Multiply. Write your answer as a fraction in simplest form 9/10 x 2/3
The Correct Answer and Explanation is:
To multiply two fractions, follow these steps:
Step 1: Multiply the numerators.
The numerator is the top number of a fraction. In this case, the numerators of ( \frac{9}{10} ) and ( \frac{2}{3} ) are 9 and 2, respectively. To begin, multiply these two numbers:
[
9 \times 2 = 18
]
Step 2: Multiply the denominators.
The denominator is the bottom number of a fraction. For ( \frac{9}{10} ) and ( \frac{2}{3} ), the denominators are 10 and 3, respectively. Multiply these two numbers:
[
10 \times 3 = 30
]
Step 3: Write the product as a fraction.
Now, place the product of the numerators over the product of the denominators:
[
\frac{9}{10} \times \frac{2}{3} = \frac{18}{30}
]
Step 4: Simplify the fraction.
Next, simplify the fraction ( \frac{18}{30} ). To simplify, find the greatest common divisor (GCD) of 18 and 30. The factors of 18 are ( 1, 2, 3, 6, 9, 18 ), and the factors of 30 are ( 1, 2, 3, 5, 6, 10, 15, 30 ). The greatest common divisor of 18 and 30 is 6.
Now, divide both the numerator and the denominator by 6:
[
\frac{18 \div 6}{30 \div 6} = \frac{3}{5}
]
Thus, the simplified form of ( \frac{18}{30} ) is ( \frac{3}{5} ).
Final Answer:
The result of multiplying ( \frac{9}{10} ) by ( \frac{2}{3} ) is ( \frac{3}{5} ).
Explanation:
Multiplying fractions is straightforward: multiply the numerators to get the new numerator and multiply the denominators to get the new denominator. After that, simplifying the fraction ensures the result is in its simplest form. In this case, after performing the necessary multiplication, we found that ( \frac{18}{30} ) simplifies to ( \frac{3}{5} ) by dividing both the numerator and the denominator by their greatest common divisor.