Fraction calculator

Work with fractions

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:

1/3 + 1/5 + 1/2 = 31 / 30 = 1 1 / 30 ≅ 1.0333333

Spelled result in words is thirty-one thirtieths (or one and one thirtieth).

How do you solve fractions step by step?

  1. Add: 1 / 3 + 1 / 5 = 1 · 5 / 3 · 5 + 1 · 3 / 5 · 3 = 5 / 15 + 3 / 15 = 5 + 3 / 15 = 8 / 15
    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, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - one third plus one fifth = eight fifteenths.
  2. Add: the result of step No. 1 + 1 / 2 = 8 / 15 + 1 / 2 = 8 · 2 / 15 · 2 + 1 · 15 / 2 · 15 = 16 / 30 + 15 / 30 = 16 + 15 / 30 = 31 / 30
    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(15, 2) = 30. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 2 = 30. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - eight fifteenths plus one half = thirty-one thirtieths.

Rules for expressions with fractions:

Fractions - simply use a forward 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 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:

  • Frank
    bicycle_gears Frank will be riding his bike to school this year. The distance from his house to the end of the street is ⅜ mile. The distance from the end of the street to the school is ⅚ mile. How far is Frank's house from school?
  • One quarter
    quarter Which of the following has a sum of 3/4? A. 1/2+1/4 B. 1/2+1/3 C. 1/4+1/8 D. 1/9+1/12​
  • Mac painter
    painter Mac is mixing red and white paint to make pink for his candy painting. He uses 1/4 ounce of red paint and 2/3 ounce of white paint. How many ounces of paint did he use?
  • Evaluate expression
    mixed_fractions Evaluate expression using BODMAS rule: 1 1/4+1 1/5÷3/5-5/8
  • Length subtracting
    meter Express in mm: 5 3/10 cm - 2/5 mm
  • Martin
    wood Martin is making a model of a Native American canoe. He has 5 1/2 feet of wood. He uses 2 3/4 feet for the hull and 1 1/4 feet for a paddle. How much wood does he have left? Martin has feet of wood left.
  • Fraction
    Gauss_stamp Fraction frac(0, overline(38))(0,38) write as fraction a/b, a, b is integers numerator/denominator.
  • Team run
    runners The first team member in a 926-person relay race must run 2 1/4 laps, the second team member must run 1 1/2 laps, and the third team member must run 3 1/4 laps. How many laps in all must each team run?
  • Sum of 18
    mixed_fractions Sum of two fractions is 4 3/7. If one of the fractions is 2 1/5 find the other one .
  • A dump
    truck A dump truck bought 1/3 of a ton of rock on the first trip, 1/2 of a ton on the second trip, and 4/5 of a ton on the third trip. What was the total weight of the rock?
  • The pet
    mrkva2 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
  • Tartlets
    tartlet After a special event, a caterer examined the leftovers on the serving table. She saw 10/11 of a tartlet with apples, 2/3 of a tartlet with strawberries, and 10/11 of a tartlet with raspberries. How many leftover tartlets did the caterer have?
  • Food weight
    vaha Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal, today she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 o

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