# 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:

### 163/9 - 102/5 = 89/15 = 5 14/15 ≅ 5.9333333

Spelled result in words is eighty-nine fifteenths (or five and fourteen fifteenths).

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

1. Conversion a mixed number 16 3/9 to a improper fraction: 16 3/9 = 16 3/9 = 16 · 9 + 3/9 = 144 + 3/9 = 147/9

To find new numerator:
a) Multiply the whole number 16 by the denominator 9. Whole number 16 equally 16 * 9/9 = 144/9
b) Add the answer from previous step 144 to the numerator 3. New numerator is 144 + 3 = 147
c) Write a previous answer (new numerator 147) over the denominator 9.

Sixteen and three ninths is one hundred forty-seven ninths
2. Conversion a mixed number 10 2/5 to a improper fraction: 10 2/5 = 10 2/5 = 10 · 5 + 2/5 = 50 + 2/5 = 52/5

To find new numerator:
a) Multiply the whole number 10 by the denominator 5. Whole number 10 equally 10 * 5/5 = 50/5
b) Add the answer from previous step 50 to the numerator 2. New numerator is 50 + 2 = 52
c) Write a previous answer (new numerator 52) over the denominator 5.

Ten and two fifths is fifty-two fifths
3. Subtract: 147/9 - 52/5 = 147 · 5/9 · 5 - 52 · 9/5 · 9 = 735/45 - 468/45 = 735 - 468/45 = 267/45 = 3 · 89/3 · 15 = 89/15
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(9, 5) = 45. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 5 = 45. In the next intermediate step, , cancel by a common factor of 3 gives 89/15.
In words - one hundred forty-seven ninths minus fifty-two fifths = eighty-nine fifteenths.

#### 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:

• Circular garden
Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante
• Visit to grandfather
Shane's family traveled 3/10 of the distance to his grandfather’s house on Saturday. They traveled 4/7 of the remaining distance on Sunday. What fraction of the total distance to his grandfather’s house was traveled on Sunday?
• Lunch time
In a cafeteria, 3/10 of the students are eating salads, and 3/5 are eating sandwiches. There are 30 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
• The boy
The boy scouts spent 10/12 hour doing their daily exercises. They only used 1/4 hour in hiking. How much time did they use for other body exercises?
• Cereals
Ari and Joey share a 30-ounce box of cereal. By the end of the week, Ari has eaten 3/10 of the box, and Joey has eaten 3/5 of the box of cereal. How many ounces are left in the box?
To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?