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:

(1/2) : (5/64) = 32/5 = 6 2/5 = 6.4

Spelled result in words is thirty-two fifths (or six and two fifths).

How do you solve fractions step by step?

  1. Divide: 1/2 : 5/64 = 1/2 · 64/5 = 1 · 64/2 · 5 = 64/10 = 2 · 32 /2 · 5 = 32/5
    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 5/64 is 64/5) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 2 gives 32/5.
    In words - one half divided by five sixty-fourths = thirty-two fifths.

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:

  • Barbara 2
    pizza Barbara get 6 pizzas to divide equally among 4 people. How much of a pizza can each person have?
  • Quotient and division
    fractions Find the quotient of 3/4 and 1/4.
  • Four people
    cake Four people want waffles for breakfast. There are 6 waffles left. How can 6 waffles be shared equally among 4 people? How much does each person get? Draw a picture and write a division expression to model the problem.
  • Cake 7
    cake 1/3 of a cake shared with 4 people. What share of the whole cake has each people?
  • Minutes
    watch Write as fraction in basic form which part of the week is 980 minutes.
  • The physical
    clocks2 The physical therapist asks Mr. Smith to walk 20 minutes in one hour to improve his ambulation. What fractional part of an hour is Mr. Smith to exercise?
  • Rose spends
    clocks2 Rose spends 2 1/3 hours studying Math, 1 3/4 hours studying English, and 2 1/4 hours studying Science. Find her average time studying the three subjects.
  • Ornamental shrubs
    delnik Children committed to planting 240 ornamental shrubs. Their commitment, however, exceeded by 48 shrubs. Write the ratio of actually planted shrubs and commitment by lowest possible integers a/b.
  • The quotient
    12466 The quotient of g and 55 is the same as 279. What is g?
  • Reciprocal
    reciprocal Calculate the reciprocal numbers for the given real numbers.
  • Quotient and division
    seq What is the quotient of 2/9 and 1/8?
  • Lemonade 4
    lemonade Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
  • 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?


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