# 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:

### (3/4) : (51/5) = 15/104 ≅ 0.1442308

Spelled result in words is fifteen one-hundred fourths.

### How do you solve fractions step by step?

1. Conversion a mixed number 5 1/5 to a improper fraction: 5 1/5 = 5 1/5 = 5 · 5 + 1/5 = 25 + 1/5 = 26/5

To find new numerator:
a) Multiply the whole number 5 by the denominator 5. Whole number 5 equally 5 * 5/5 = 25/5
b) Add the answer from previous step 25 to the numerator 1. New numerator is 25 + 1 = 26
c) Write a previous answer (new numerator 26) over the denominator 5.

Five and one fifth is twenty-six fifths
2. Divide: 3/4 : 26/5 = 3/4 · 5/26 = 3 · 5/4 · 26 = 15/104
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 26/5 is 5/26) 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 - three quarters divided by twenty-six fifths = fifteen one-hundred fourths.

#### 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:

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:

• Camp In the camp are children. 1/2 went on a trip, 1/4 went to bathe, and 38 children remained in the room. How many children are in the camp?
• Julian 2 Julian and two of his friends are going to share 1/4 of a pizza. How much will each person get?
• Reciprocals Which among the given reciprocal is correct a. 3/15x1/3= 1 b. 3/20x20/3=1 c. 7/14x7/7=1 d. 34/3x34/34=1
• Almonds Rudi has 4 cups of almonds. His trail mix recipe calls for 2/3 cup of almonds. How many batches of trail mix can he make? Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
• 6/24 change 6/24 change to a fraction in lowest terms
• Mrs. Zarka Mrs. Zarka has 3 pies for a party. She calculates that if she splits the pies evenly among the guests, they will each receive 1/6 of a pie. How many guests are there?
• Divide 11 Divide the product of 4 and 5/8 by 1 1/2. Write your answer as a mixed number.
• Fruit punch Kelly made fruit punch to serve at a party for her chess team. She mixed 1 2/5  liters of cranberry juice and 1 3/5  liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each
• Chestnuts Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of
• Leaking swimming pool Between 10 P. M. and 7:10 A. M. , the water level in a swimming pool decreased by 5/12 inches . Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
• Product of two fractions Product of two fractions is 9 3/5 . If one of the fraction is 9 3/7. Find the other fraction.
• Balls The boys changed stamps, beads and balls. For 9 balls is 3 stamps, 2 balls is 44 stamps. How many beads is for 1 ball?