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Question 1: Which of these is a valid way to write a ratio?
- 3 minus 2
- 3 to 2
- 3 plus 2
- 3 times 2
Answer: B. 3 to 2
Explanation: Ratios are multiplicative comparisons between two quantities. The three standard formats for writing them are word form (3 to 2), colon form (3:2), and fraction form (3/2).
Question 2: What is the colon form of the ratio 'five to four'?
- 5/9
- 4:5
- 5+4
- 5:4
Answer: D. 5:4
Explanation: The colon form of a ratio directly translates the word form by placing a colon between the two numbers in the order they are stated.
Question 3: Which ratio is equivalent to 3:2?
- 5:4
- 9:5
- 4:3
- 6:4
Answer: D. 6:4
Explanation: Equivalent ratios are found by multiplying or dividing both terms by the same non-zero number. Multiplying both 3 and 2 by 2 results in 6:4.
Question 4: What is a unit rate?
- A ratio where the first term is 1
- A ratio that cannot be simplified
- A ratio where the second term is 1
- A ratio with only negative numbers
Answer: C. A ratio where the second term is 1
Explanation: A unit rate is a specific type of ratio that compares a quantity to exactly one unit of another quantity, such as miles per hour.
Question 5: How is the unit rate for a ratio a:b calculated?
- a plus b
- b divided by a
- a times b
- a divided by b
Answer: D. a divided by b
Explanation: To find the unit rate for a ratio a:b, you divide the first term by the second term, which is represented by the fraction a/b.
Question 6: Which of these is a common real-world example of a unit rate?
- Miles per hour
- Difference in age
- Total number of items
- Sum of two weights
Answer: A. Miles per hour
Explanation: Speed, such as miles per hour, is a classic example of a unit rate because it measures distance covered per one unit of time.
Question 7: What does a graph of a proportional relationship look like?
- A circle
- A curved line
- A series of disconnected dots
- A straight line through the origin
Answer: D. A straight line through the origin
Explanation: Proportional relationships maintain a constant ratio, which results in a straight line on a coordinate plane that must pass through the origin point (0,0).
Question 8: On a graph of a proportional relationship, what does the point (1, r) represent?
- The unit rate
- The total sum
- The origin
- The negative intercept
Answer: A. The unit rate
Explanation: In a proportional relationship, the y-coordinate 'r' at the x-coordinate of 1 represents the constant of proportionality, also known as the unit rate.
Question 9: Which of these is a practical application of proportional relationships?
- Measuring the height of a door
- Calculating simple interest
- Listing prime numbers
- Counting total pages in a book
Answer: B. Calculating simple interest
Explanation: In Grade 7 math, proportional relationships are used to solve real-world financial problems, including calculating simple interest, tax, and markups.
Question 10: If you walk 1/2 mile in 1/4 hour, what is your unit rate in miles per hour?
- 1 mile per hour
- 0.5 miles per hour
- 2 miles per hour
- 4 miles per hour
Answer: C. 2 miles per hour
Explanation: To find the unit rate, divide 1/2 by 1/4. Dividing by a fraction is the same as multiplying by its reciprocal: 1/2 times 4/1 equals 2.