# Prove By Mathematical Induction, 1

This calculator performs basic và advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

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Conversion a mixed number 3 một nửa to a improper fraction: 3 1/2 = 3 một nửa = 3 · 2 + 1/2 = 6 + 1/2 = 7/2To find a new numerator:a) Multiply the whole number 3 by the denominator 2. Whole number 3 equally 3 * 2/2 = 6/2b) địa chỉ the answer from previous step 6 khổng lồ the numerator 1. New numerator is 6 + 1 = 7c) Write a previous answer (new numerator 7) over the denominator 2.Three & one half is seven halfs Conversion a mixed number 2 2/3 to lớn a improper fraction: 2 2/3 = 2 2/3 = 2 · 3 + 2/3 = 6 + 2/3 = 8/3To find a new numerator:a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3b) showroom the answer from previous step 6 khổng lồ the numerator 2. New numerator is 6 + 2 = 8c) Write a previous answer (new numerator 8) over the denominator 3.Two và two thirds is eight thirds
Rules for expressions with fractions: Fractions - use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole và fraction parts.Mixed numerals (mixed numbers or fractions) keep one space between the integer andfraction and use a forward slash to đầu vào fractions i.e., 12/3 . An example of a negative mixed fraction: -5 1/2.Because slash is both signs for fraction line & division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.Decimals (decimal numbers) enter with a decimal point .

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và they are automatically converted khổng lồ fractions - i.e. 1.45.

### Math Symbols

SymbolSymbol nameSymbol MeaningExample
-minus signsubtraction 1 một nửa - 2/3
*asteriskmultiplication 2/3 * 3/4
×times signmultiplication 2/3 × 5/6
:division signdivision 1/2 : 3
/division slashdivision 1/3 / 5
:coloncomplex fraction 1/2 : 1/3
^caretexponentiation / power 1/4^3
()parenthesescalculate 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: một nửa : 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 và fraction: 5 ÷ 1/2• complex fractions: 5/8 : 2 2/3• decimal to lớn 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 và 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: ba phần tư of 5/7• fractions multiple: 2/3 of 3/5• divide to lớn find the quotient: 3/5 ÷ 2/3
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.

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MDAS - Multiplication & Division have the same precedence over Addition và Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule. Be careful; always do multiplication và division before addition & subtraction. Some operators (+ and -) and (* and /) has the same priority & then must evaluate from left khổng lồ right.