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:

3/5 * 3/4 = 9/20 = 0.45

Spelled result in words is nine twentieths.

How do you solve fractions step by step?

  1. Multiple: 3/5 * 3/4 = 3 · 3/5 · 4 = 9/20
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(9, 20) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - three fifths multiplied by three quarters = 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:

  • Withdrawal
    penize If I withdrew 2/5 of my total savings and spent 7/10 of that amount. What fraction do I have in left in my savings?
  • Cupcakes 2
    cake Susi has 25 cupcakes. She gives 4/5. How much does she have left?
  • Ratio 11
    zlomky Simplify this ratio 10 : 1/4
  • Cakes
    cookies On the bowl were a few cakes. Jane ate one-third of them, and Dana ate a quarter of those cakes that remained. a) What part (of the original number of cakes) Dana ate? b) At least how many cakes could be (initially) on the bowl?
  • Passenger boat
    boy Two-fifths of the passengers in the passenger boat were boys. 1/3 of them were girls and the rest were adult. If there were 60 passengers in the boat, how many more boys than adult were there?
  • Miss competition
    dancers How many girls took part in the Miss School competition if the nines grade made up half of the contestants, two-thirds of the remaining girls were eighth grade, and the seventh grade were three?
  • Milk
    milk At the kindergarten, every child got 1/5 liter of milk in the morning and another 1/8 liter of milk in the afternoon. How many liters were consumed per day for 20 children?
  • Write 3
    plusminus Write a real world problem involving the multiplication of a fraction and a whole number with a product that is between 8 and 10 then solve the problem
  • Farmers 2
    tomato On Wednesday the farmers at the Grant Farm picked 2 barrels of tomatoes. Thursday, the farmers picked 1/2 as many tomatoes as on Wednesday. How many barrels of tomatoes did the farmers pick on Thursday?
  • Watching TV
    tv2 One evening 2/3 students watch TV. Of those students, 3/8 watched a reality show. Of the students that watched the show, 1/4 of them recorded it. What fraction of the students watched and recorded reality tv.
  • Pears
    hrusky There were pears in the basket, I took two-fifths of them, and left six in the basket. How many pears did I take?
  • Simple equation 5
    eq222 Solve equation with fractions: X × 3/8 = 1/2
  • Unknown number
    fractions I think the number - its sixth is 3 smaller than its third.


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