Multiply 5/12 times 2. Write the answer in simplest form.
The Correct Answer and Explanation is :
To multiply ( \frac{5}{12} \times 2 ), follow these steps:
Step 1: Convert the whole number to a fraction
The number 2 can be written as ( \frac{2}{1} ) because any whole number can be expressed as a fraction with a denominator of 1.
Step 2: Multiply the fractions
Now you can multiply the fractions:
[
\frac{5}{12} \times \frac{2}{1} = \frac{5 \times 2}{12 \times 1} = \frac{10}{12}
]
Step 3: Simplify the fraction
To simplify ( \frac{10}{12} ), find the greatest common divisor (GCD) of 10 and 12. The factors of 10 are 1, 2, 5, and 10, and the factors of 12 are 1, 2, 3, 4, 6, and 12. The greatest common divisor is 2.
Now, divide both the numerator and the denominator of ( \frac{10}{12} ) by 2:
[
\frac{10}{12} = \frac{10 \div 2}{12 \div 2} = \frac{5}{6}
]
So, ( \frac{5}{12} \times 2 = \frac{5}{6} ).
Explanation:
When multiplying fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together. In this case, ( 5 \times 2 = 10 ) and ( 12 \times 1 = 12 ), giving us ( \frac{10}{12} ). To express the result in its simplest form, you must divide both the numerator and denominator by their greatest common factor (GCD). For 10 and 12, the GCD is 2, so after simplifying, the result is ( \frac{5}{6} ).
Final Answer:
The answer to ( \frac{5}{12} \times 2 ) is ( \frac{5}{6} ).