Multiplying Fractions with Common
Factors
The Importance of Fraction Reduction
Fraction reduction is crucial when multiplying fractions with common
factors. It simplifies the fractions, making the multiplication process
simpler and the final answer easier to understand.
Simplifying Fractions through Multiplication
When multiplying fractions that have common factors, it is important to
first identify and reduce the common factors. This can be done by
dividing both the numerator and the denominator of each fraction by
their greatest common divisor (GCD). The product of the simplified
fractions is equivalent to the product of the original fractions, but is in a
simpler form.
Example:
Multiply the fractions 4/6 and 10/12.
1. Identify the common factors in the fractions: 2 is a common
factor in both the numerator and denominator of each fraction.
2. Divide both the numerator and denominator of each fraction by
their GCD: 4/6 simplifies to 2/3 (GCD of 4 and 6 is 2), and
10/12 simplifies to 5/6 (GCD of 10 and 12 is 2).
3. Multiply the simplified fractions: 2/3 * 5/6 = 10/18.
4. Simplify the final answer: The GCD of 10 and 18 is 2, so the final
answer is 5/9.
In conclusion, when multiplying fractions with common factors, it is
important to first reduce the fractions to their simplest form. This
Factors
The Importance of Fraction Reduction
Fraction reduction is crucial when multiplying fractions with common
factors. It simplifies the fractions, making the multiplication process
simpler and the final answer easier to understand.
Simplifying Fractions through Multiplication
When multiplying fractions that have common factors, it is important to
first identify and reduce the common factors. This can be done by
dividing both the numerator and the denominator of each fraction by
their greatest common divisor (GCD). The product of the simplified
fractions is equivalent to the product of the original fractions, but is in a
simpler form.
Example:
Multiply the fractions 4/6 and 10/12.
1. Identify the common factors in the fractions: 2 is a common
factor in both the numerator and denominator of each fraction.
2. Divide both the numerator and denominator of each fraction by
their GCD: 4/6 simplifies to 2/3 (GCD of 4 and 6 is 2), and
10/12 simplifies to 5/6 (GCD of 10 and 12 is 2).
3. Multiply the simplified fractions: 2/3 * 5/6 = 10/18.
4. Simplify the final answer: The GCD of 10 and 18 is 2, so the final
answer is 5/9.
In conclusion, when multiplying fractions with common factors, it is
important to first reduce the fractions to their simplest form. This
