3/4 • 5/6 = In simplest form
The Correct Answer and Explanation is:
To solve ( \frac{3}{4} \times \frac{5}{6} ), follow these steps:
Step 1: Multiply the numerators
First, multiply the two numerators together:
[
3 \times 5 = 15
]
Step 2: Multiply the denominators
Next, multiply the two denominators together:
[
4 \times 6 = 24
]
Thus, the product of the fractions is:
[
\frac{15}{24}
]
Step 3: Simplify the fraction
Now, simplify the fraction ( \frac{15}{24} ). To do this, find the greatest common divisor (GCD) of the numerator (15) and the denominator (24). The factors of 15 are 1, 3, 5, and 15, while the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest common factor between 15 and 24 is 3.
Divide both the numerator and the denominator by their GCD (3):
[
\frac{15}{24} \div \frac{3}{3} = \frac{15 \div 3}{24 \div 3} = \frac{5}{8}
]
Thus, the simplified form of ( \frac{15}{24} ) is ( \frac{5}{8} ).
Final Answer:
The correct simplified form of ( \frac{3}{4} \times \frac{5}{6} ) is ( \frac{5}{8} ).
Explanation:
Multiplying fractions involves multiplying the numerators together and the denominators together, which gives the product of the fractions. However, the result must be simplified if possible. Simplification involves finding the GCD of the numerator and denominator and dividing both by that number to reduce the fraction to its simplest form. In this case, simplifying ( \frac{15}{24} ) by dividing both terms by 3 yields the final simplified answer ( \frac{5}{8} ), which is the most reduced form of the product.