Express 80 inches in standard notation using feet and inches. Select one: a. 1 yd 3 ft 8 in. b. 2 yd 8 in. c. 2 yd 8 ft d. 6 ft 10 in. Find the midpoint between 1.7 cm and 3.2 cm on a metric rule. Select one: a. 2.5 cm b. 4.9 cm c. 1.5 cm d. 2.45 cm
The Correct Answer and Explanation is:
Question 1: Express 80 inches in standard notation using feet and inches.
Given:
We are asked to convert 80 inches into feet and inches.
Step 1: Understand the relationship between inches and feet.
We know that:
- 1 foot = 12 inches.
Step 2: Convert inches into feet.
We divide the total inches by 12 to determine the number of feet: 80÷12=6 feet with a remainder.80 \div 12 = 6 \text{ feet with a remainder.}80÷12=6 feet with a remainder.
Step 3: Calculate the remainder inches. 12×6=72 inches12 \times 6 = 72 \text{ inches}12×6=72 inches 80−72=8 inches80 – 72 = 8 \text{ inches}80−72=8 inches
So, 80 inches is equal to 6 feet 8 inches.
Step 4: Compare to the options.
The correct option should say “6 ft 8 in.” but the closest and correctly formatted option is not listed. However, the closest matching correct option provided is:
Answer: d. 6 ft 10 in.
But this option is incorrect based on correct conversion. There seems to be an error in the provided options. The accurate conversion result is 6 ft 8 in.
Question 2: Find the midpoint between 1.7 cm and 3.2 cm on a metric rule.
Given:
Two measurements: 1.7 cm and 3.2 cm.
Step 1: Use the midpoint formula.
The midpoint between two numbers is found by: Midpoint=(a+b)2\text{Midpoint} = \frac{(a + b)}{2}Midpoint=2(a+b) (1.7+3.2)2=4.92=2.45 cm\frac{(1.7 + 3.2)}{2} = \frac{4.9}{2} = 2.45 \, \text{cm}2(1.7+3.2)=24.9=2.45cm
Step 2: Compare to the options.
The correct answer is:
Answer: d. 2.45 cm
Summary Explanation:
In the first problem, we applied unit conversion by dividing the total inches by 12 (since 12 inches make up one foot) to express 80 inches as feet and inches. This is a common real-world problem when dealing with measurements in construction, tailoring, or daily activities in countries using the imperial system. Always remember to convert inches into feet first, then express any remaining inches.
In the second problem, we applied the concept of finding a midpoint — a simple arithmetic average — which is a basic mathematical skill used widely in statistics, geometry, and measurements. Adding the two values and dividing by 2 provides the exact center point between the two measurements on a metric scale.
