Reduce (simplify) fractions to their lowest terms equivalents:
There are numerators and denominators of equal values.
Fraction: 7/7 = 1
Rewrite the equivalent simplified operation:
Multiplication by one (1) does not change the final result of the operation.
7/7 × 8/16 × 16/7 × 9/15 =
1 × 8/16 × 16/7 × 9/15 =
8/16 × 16/7 × 9/15
These fractions reduce each other.
They have numerators and denominators of equal values:
Fractions: 8/16 × 16/7 = 8/7
Rewrite the equivalent simplified operation:
8/16 × 16/7 × 9/15 =
8/7 × 9/15
Reduce (simplify) fractions to their lowest terms equivalents:
Factor all the numbers in order to easily reduce (simplify) the end fraction.
Fraction: 8/7 already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
8 = 23;
7 is a prime number, it cannot be factored into other prime factors;
Fraction: 9/15 =
32/(3 × 5) =
(32 ÷ 3)/((3 × 5) ÷ 3) =
(32 ÷ 3)/(3 ÷ 3 × 5) =
3(2 - 1)/(1 × 5) =
31/(1 × 5) =
3/(1 × 5) =
3/5;
Rewrite the equivalent simplified operation:
8/7 × 9/15 =
8/7 × 3/5
Multiply the numerators and denominators of the fractions separately:
8/7 × 3/5 =
(8 × 3) / (7 × 5) =
(23 × 3) / (7 × 5) =
(23 × 3) / (5 × 7)
Reduce (simplify) the fraction to its lowest terms equivalent:
Calculate the greatest common factor, GCF:
Multiply all the common prime factors, by the lowest exponents.
But, the numerator and denominator have no common factors.
gcf(23 × 3; 5 × 7) = 1
Divide the numerator and denominator by GCF.
The numerator and denominator of the fraction are coprime numbers (no common prime factors, GCF = 1). The fraction cannot be reduced (simplified): irreducible fraction.
(23 × 3) / (5 × 7) =
24/35
Rewrite the fraction