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 1/3 + 6 3/5 = 134/15 = 8 14/158.9333333

Spelled result in words is one hundred thirty-four fifteenths (or eight and fourteen fifteenths).

How do you solve fractions step by step?

  1. Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
    b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
    c) Write a previous answer (new numerator 7) over the denominator 3.

    Two and one third is seven thirds
  2. Conversion a mixed number 6 3/5 to a improper fraction: 6 3/5 = 6 3/5 = 6 · 5 + 3/5 = 30 + 3/5 = 33/5

    To find a new numerator:
    a) Multiply the whole number 6 by the denominator 5. Whole number 6 equally 6 * 5/5 = 30/5
    b) Add the answer from previous step 30 to the numerator 3. New numerator is 30 + 3 = 33
    c) Write a previous answer (new numerator 33) over the denominator 5.

    Six and three fifths is thirty-three fifths
  3. Add: 7/3 + 33/5 = 7 · 5/3 · 5 + 33 · 3/5 · 3 = 35/15 + 99/15 = 35 + 99/15 = 134/15
    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 - seven thirds plus thirty-three fifths = one hundred thirty-four fifteenths.

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:

  • Math test
    Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer.
  • Weigh in total
    I put 3/5 kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total?
  • Honey 3
    Honey jogged 1 3/4 km on Monday,1 1/2 km on Wednesday and 1  2/3 km on Friday . how far did he jog?
  • Interior designer
    To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies?
  • Submerging
    Monika dove 9 meters below the ocean's surface. She then dove 13 meters deeper. Then she rose 19 and one-fourth meters. What was her position concerning the water's surface (the water surface = 0, minus values = above water level, plus = above water level
  • Fractions mul add sum
    To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
  • Decimal to fraction
    Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
  • Simplify 9
    Simplify and express the result as a rational number in its simplest form 1/2+ 1/5+ 6.25+0.25
  • Pizza fractions
    Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • Add sub fractions
    What is 4 1/2+2/7-213/14?
  • Fitness center
    Every Wednesday, Monica works out for 3/4  of an hour at the fitness center. Every Saturday, he goes to the fitness center again and exercises for 3 times as long. How much time does Wayne spend at the fitness center in all each week?
  • Rose spends
    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.
  • Fractions and mixed numerals
    (a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to a mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate the follow


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