Fraction calculator

This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.

The result:

7 1/4 ÷ 1 7/8 = 58/15 = 3 13/15 ≅ 3.8666667

The spelled result in words is fifty-eight fifteenths (or three and thirteen fifteenths).

How do we solve fractions step by step?

Conversion a mixed number 7 1/4 to a improper fraction: 7 1/4 = 7 1/4 = 7 · 4 + 1/4 = 28 + 1/4 = 29/4

To find a new numerator:
a) Multiply the whole number 7 by the denominator 4. Whole number 7 equally 7 * 4/4 = 28/4
b) Add the answer from the previous step 28 to the numerator 1. New numerator is 28 + 1 = 29
c) Write a previous answer (new numerator 29) over the denominator 4.

Seven and one quarter is twenty-nine quarters.
Conversion a mixed number 1 7/8 to a improper fraction: 1 7/8 = 1 7/8 = 1 · 8 + 7/8 = 8 + 7/8 = 15/8

To find a new numerator:
a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8/8 = 8/8
b) Add the answer from the previous step 8 to the numerator 7. New numerator is 8 + 7 = 15
c) Write a previous answer (new numerator 15) over the denominator 8.

One and seven eighths is fifteen eighths.
Divide: 29/4 : 15/8 = 29/4 · 8/15 = 29 · 8/4 · 15 = 232/60 = 4 · 58 /4 · 15 = 58/15
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 15/8 is 8/15) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 4 gives 58/15.
In other words - twenty-nine quarters divided by fifteen eighths is fifty-eight fifteenths.

Rules for expressions with fractions:

Fractions - write a forward slash to separate the numerator and the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.

Mixed numerals (mixed numbers or fractions) - keep one space between the whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . and they are automatically converted to fractions - i.e. 1.45.

Math Symbols

Symbol	Symbol name	Symbol Meaning	Example
+	plus sign	addition	1/2 + 1/3
-	minus sign	subtraction	1 1/2 - 2/3
*	asterisk	multiplication	*2/3 3/4**
×	times sign	multiplication	2/3 × 5/6
:	division sign	division	1/2 : 3
/	division slash	division	1/3 / 5
:	colon	complex fraction	1/2 : 1/3
^	caret	exponentiation / power	1/4^3
()	parentheses	calculate expression inside first	-3/5 - (-1/4)

The calculator follows well-known rules for the 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.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.