys are scouts, how many scouts are there in a school of 1878 students?
• Kelly
Kelly and Dan are collecting clothes for a clothing drive. Dan collected 1/2 as many clothes as Kelly did. If Kelly collected 3 bags of clothes, how many bags of clothes did Dan collect?
• A shopkeeper
A shopkeeper cuts a wheel of cheese into 10 equal wedges. A customer buys one-fifth of the wheel. How many wedges does the customer buy? Use the number line to help find the solution.
• 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?
• Ricky
Ricky painted 3/5 of the side of the garage. When he repainted ½ of this part, what part of the side of the garage did he painted twice?
• Farmer Peter
Farmer Peter paints 12 chicken coop. He started painting this day morning. Now he only has 1/4 of the chicken coop left to paint this afternoon. How many chicken coops did farmer Peter paint this morning?
• Fraction of a fraction
What is two-quarters of twelve?
• Equivalent fractions
Are these two fractions equivalent -4/9 and 11/15?