What is the ratio 42 to 48 as a fraction in simplest form?
The correct answer and explanation is:
Correct Answer:
The ratio 42 to 48 as a fraction in simplest form is: 4248=78\frac{42}{48} = \frac{7}{8}
Explanation (300 Words):
To express a ratio as a fraction in simplest form, we begin by writing the ratio as a fraction: 4248\frac{42}{48}
The next step is to simplify the fraction by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). The GCD is the largest number that evenly divides both numbers.
Step 1: Find the GCD of 42 and 48.
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors of 42 and 48 are: 1, 2, 3, 6
The greatest of these is 6.
Step 2: Divide both the numerator and denominator by the GCD (6):
42÷648÷6=78\frac{42 \div 6}{48 \div 6} = \frac{7}{8}
So, the simplified form of the ratio 42:48 is 7:8, or as a fraction, 78\frac{7}{8}.
Understanding Ratios and Fractions:
A ratio compares two quantities. The ratio 42 to 48 means for every 42 of something, there are 48 of something else. When written as a fraction, it becomes 4248\frac{42}{48}, which helps us understand the proportion between the two numbers. Simplifying the fraction is important because it shows the most basic form of that relationship. It tells us that the same proportion could be represented with smaller, simpler numbers—7 to 8.
Simplifying fractions also makes them easier to compare, work with, and understand in real-world contexts like recipes, measurements, or statistics. So, always reduce ratios or fractions to their simplest form when possible.