Question

find the sum 1/10+1/40+1/88+1/154+1/238

Answer 1

Reduce (simplify) fractions to their lowest terms equivalents:

Fraction: 1/10 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization: 
1 cannot be prime factorized and 10 = 2 * 5;

Fraction: 1/40 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization: 
1 cannot be prime factorized and 40 = 23 * 5;

Fraction: 1/88 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization: 
1 cannot be prime factorized and 88 = 23 * 11;

Fraction: 1/154 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization: 
1 cannot be prime factorized and 154 = 2 * 7 * 11;

Fraction: 1/238 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization: 
1 cannot be prime factorized and 238 = 2 * 7 * 17;

Fraction: 1/340 already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization: 
1 cannot be prime factorized and 340 = 22 * 5 * 17;

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:

10 = 2 * 5;

40 = 23 * 5;

88 = 23 * 11;

154 = 2 * 7 * 11;

238 = 2 * 7 * 17;

340 = 22 * 5 * 17;

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

LCM (10; 40; 88; 154; 238; 340) = 23 * 5 * 7 * 11 * 17 = 52,360

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

For fraction 1/10 is 52,360 ÷ 10 = (23 * 5 * 7 * 11 * 17) ÷ (2 * 5) = 5,236;

For fraction 1/40 is 52,360 ÷ 40 = (23 * 5 * 7 * 11 * 17) ÷ (23 * 5) = 1,309;

For fraction 1/88 is 52,360 ÷ 88 = (23 * 5 * 7 * 11 * 17) ÷ (23 * 11) = 595;

For fraction 1/154 is 52,360 ÷ 154 = (23 * 5 * 7 * 11 * 17) ÷ (2 * 7 * 11) = 340;

For fraction 1/238 is 52,360 ÷ 238 = (23 * 5 * 7 * 11 * 17) ÷ (2 * 7 * 17) = 220;

For fraction 1/340 is 52,360 ÷ 340 = (23 * 5 * 7 * 11 * 17) ÷ (22 * 5 * 17) = 154;

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:

1/10 + 1/40 + 1/88 + 1/154 + 1/238 + 1/340 =

(5,236 * 1)/(5,236 * 10) + (1,309 * 1)/(1,309 * 40)+ (595 * 1)/(595 * 88) + (340 * 1)/(340 * 154) +(220 * 1)/(220 * 238) + (154 * 1)/(154 * 340) =5,236/52,360 + 1,309/52,360 + 595/52,360 +340/52,360 + 220/52,360 + 154/52,360 =(5,236 + 1,309 + 595 + 340 + 220 + 154)/52,360 =7,854/52,360

Reduce (simplify) fraction to its lowest terms equivalent:

7,854/52,360 = (2 * 3 * 7 * 11 * 17)/(23 * 5 * 7 * 11 * 17) = ((2 * 3 * 7 * 11 * 17) ÷ (2 * 7 * 11 * 17))/((23 * 5 * 7 * 11 * 17) ÷ (2 * 7 * 11 * 17)) = 3/20;

Rewrite result:

3 ÷ 20 = 0.15 as a decimal number.

Final answer: 
:: written in two ways ::

As a proper fraction: 
1/10 + 1/40 + 1/88 + 1/154 + 1/238 +1/340 = 3/20 

As a decimal number: 
1/10 + 1/40 + 1/88 + 1/154 + 1/238 +1/340 = 0.15

Answer 2

I hope it will help you