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Ratios Rates and Simplest Form
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Ratios Rates and Simplest Form
Ratios Rates and Simplest Form
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1
Question
What is a ratio as defined in this chapter?
Answer
A comparison of two quantities of the same kind measured in the same unit.
2
Question
How is the ratio a:b written, given a and b are quantities of the same kind with b ≠ 0?
Answer
a : b
3
Question
In the context of ratios, does a ratio have units?
Answer
No, a ratio has no units.
4
Question
If there are 17 boys and 19 girls, what is the ratio of boys to girls?
Answer
17:19
5
Question
With the same numbers, what is the ratio of girls to boys in 17 boys and 19 girls?
Answer
19:17
6
Question
What must you remember about the order when expressing a ratio?
Answer
The order is important; a:b differs from b:a.
7
Question
If there are 33 lemons and 20 pears, what is the ratio of lemons to pears?
Answer
33:20
8
Question
In the same basket, what is the ratio of pears to total fruits if there are 33 lemons and 20 pears?
Answer
20:53
9
Question
Define equivalent ratios in simple terms.
Answer
Ratios that represent the same proportional value after scaling.
10
Question
Which ratio is in simplest form for 6:12?
Answer
1:2
11
Question
Are 23:46 and 1/6:1/3 equivalent to 1:2?
Answer
Yes, both are equivalent to 1:2.
12
Question
What operation demonstrates that 6:12 simplifies to 1:2 using division?
Answer
Divide both parts by 6.
13
Question
What operation demonstrates that 1/6 : 1/3 simplifies to 1:2?
Answer
Multiply both parts by 6.
14
Question
What is meant by the simplest form of a ratio?
Answer
When x:y has no common factors other than 1.
15
Question
What is the simplest form of the ratio 6:12?
Answer
1:2
16
Question
What is the role of LCM in simplifying ratios like 1/6:1/3?
Answer
Multiply both parts by the LCM to obtain integers for simplification.
17
Question
What is equivalent to 6:12 after expressing in lowest terms?
Answer
1:2
18
Question
What is the general mathematical principle behind equivalent ratios you can apply to any a:b?
Answer
Multiply or divide both parts by the same nonzero constant.
19
Question
In the Worked Example 2(a), how do you convert 600 g to match 1.6 kg for ratio simplification?
Answer
Convert to the same unit: 600 g : 1600 g.
20
Question
What is the final simplified ratio for 600 g : 1.6 kg?
Answer
3:8
21
Question
Define a ratio in terms of common units: what is required for a valid ratio?
Answer
Quantities must be of the same kind and same unit.
22
Question
What is a key interpretation of the equivalence 6:12 = 2:4 = 1:2?
Answer
They all express the same proportional relationship.
23
Question
Why is the order in a ratio important?
Answer
Because a:b represents a different proportion than b:a.
24
Question
What is a practical example of a ratio from the chapter objectives?
Answer
Interest rate, currency exchange rate, and speed are real-life ratios.
25
Question
What does a ratio compare when expressed as a:b?
Answer
Two quantities of the same kind in the same unit.
26
Question
How would you express the ratio of boys to girls in a class with 17 boys and 19 girls?
Answer
17:19
27
Question
How would you express the ratio of girls to total students in a class with 19 girls out of 36 total students?
Answer
19:36
28
Question
What is the relationship between a ratio and a fraction?
Answer
A ratio a:b can be represented as the fraction a/b.
29
Question
If a:b is equivalent to c:d, what must hold true for all scaled versions?
Answer
a/b = c/d and ah = cm, bh = dn for some nonzero h.
30
Question
What is the importance of units in a ratio?
Answer
A ratio compares like quantities; units cancel out, leaving a unitless ratio.