51/74 + 41/74 = ? Adding Up Common (Ordinary) Fractions, Online Calculator. Addition Operation Explained Step by Step
Fractions' addition: 51/74 + 41/74 = ?
Perform the operation of calculating the fractions
All the fractions have equal denominators (the same denominator):
- This is the simplest and happiest case when we add or subtract fractions.
- We work only with their numerators and keep the common denominator.
51/74 + 41/74 =
(51 + 41)/74 =
92/74
Reduce (simplify) the fraction to its lowest terms equivalent:
- To reduce a fraction to its lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.
- 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.
Calculate the greatest common factor, GCF,
of the numerator and denominator of the fraction:
- The prime factorizations of the numerator and denominator:
- 92 = 22 × 23
- 74 = 2 × 37
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 (92; 74) = GCF (22 × 23; 2 × 37) = 2
The fraction can be reduced (simplified):
Divide both the numerator and denominator by their greatest common factor, GCF.
92/74 =
(92 ÷ 2)/(74 ÷ 74) =
46/37
We could have simplified the fraction without calculating the GCF. Just factor the numerator and denominator and cross out the common prime factors.
92/74 =
(22 × 23)/(2 × 37) =
((22 × 23) ÷ 2)/((2 × 37) ÷ 2) =
(2 × 23)/37 =
46/37
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
92/74 =
46/37
Rewrite the fraction
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:
46 ÷ 37 = 1 and the remainder = 9 ⇒
46 = 1 × 37 + 9 ⇒
46/37 =
(1 × 37 + 9)/37 =
(1 × 37)/37 + 9/37 =
1 + 9/37 =
1 9/37
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
1 + 9/37 =
1 + 9 ÷ 37 ≈
1.243243243243 ≈
1.24
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.
1.243243243243 =
1.243243243243 × 100/100 =
(1.243243243243 × 100)/100 =
124.324324324324/100 ≈
124.324324324324% ≈
124.32%
External link » Convert and write integer and decimal numbers, fractions and ratios as percentages, online calculator
The final answer:
:: written in four ways ::
As a positive improper fraction:
(the numerator >= the denominator)
51/74 + 41/74 = 46/37
As a mixed number (also called a mixed fraction):
51/74 + 41/74 = 1 9/37
As a decimal number:
51/74 + 41/74 ≈ 1.24
As a percentage:
51/74 + 41/74 ≈ 124.32%
How are the numbers written: comma ',' used as a thousands separator; point '.' as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The symbols used: '/' fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.