Answer :
Sure! Let's determine whether each pair of ratios forms a proportion. A proportion is when two ratios are equal.
1. [tex]\(2:1 = 4:2\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{2}{1} \)[/tex] and [tex]\( \frac{4}{2} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{2}{1} = 2 \)[/tex]
- [tex]\( \frac{4}{2} = 2 \)[/tex]
Since both fractions are equal, this is a proportion.
Answer: YES
2. [tex]\(3:4 = 2:6\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{2}{6} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{3}{4} = 0.75 \)[/tex]
- [tex]\( \frac{2}{6} = \frac{1}{3} \approx 0.333 \)[/tex]
Since the fractions are not equal, this is not a proportion.
Answer: NO
3. [tex]\(4:6 = 2:3\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{4}{6} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{4}{6} = \frac{2}{3} \)[/tex]
The fractions are equal, so this is a proportion.
Answer: YES
4. [tex]\(4:1 = 9:2\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{4}{1} \)[/tex] and [tex]\( \frac{9}{2} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{4}{1} = 4 \)[/tex]
- [tex]\( \frac{9}{2} = 4.5 \)[/tex]
Since the fractions are not equal, this is not a proportion.
Answer: NO
5. [tex]\(4:5 = 9:2\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{4}{5} \)[/tex] and [tex]\( \frac{9}{2} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{4}{5} = 0.8 \)[/tex]
- [tex]\( \frac{9}{2} = 4.5 \)[/tex]
Since the fractions are not equal, this is not a proportion.
Answer: NO
For numbers 6 to 10, they are not complete ratios or proportions as given in the original list, so we cannot evaluate them to form any proportions until both sides of the equations are complete.
For our given question, the correct responses are:
1. YES
2. NO
3. YES
4. NO
5. NO
1. [tex]\(2:1 = 4:2\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{2}{1} \)[/tex] and [tex]\( \frac{4}{2} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{2}{1} = 2 \)[/tex]
- [tex]\( \frac{4}{2} = 2 \)[/tex]
Since both fractions are equal, this is a proportion.
Answer: YES
2. [tex]\(3:4 = 2:6\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{2}{6} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{3}{4} = 0.75 \)[/tex]
- [tex]\( \frac{2}{6} = \frac{1}{3} \approx 0.333 \)[/tex]
Since the fractions are not equal, this is not a proportion.
Answer: NO
3. [tex]\(4:6 = 2:3\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{4}{6} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{4}{6} = \frac{2}{3} \)[/tex]
The fractions are equal, so this is a proportion.
Answer: YES
4. [tex]\(4:1 = 9:2\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{4}{1} \)[/tex] and [tex]\( \frac{9}{2} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{4}{1} = 4 \)[/tex]
- [tex]\( \frac{9}{2} = 4.5 \)[/tex]
Since the fractions are not equal, this is not a proportion.
Answer: NO
5. [tex]\(4:5 = 9:2\)[/tex]
Convert the ratios to fractions: [tex]\( \frac{4}{5} \)[/tex] and [tex]\( \frac{9}{2} \)[/tex].
Simplify both fractions:
- [tex]\( \frac{4}{5} = 0.8 \)[/tex]
- [tex]\( \frac{9}{2} = 4.5 \)[/tex]
Since the fractions are not equal, this is not a proportion.
Answer: NO
For numbers 6 to 10, they are not complete ratios or proportions as given in the original list, so we cannot evaluate them to form any proportions until both sides of the equations are complete.
For our given question, the correct responses are:
1. YES
2. NO
3. YES
4. NO
5. NO
