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:

1/8 + 3/8 + 4/8 = 1/1 = 1

Spelled result in words is one.

How do you solve fractions step by step?

  1. Add: 1/8 + 3/8 = 1 + 3/8 = 4/8 = 4 · 1/4 · 2 = 1/2
    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(8, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the next intermediate step, , cancel by a common factor of 4 gives 1/2.
    In words - one eighth plus three eighths = one half.
  2. Add: the result of step No. 1 + 4/8 = 1/2 + 4/8 = 1 · 4/2 · 4 + 4/8 = 4/8 + 4/8 = 4 + 4/8 = 8/8 = 8 · 1/8 · 1 = 1
    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(2, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the next intermediate step, , cancel by a common factor of 8 gives 1/1.
    In words - one half plus four eighths = one.

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:

  • Denominator 2
    fractions Denominator of a fraction is 5 and numerator is 7. Write the fraction .
  • Chocolate to sweets
    cokolada I have 30 basket sweets and 15 chocolate in a basket. If take 5 sweet out of the basket what is the ratio in simplest form of the chocolate to the numbers of sweet left in the basket?
  • Double division
    plusminus 0.25 divided by 1/2 divided by 14
  • Which 3
    ratios2 Which is an equivalent ratio for 12:36
  • Mass fraction
    cukr 2 teaspoons (24 g) of sugar are dissolved in a cup with 500 g of tea. Calculate the weight fraction of sugar in the tea.
  • Dinner tickets
    dino At the spring festival, 7 out of the first 25 attendees had pre-purchased their dinner tickets. Based on this information, if 600 people attended the spring festival, then how many attendees could be expected to have pre-purchased their dinner tickets?
  • Forest nursery
    lesna_skolka In Forest nursery plant one pine to 1.9 m2. Calculate how many plants are planting in area 362 acres.
  • Tractors
    tractor 6 tractors started plowing the field that they together take 12 days. Agronomist hesitates to A) after 2 days to withdraw 2 tractors, or B) after 3 days to withdraw 3 tractors. Help him which of these two cases will be plowing done sooner.
  • Tablespoon of salt
    vaha Mrs. Monika uses 3/4 tablespoons of salt for every kilogram of ground pork. How many tablespoons of salt will she use for 3 1/2 kilograms of ground pork?
  • Equivalent expressions
    pizza A coach took his team out for pizza after their last game. There were 14 players, so they had to sit in smaller groups at different tables. Six players sat at one table and got 4 small pizzas to share equally. The other players sat at the different table
  • Strawberries
    strawberries Father collects strawberries himself in 4 hours, son in 14 hours. How long will it take them along when dad comes to help his son collect strawberries after 3 hours?
  • Players - baseball
    balls2 There are 20 players on each of two baseball teams. If 2/5 of the players on team 1 miss practice and 1/4 of the players on team two miss practice, how many more players from team 1 missed practice then team 2?
  • A serving
    bagSoil A serving of rice is 1/2 of a cup. How many servings are there in a 3 1/2-cup bag of rice?


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