- 35/20,840 + 30/17 = ? Subtracting Common (Ordinary) Fractions, Online Calculator. Subtraction Operation Explained Step by Step
Fractions' subtraction: - 35/20,840 + 30/17 = ?
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: - 35/20,840
- The prime factorizations of the numerator and denominator:
- 35 = 5 × 7
- 20,840 = 23 × 5 × 521
- 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 (35; 20,840) = 5
- 35/20,840 = - (35 ÷ 5)/(20,840 ÷ 5) = - 7/4,168
Yet another method to simplify the fraction:
- Without calculating GCF, factor the numerator and denominator and cross out all the common prime factors.
- 35/20,840 = - (5 × 7)/(23 × 5 × 521) = - ((5 × 7) ÷ 5)/((23 × 5 × 521) ÷ 5) = - 7/4,168
The fraction: 30/17
30/17 is already reduced to the lowest terms.
- The numerator and denominator have no common prime factors.
- Their prime factorization: 30 = 2 × 3 × 5
- 17 is a prime number
- GCF (2 × 3 × 5; 17) = 1
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
- 35/20,840 + 30/17 =
- 7/4,168 + 30/17
Rewrite the improper fractions:
- An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.
- A proper fraction: the value of the numerator is smaller than the value of the denominator.
- Each improper fraction will be rewritten as a whole number and a proper fraction, both having the same sign: divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below.
- Why do we rewrite the improper fractions?
- By reducing the value of the numerator of a fraction the calculations are getting easier to perform.
The fraction: 30/17
30 ÷ 17 = 1 and the remainder = 13 ⇒ 30 = 1 × 17 + 13
30/17 = (1 × 17 + 13)/17 = (1 × 17)/17 + 13/17 = 1 + 13/17
Rewrite the equivalent simplified operation:
- 7/4,168 + 30/17 =
- 7/4,168 + 1 + 13/17 =
1 - 7/4,168 + 13/17
Perform the operation of calculating the fractions.
To add or subtract fractions we need them to have equal denominators (the same common denominator).
- To perform the operation of calculating the fractions we have to:
- 1) find their common denominator
- 2) then calculate the expanding number of each fraction
- 3) then make their denominators the same by expanding the fractions to equivalent forms - which all have equal denominators (the same denominator)
- * The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.
- The LCM will be the common denominator of the fractions that we work with.
1) Find the common denominator
Calculate the LCM of the denominators:
The prime factorization of the denominators:
4,168 = 23 × 521
17 is a prime number
Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).
LCM (4,168; 17) = 23 × 17 × 521 = 70,856
2) Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
- 7/4,168 ⟶ 70,856 ÷ 4,168 = (23 × 17 × 521) ÷ (23 × 521) = 17
13/17 ⟶ 70,856 ÷ 17 = (23 × 17 × 521) ÷ 17 = 4,168
3) Make fractions' denominators the same:
- Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above. This way all the fractions will have the same denominator.
- Then keep the common denominator and work only with the numerators of the fractions.
1 - 7/4,168 + 13/17 =
1 - (17 × 7)/(17 × 4,168) + (4,168 × 13)/(4,168 × 17) =
1 - 119/70,856 + 54,184/70,856 =
1 + ( - 119 + 54,184)/70,856 =
1 + 54,065/70,856
Reduce (simplify) the fraction to its lowest terms equivalent:
54,065/70,856 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
- Their prime factorization:
- 54,065 = 5 × 11 × 983
- 70,856 = 23 × 17 × 521
- GCF (5 × 11 × 983; 23 × 17 × 521) = 1
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the result
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.
1 + 54,065/70,856 = 1 54,065/70,856
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.
1 + 54,065/70,856 =
(1 × 70,856)/70,856 + 54,065/70,856 =
(1 × 70,856 + 54,065)/70,856 =
124,921/70,856
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
1 + 54,065/70,856 =
1 + 54,065 ÷ 70,856 ≈
1.763026419781 ≈
1.76
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.