37/2,737 + 70/25 = ? Adding ordinary (common) fractions, online calculator, addition operation explained in detail. The answer, written in four ways. As a mixed number. As a positive improper fraction (the numerator >= the denominator). As a decimal number. As a percentage.
37/2,737 + 70/25 = ?
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.
* Why do we try to reduce (simplify) the fractions?
By reducing the values of the numerators and the denominators of the fractions the calculations are easier to make.
A fully reduced (simplified) fraction 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: 37/2,737 is already reduced to the lowest terms. The numerator and denominator have no common prime factors. Their prime factorization: 37 is a prime number 2,737 = 7 × 17 × 23 GCF (37; 7 × 17 × 23) = 1
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: 14/5
14 ÷ 5 = 2 and the remainder = 4 => 14 = 2 × 5 + 4
14/5 = (2 × 5 + 4)/5 = (2 × 5)/5 + 4/5 = 2 + 4/5
Rewrite the equivalent simplified operation:
37/2,737 + 14/5 =
37/2,737 + 2 + 4/5 =
2 + 37/2,737 + 4/5
Perform the operation of calculating the fractions.
To add or subtract fractions we need them to have equal denominators (the same common denominator).
To calculate the fractions' operation we have to:
1) find their common denominator
2) then calculate the expanding number of each fraction
3) then build up 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:
2,737 = 7 × 17 × 23
5 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).
As a mixed number (also called a mixed fraction): 37/2,737 + 70/25 = 2 11,133/13,685
As a positive improper fraction: (the numerator >= the denominator) 37/2,737 + 70/25 = 38,503/13,685
As a decimal number: 37/2,737 + 70/25 ≈ 2.81
As a percentage: 37/2,737 + 70/25 ≈ 281.35%
How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.
Fractions subtractions: the latest fractions subtracted by the users
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.