Fraction Calculator - Calculation: 3 56/34-5 1/2

Fraction Calculator Enter fraction expression: 3 56/34-5 1/2 This fraction calculator performs all basic fraction operations – addition, subtraction, multiplication, and division – and evaluates expressions with fractions. Each calculation includes a detailed step-by-step explanation.

The result:

3 56/34 - 5 1/2 = -29/34 ≅ -0.8529412

Spelled out: minus twenty-nine thirty-fourths.

How do we solve fractions step by step?

1. Conversion a mixed number 3 56/34 to a improper fraction: 3 56/34 = 3 56/34 = 3 · 34 + 56/34 = 102 + 56/34 = 158/34To find a new numerator: a) Multiply the whole number 3 by the denominator 34. Whole number 3 equally 3 * 34/34 = 102/34 b) Add the answer from the previous step 102 to the numerator 56. New numerator is 102 + 56 = 158 c) Write a previous answer (new numerator 158) over the denominator 34.Three and fifty-six thirty-fourths is one hundred fifty-eight thirty-fourths.
2. Conversion a mixed number 5 1/2 to a improper fraction: 5 1/2 = 5 1/2 = 5 · 2 + 1/2 = 10 + 1/2 = 11/2To find a new numerator: a) Multiply the whole number 5 by the denominator 2. Whole number 5 equally 5 * 2/2 = 10/2 b) Add the answer from the previous step 10 to the numerator 1. New numerator is 10 + 1 = 11 c) Write a previous answer (new numerator 11) over the denominator 2.Five and a half is eleven halves.
3. Subtract: 158/34 - 11/2 = 158/34 - 11 · 17/2 · 17 = 158/34 - 187/34 = 158 - 187/34 = -29/34 It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(34, 2) = 34. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 34 × 2 = 68. In the following intermediate step, the fraction cannot be simplified further by canceling.In other words, one hundred fifty-eight thirty-fourths minus eleven halves equals minus twenty-nine thirty-fourths.

Rules for expressions with fractions:

Fractions - Use a forward slash to separate the numerator and denominator. For example, for five-hundredths, enter 5/100. Mixed numbers Leave one space between the whole number and the fraction part, and use a forward slash for the fraction. For example, enter 1 2/3 . For negative mixed numbers, write the negative sign before the whole number, such as -5 1/2. Division of fractions - Since the forward slash is used for both fraction lines and division, use a colon (:) to divide fractions. For example, to divide 1/2 by 1/3, enter 1/2 : 1/3. Decimals Enter decimal numbers using a decimal point (.), and they will be automatically converted to fractions. For example, enter 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)

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• reciprocal of a fraction: 1 : 3/4• square of a fraction: 2/3 ^ 2• cube of a fraction: 2/3 ^ 3• exponentiation of a fraction: 1/2 ^ 4• 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• square root of a fraction: sqrt(1/16)• expression with brackets: 1/3 * (1/2 - 3 3/8)• compound fraction: 3/4 of 5/7• multiplying fractions: 2/3 of 3/5• divide to find the quotient: 3/5÷2/3 Order of Operations Ever wondered why calculators don't just work left to right? This calculator follows the mathematical order of operations — a set of rules that ensures everyone solves expressions the same way, every time. Popular Memory Tricks Different regions use different mnemonics to remember this order: * PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction * BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction * BODMAS - Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction * GEMDAS - Grouping symbols (parentheses, brackets, braces: (){}), Exponents, Multiplication, Division, Addition, Subtraction The Golden Rules Rule 1: Multiplication and division always come before addition and subtraction. Think of them as the VIPs that skip to the front of the line! Rule 2: When operations have equal priority (like × and ÷, or + and −), work from left to right—just like reading a book. Rule 3: Parentheses change the natural order of evaluation of operations.

Fractions in word problems:

• From the intersection From the intersection to the school is 6/5 km, to the shop 9/10 km, to the bank 5/8 km, and to the park 21/8 km. Which place is closest to the intersection?
• Identify improper fraction How do you identify improper fractions? Which is improper: A) 3/4 B) 32/15 C) 3/9 D) 2 2/11
• The fuel The car's fuel was ¾ full at the beginning of the week. At the end of the week, there was ⅛ of a tank left. a. Did the car use more or less than ½ of a fuel tank? How do you know? b. How much more or less than ½ of a tank did it use? Show your work using
• Dividends The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most, and which got the least?
• For each For each pair of expressions, circle the greater product without finding the product. (write 1=left expression, 2=right expression) a. 3/4 x 2/3 and 3/4 x 1/2 b. 2/3 x 3 1/4 and 4/3 x 3 1/4 c. 3/8 x 3/8 and 3/8 x 1/2
• Buing Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK?
• Justify 50 bottles of red wine are purchased for a company party. In the first store, a bottle of wine costs €6.90. Here they have a promotion that when you buy 4 bottles, the fifth one is free. In the second store, the same bottle of wine costs €8.50. However, t

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Last Modified: March 6, 2026

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