- 108/5,469 + 102/17 = ? Subtracting Common (Ordinary) Fractions, Online Calculator. Subtraction Operation Explained Step by Step
Fractions' subtraction: - 108/5,469 + 102/17 = ?
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
- To reduce a fraction to its lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.
- * Why do we reduce (simplify) the fractions?
- By reducing the values of the numerators and denominators of fractions, further calculations with these fractions become easier to do.
- A fraction that was reduced (simplified) to the lowest terms is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.
* * *
The fraction: - 108/5,469
- The prime factorizations of the numerator and denominator:
- 108 = 22 × 33
- 5,469 = 3 × 1,823
- Multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).
- GCF (108; 5,469) = 3
- 108/5,469 = - (108 ÷ 3)/(5,469 ÷ 3) = - 36/1,823
Yet another method to simplify the fraction:
- Without calculating GCF, factor the numerator and denominator and cross out all the common prime factors.
- 108/5,469 = - (22 × 33)/(3 × 1,823) = - ((22 × 33) ÷ 3)/((3 × 1,823) ÷ 3) = - 36/1,823
The fraction: 102/17
- 102 = 2 × 3 × 17
- 17 is a prime number
- GCF (102; 17) = 17
102/17 = (102 ÷ 17)/(17 ÷ 17) = 6/1 = 6
- We could have simplified the fraction without calculating the GCF. Just factor the numerator and denominator and cross out the common prime factors.
102/17 = (2 × 3 × 17)/17 = ((2 × 3 × 17) ÷ 17)/(17 ÷ 17) = 6/1 = 6
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
- 108/5,469 + 102/17 =
- 36/1,823 + 6 =
6 - 36/1,823
Rewrite the result
As a positive improper fraction:
(the numerator >= the denominator)
- An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.
6 - 36/1,823 =
(6 × 1,823)/1,823 - 36/1,823 =
(6 × 1,823 - 36)/1,823 =
10,902/1,823
As a mixed number (also called a mixed fraction):
- A mixed number: a whole number and a proper fraction, both having the same sign.
- A proper fraction: the value of the numerator is smaller than the value of the denominator.
- Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:
10,902 ÷ 1,823 = 5 and the remainder = 1,787 ⇒
10,902 = 5 × 1,823 + 1,787 ⇒
10,902/1,823 =
(5 × 1,823 + 1,787)/1,823 =
(5 × 1,823)/1,823 + 1,787/1,823 =
5 + 1,787/1,823 =
5 1,787/1,823
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
5 + 1,787/1,823 =
5 + 1,787 ÷ 1,823 ≈
5.980252331322 ≈
5.98
As a percentage:
- A percentage value p% is equal to the fraction: p/100, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.
- To do that, multiply the number by the fraction 100/100.
- The value of the fraction 100/100 = 1, so by multiplying the number by this fraction the result is not changing, only the form.