Menu Subtract fractions: - ^{104} /_{1,990} + ^{23} /_{10} = ? Subtraction of ordinary (simple, common) fractions, result explained
- ^{104} /_{1,990} + ^{23} /_{10} = ? Reduce (simplify) fractions to their lowest terms equivalents: To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF.
Fraction: - ^{104} /_{1,990} = - ^{(23 × 13)} /_{(2 × 5 × 199)} = - ^{((23 × 13) ÷ 2)} /_{((2 × 5 × 199) ÷ 2)} = - ^{52} /_{995} ; Fraction: ^{23} /_{10} already reduced to the lowest terms. The numerator and denominator have no common prime factors. Their prime factorization: 23 is a prime number; 10 = 2 × 5; gcf (23; 2 × 5) = 1; Rewrite the equivalent simplified operation:
- ^{104} /_{1,990} + ^{23} /_{10} = - ^{52} /_{995} + ^{23} /_{10} Rewrite the improper fractions:
Fraction : ^{23} /_{10} 23 ÷ 10 = 2 and remainder = 3 => 23 = 2 × 10 + 3 ^{23} /_{10} = ^{(2 × 10 + 3)} /_{10} = ^{(2 × 10)} /_{10} + ^{3} /_{10} = 2 + ^{3} /_{10} ;
Rewrite the equivalent simplified operation:
- ^{52} /_{995} + ^{23} /_{10} = - ^{52} /_{995} + 2 + ^{3} /_{10} = 2 - ^{52} /_{995} + ^{3} /_{10} To operate fractions, build up their denominators the same. Calculate LCM, the least common multiple of the denominators of the fractions: LCM will be the common denominator of the fractions that we work with.
The prime factorization of the denominators: 995 = 5 × 199; 10 = 2 × 5; Multiply all the unique prime factors, by the largest exponents: LCM (995; 10) = 2 × 5 × 199 = 1,990 Calculate the expanding number of each fraction:
Divide LCM by the numerator of each fraction. For fraction: - ^{52} /_{995} is 1,990 ÷ 995 = (2 × 5 × 199) ÷ (5 × 199) = 2; For fraction: ^{3} /_{10} is 1,990 ÷ 10 = (2 × 5 × 199) ÷ (2 × 5) = 199;
Build up the fractions to the same denominator:
Expand each fraction - multiply the numerator and denominator by the expanding number. Then work with the numerators of the fractions.
2 - ^{52} /_{995} + ^{3} /_{10} = 2 - ^{(2 × 52)} /_{(2 × 995)} + ^{(199 × 3)} /_{(199 × 10)} = 2 - ^{104} /_{1,990} + ^{597} /_{1,990} = 2 + ^{( - 104 + 597)} /_{1,990} = 2 + ^{493} /_{1,990} Reduce (simplify) the fraction to its lowest terms equivalent: To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF.
^{493} /_{1,990} already reduced to the lowest terms. The numerator and denominator have no common prime factors. Their prime factorization: 493 = 17 × 29; 1,990 = 2 × 5 × 199; gcf (17 × 29; 2 × 5 × 199) = 1; Rewrite the expression: As a mixed number (also called a mixed fraction):
Mixed number = a whole number and a proper fraction, of the same sign. Proper fraction = numerator smaller than denominator. 2 + ^{493} /_{1,990} = 2 ^{493} /_{1,990}
As a positive improper fraction (numerator >= denominator):
2 + ^{493} /_{1,990} = ^{(2 × 1,990)} /_{1,990} + ^{493} /_{1,990} = ^{(2 × 1,990 + 493)} /_{1,990} = ^{4,473} /_{1,990} As a decimal number:
2 + ^{493} /_{1,990} = 2 + 493 ÷ 1,990 ≈ 2.247738693467 ≈ 2.25 As a percentage:
2.247738693467 = 2.247738693467 × ^{100} /_{100} = ^{(2.247738693467 × 100)} /_{100} = ^{224.773869346734} /_{100} ≈ 224.773869346734% ≈ 224.77% The final answer: :: written in four ways ::
As a mixed number (also called a mixed fraction): - ^{104} /_{1,990} + ^{23} /_{10} = 2 ^{493} /_{1,990} As a positive improper fraction (numerator >= denominator): - ^{104} /_{1,990} + ^{23} /_{10} = ^{4,473} /_{1,990} As a decimal number: - ^{104} /_{1,990} + ^{23} /_{10} ≈ 2.25 As a percentage: - ^{104} /_{1,990} + ^{23} /_{10} ≈ 224.77% More operations of this kind: Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark; numbers rounded to max. 12 decimals (whenever the case); Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; ≈ approximation; Subtract ordinary fractions, online calculator The latest subtracted fractions How to: Subtracting ordinary (simple, common) math fractions. Steps. There are two cases regarding the denominators when we subtract ordinary fractions:
A. the fractions have like denominators; B. the fractions have unlike denominators.
A. How to subtract ordinary fractions that have like denominators?
Simply subtract the numerators of the fractions. The denominator of the resulting fraction will be the common denominator of the fractions. Reduce the resulting fraction.
An example of subtracting ordinary fractions that have like denominators, with explanations ^{3} /_{18} + ^{4} /_{18} - ^{5} /_{18} = ^{(3 + 4 - 5)} /_{18} = ^{2} /_{18} ; We simply subtracted the numerators of the fractions: 3 + 4 - 5 = 2; The denominator of the resulting fraction is: 18; The resulting fraction is being reduced as: ^{2} /_{18} = ^{(2 ÷ 2)} /_{(18 ÷ 2)} = ^{1} /_{9} . B. To subtract fractions with different denominators (unlike denominators), build up the fractions to the same denominator. How is it done? 1. Reduce the fractions to the lowest terms (simplify them). Factor the numerator and the denominator of each fraction, break them down to prime factors (run their prime factorization). Calculate GCF, the greatest common factor of the numerator and of the denominator of each fraction. GCF is the product of all the unique common prime factors of the numerator and of the denominator, multiplied by the lowest exponents. Divide the numerator and the denominator of each fraction by their GCF - after this operation the fraction is reduced to its lowest terms equivalent. 2. Calculate the least common multiple, LCM, of all the fractions' new denominators: LCM is going to be the common denominator of the added fractions, also called the lowest common denominator (the least common denominator) . Factor all the new denominators of the reduced fractions (run the prime factorization). The least common multiple, LCM, is the product of all the unique prime factors of the denominators, multiplied by the largest exponents. 3. Calculate each fraction's expanding number: The expanding number is the non-zero number that will be used to multiply both the numerator and the denominator of each fraction, in order to build all the fractions up to the same common denominator. Divide the least common multiple, LCM, calculated above, by the denominator of each fraction, in order to calculate each fraction's expanding number. 4. Expand each fraction: Multiply each fraction's both numerator and denominator by the expanding number. At this point, fractions are built up to the same denominator. 5. Subtract the fractions: In order to subtract all the fractions simply subtract all the fractions' numerators. The end fraction will have as a denominator the least common multiple, LCM, calculated above. 6. Reduce the end fraction to the lowest terms, if needed. More on ordinary (common) math fractions theory: