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:

(2/3) : (3/4) = 8/9 ≅ 0.8888889

Spelled result in words is eight ninths.

How do you solve fractions step by step?

  1. Divide: 2/3 : 3/4 = 2/3 · 4/3 = 2 · 4/3 · 3 = 8/9
    Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/4 is 4/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - two thirds divided by three quarters = eight ninths.

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:

  • Fractions 4
    fractions How many 2/3s are in 6?
  • Women
    smajlik In a company of 1050 employees are 2/3 women. How many women work in the company?
  • Chocolate
    choko Children break chocolate first to third and then every part of another half. What kind got each child? Draw a picture. What part would have received if each piece have halved?
  • Unit rate
    question Find unit rate: 6,840 customers in 45 days
  • Minutes
    watch Write as fraction in basic form which part of the week is 980 minutes.
  • Container
    konva How many three-quarters liters jar fill 30 liters container?
  • Find the 11
    fractions14 Find the quotient of 229.12 and 12.32
  • Division of money
    euro Calculate how many euros have Matthew, Miriam, Lucy, Michael, Janka when together have 2,700 euros and the amounts are at a ratio of 1:5:6:7:8.
  • Evaluate
    calculator The division of numbers $a and $b increase by-product of the numbers $c and $d
  • Soup from canteen
    soup For how many people is 90 liters of soup enough if we assume 3/8 liter of soup per person in the canteen?
  • Self
    Self-books A math text book is 2 2/9 inches thick. how many of these books will fit on a 120-inch self?
  • Sewing
    sewing Beth's mother can sew 235 pairs of short pants in 6 days while Lourdes can sew 187 pairs in 8 days. How many more pairs of short pants can Beth's mother sew?
  • The third
    meter The one-third rod is blue, one-half of the rod is red, the rest of the rod is white and measures 8 cm. How long is the whole rod?


next math problems »