The three different notations express the same ratio of 1.5-inch screws to 2.5-inch screws using different formats, as requested.
How did we arrive at this assertion?
1. Colon Notation (a:b):
- The ratio of 1.5-inch screws to 2.5-inch screws is
.
- This is derived from the quantities given: 36 screws that are 1.5 inches long and 12 screws that are 2.5 inches long.
2. Fraction Notation (a/b):
- The ratio of 1.5-inch screws to 2.5-inch screws is
.
- This is obtained by placing the quantity of 1.5-inch screws (36) as the numerator and the quantity of 2.5-inch screws (12) as the denominator.
3. Word Notation:
- The ratio of 1.5-inch screws to 2.5-inch screws is "36 to 12".
- This is a verbal representation of the relationship between the two quantities.
In summary, the three different notations express the same ratio of 1.5-inch screws to 2.5-inch screws using different formats, as requested.
Complete question:
A carpenter needs 36 screws that are 1.5 inches long, 24 screws that are 2 inches long, and 12 screws that are 2.5 inches long. There are three different sized screws shown. The screws are marked as two and a half inches, two inches, and one and a half inches. What is the ratio of 1.5-inch screws to 2.5-inch screws, written in three different ways? Do not reduce.