7 + 11/18 - 4 + 1/15 = 331/90 = 3 61/90 = 3.67777777778; Result written as: an improper fraction, a mixed number (also called a mixed fraction) and a decimal number. Ordinary (simple, common) math fractions subtracted, subtraction results explained below

Executed (ordinary fractions) operation:
7 + 11/18 - 4 + 1/15

Reduce (simplify) fractions to their lowest terms equivalents:

Fraction: 11/18 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:
11 is a prime number and 18 = 2 * 32;


Fraction: 1/15 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:
1 cannot be prime factorized and 15 = 3 * 5;

Rewrite equivalent simplified operation:

7 + 11/18 - 4 + 1/15 =
3 + 11/18 + 1/15

LCM (lowest common multiple) of the reduced fractions' denominators will be the common denominator of the fractions we work with:

Denominators' prime factorization:


18 = 2 * 32;

15 = 3 * 5;

For LCM, take all the unique prime factors, by the highest powers:


LCM (18; 15) = 2 * 32 * 5 = 90

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

For fraction 11/18 is 90 ÷ 18 = (2 * 32 * 5) ÷ (2 * 32) = 5;


For fraction 1/15 is 90 ÷ 15 = (2 * 32 * 5) ÷ (3 * 5) = 6;

Expand fractions to make the denominators the same, then work with numerators:

3 + 11/18 + 1/15 =
3 + (5 * 11)/(5 * 18) + (6 * 1)/(6 * 15) =
3 + 55/90 + 6/90 =
3 + (55 + 6)/90 =
3 + 61/90

Reduce (simplify) fraction to its lowest terms equivalent:

61/90 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:
61 is a prime number and 90 = 2 * 32 * 5;

Rewrite result:

3 + 61/90 = 3 61/90 as a mixed number (also called a mixed fraction).
Rewrite the mixed number (also called a mixed fraction) as an improper fraction:
3 + 61/90 = (3 * 90)/90 + 61/90 = (3 * 90 + 61)/90 = 331/90 as an improper fraction.


3 + 61 ÷ 90 = 3.67777777778 as a decimal number.

Final answer:
:: written in three ways ::

As an improper fraction:
7 + 11/18 - 4 + 1/15 = 331/90

As a mixed number (also called a mixed fraction):
7 + 11/18 - 4 + 1/15 = 3 61/90

As a decimal number:
7 + 11/18 - 4 + 1/15 = 3.67777777778

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

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

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