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:

1/3 / 1/4 = 4/3 = 1 1/3 ≅ 1.3333333

Spelled result in words is four thirds (or one and one third).

How do you solve fractions step by step?

  1. Divide: 1/3 : 1/4 = 1/3 · 4/1 = 1 · 4/3 · 1 = 4/3
    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 1/4 is 4/1) 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 - one third divided by one quarter = four thirds.

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:

  • Cutting wire
    meter If you cut a 3 ½ ft length wire into pieces that are 2 inches long, how many pieces of wire will you have?
  • Imagine 2
    cukriky Imagine that you are filling treat bags with jellybeans. You have 3 3/8 cups of jellybeans, and each treat bag will contain 1/4 cup of jellybeans. How many treat bags can you fill before you run out of jellybeans? Show your work (please).
  • Evaluate expression
    mixed_fractions Evaluate expression using BODMAS rule: 1 1/4+1 1/5÷3/5-5/8
  • Unknown number
    eq222 If I reduced the sum of the numbers 70 and the unknown number three times, I would get 100. what is the unknown number?
  • Metal rod
    meter You have a metal rod that’s 51/64 inches long. The rod needs to be trimmed. You cut 1/64 inches from one end and 1/32 inches from the other end. Next, you cut the rod into 6 equal pieces. What will be the final length of each piece?
  • The cost 2
    apples The cost of 5 apples is $3.45  and 5 oranges is $1.23. If Rachel buys one apple and one orange, then how much must she pay?
  • Fraction expression
    fractions Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
  • Jerry
    pizza Jerry has 3/4 of a pizza. He needs to share it with 6 friends. What fraction of the pizza will each friend get? Only write the fraction
  • A teacher
    cookies A teacher baked 5 dozen cookies for the 16 students in her class. If the teacher divided the cookies equally among her students, how many cookies did she give each student?
  • Find the 11
    fractions14 Find the quotient of 229.12 and 12.32
  • Golf balls
    balls2 Of the 28 golf balls, 1/7 are yellow. How many golf balls are yellow? Use the model to help you. Enter your answer in the box.
  • Summerjobs
    agentura The agency give summerjobs for 2352 students in 2018. The eighth was high-school students, the rest was undergraduates. How many undergraduates works via agency in 2018?
  • Simplest form 3
    fractions What fraction is 15 of 35 in simplest form?


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