Write the ratio 2 3/5 in simplest form
The Correct Answer and Explanation is:
To express the mixed number 2 3/5 as a ratio in its simplest form, follow these steps:
Step 1: Convert the mixed number to an improper fraction.
A mixed number like 2 3/5 consists of a whole number (2) and a fraction (3/5). To convert this to an improper fraction, we first multiply the whole number (2) by the denominator of the fraction (5), and then add the numerator (3) to this product:2×5=102 \times 5 = 102×5=1010+3=1310 + 3 = 1310+3=13
So, 2 3/5 becomes the improper fraction 13/5.
Step 2: Express the ratio.
The improper fraction 13/5 is already in the form of a ratio. A ratio is simply a comparison between two numbers, which we have here as 13 to 5 or 13/5.
Step 3: Check for simplification.
The fraction 13/5 is already in its simplest form because 13 is a prime number and does not divide 5. Therefore, no further simplification is needed.
Final Answer:
The ratio of 2 3/5 is 13/5.
Explanation:
In mathematical terms, when converting a mixed number to an improper fraction, we preserve the value of the number. This process is essential in many contexts, particularly when comparing, adding, or subtracting fractions, as improper fractions are easier to manipulate mathematically. In this case, the fraction 13/5 is the simplest form of the ratio, as the numerator and denominator share no common factors besides 1.
