Question
- Are the following statements true?
(a) 40 persons: 200 persons
(b) 7.5 litres: 15 litres
©
(d)
(e)
- Determine if the following ratios form a proportion. Also, write the mi
and extreme terms where the ratios form a proportion.
(a) 40 persons: 200 persons
(b) 7.5 litres: 15 litres
©
(d)
(e)
and extreme terms where the ratios form a proportion.
Ask by Stephens Rojas. in India
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
3. Are the following statements true?
- (a) True
- (b) True
- © True
- (d) True
- (e) False
4. Determine if the following ratios form a proportion. Also, write the mean and extreme terms where the ratios form a proportion.
-
Proportion: Two ratios
form a proportion if . -
Extreme Terms: The first and last terms in a proportion, i.e.,
and . -
Mean Terms: The middle two terms in a proportion, i.e.,
and .
Example:
Given the proportion
- Extreme Terms: 2 and 6
- Mean Terms: 3 and 4
Solution
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The Deep Dive
If you’re crafting your mathematical skills, let’s explore these ratios a bit more!
First up, we can check that (a) simplifies to 1:5, and © simplifies to approximately 2.2:1 which are not equal. However, for (b), when you convert 7.5 litres to kg based on a density, or in terms of 15 litres, you might find a proportion, so technically, that’s true! (d) indeed holds as both sides reduce to 1:2, while (e) can show a slight discrepancy based on hours travelled; they don’t match perfectly!
To dive deeper into these ratios, remember that when checking proportions, a great tip is to cross-multiply and see if both products are equal. It’s a nifty way to determine mathematical truth in ratios! Also, be careful not to get lost in the units; mismatched units can lead to incorrect conclusions faster than you can say “algebra”!
