1 + 5/8 + 1/2 = 17/8 = 2 1/8 = 2.125; Result written as: an improper fraction, a mixed number (also called a mixed fraction) and a decimal number. Ordinary (simple, common) math fractions added, adition results explained below

Executed (ordinary fractions) operation:
1 + 5/8 + 1/2

Reduce (simplify) fractions to their lowest terms equivalents:

Fraction: 5/8 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:
5 is a prime number and 8 = 23;


Fraction: 1/2 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:
1 cannot be prime factorized and 2 is a prime number;

Calculate LCM, the lowest common multiple of the reduced fractions' denominators, this will be the common denominator of fractions, also called LCD, the lowest common denominator:

Denominators' prime factorization:


8 = 23;

2 is a prime number;

For LCM, take all the unique prime factors, by the largest exponents:


LCM (8; 2) = 23 = 8

Each fraction's expanding number (divide LCM by each fraction's denominator):

For fraction 5/8 is 8 ÷ 8 = 1;


For fraction 1/2 is 8 ÷ 2 = 23 ÷ 2 = 4;

Expand fractions, build up each fraction by multiplying its numerator and denominator by its expanding number so the denominator is built up to the LCM, then work with numerators:

1 + 5/8 + 1/2 =
1 + (1 * 5)/(1 * 8) + (4 * 1)/(4 * 2) =
1 + 5/8 + 4/8 =
1 + (5 + 4)/8 =
1 + 9/8

Reduce (simplify) fraction to its lowest terms equivalent:

9/8 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:
9 = 32 and 8 = 23;

Improper fraction, rewrite:

1 + 9/8 = (1 * 8)/8 + 9/8 = (1 * 8 + 9)/8 = 17/8 as an improper fraction.


17 ÷ 8 = 2 and remainder = 1 =>
17/8 = (2 * 8 + 1) / 8 = 2 + 1/8 = 2 1/8 as a mixed number (also called a mixed fraction).


2 + 1 ÷ 8 = 2.125 as a decimal number.

Final answer:
:: written in three ways ::

As an improper fraction:
1 + 5/8 + 1/2 = 17/8

As a mixed number (also called a mixed fraction):
1 + 5/8 + 1/2 = 2 1/8

As a decimal number:
1 + 5/8 + 1/2 = 2.125

Writing numbers: point '.' used as a decimal mark;

Symbols: / fraction line; ÷ divide; * multiply; + plus; = equal;

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