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Sagot :
To determine which ratio is equivalent to [tex]\(\frac{10}{9}\)[/tex], let's compare each of the given options with [tex]\(\frac{10}{9}\)[/tex].
1. Option A: [tex]\(\frac{50}{36}\)[/tex]
[tex]\[ \frac{50}{36} = \frac{50 \div 2}{36 \div 2} = \frac{25}{18} \][/tex]
Now, let's see if [tex]\(\frac{25}{18}\)[/tex] is equivalent to [tex]\(\frac{10}{9}\)[/tex].
A quick way to compare [tex]\(\frac{10}{9}\)[/tex] and [tex]\(\frac{25}{18}\)[/tex] is to see if their cross-products are equal.
[tex]\[ 10 \times 18 = 180 \quad \text{and} \quad 9 \times 25 = 225 \][/tex]
Since [tex]\(180 \neq 225\)[/tex], the ratios are not equivalent.
2. Option B: [tex]\(\frac{50}{45}\)[/tex]
[tex]\[ \frac{50}{45} = \frac{50 \div 5}{45 \div 5} = \frac{10}{9} \][/tex]
This simplifies directly to [tex]\(\frac{10}{9}\)[/tex], which is exactly the ratio we are given.
Therefore, [tex]\(\frac{50}{45}\)[/tex] is equivalent to [tex]\(\frac{10}{9}\)[/tex].
3. Option C: [tex]\(\frac{15}{14}\)[/tex]
To check if [tex]\(\frac{15}{14}\)[/tex] is equivalent to [tex]\(\frac{10}{9}\)[/tex], we can also use the cross-products method:
[tex]\[ 10 \times 14 = 140 \quad \text{and} \quad 9 \times 15 = 135 \][/tex]
Since [tex]\(140 \neq 135\)[/tex], the ratios are not equivalent.
Among the given options, only [tex]\(\frac{50}{45}\)[/tex] simplifies to [tex]\(\frac{10}{9}\)[/tex].
Thus, the ratio that is equivalent to [tex]\(\frac{10}{9}\)[/tex] is:
Option B: [tex]\(\frac{50}{45}\)[/tex]
1. Option A: [tex]\(\frac{50}{36}\)[/tex]
[tex]\[ \frac{50}{36} = \frac{50 \div 2}{36 \div 2} = \frac{25}{18} \][/tex]
Now, let's see if [tex]\(\frac{25}{18}\)[/tex] is equivalent to [tex]\(\frac{10}{9}\)[/tex].
A quick way to compare [tex]\(\frac{10}{9}\)[/tex] and [tex]\(\frac{25}{18}\)[/tex] is to see if their cross-products are equal.
[tex]\[ 10 \times 18 = 180 \quad \text{and} \quad 9 \times 25 = 225 \][/tex]
Since [tex]\(180 \neq 225\)[/tex], the ratios are not equivalent.
2. Option B: [tex]\(\frac{50}{45}\)[/tex]
[tex]\[ \frac{50}{45} = \frac{50 \div 5}{45 \div 5} = \frac{10}{9} \][/tex]
This simplifies directly to [tex]\(\frac{10}{9}\)[/tex], which is exactly the ratio we are given.
Therefore, [tex]\(\frac{50}{45}\)[/tex] is equivalent to [tex]\(\frac{10}{9}\)[/tex].
3. Option C: [tex]\(\frac{15}{14}\)[/tex]
To check if [tex]\(\frac{15}{14}\)[/tex] is equivalent to [tex]\(\frac{10}{9}\)[/tex], we can also use the cross-products method:
[tex]\[ 10 \times 14 = 140 \quad \text{and} \quad 9 \times 15 = 135 \][/tex]
Since [tex]\(140 \neq 135\)[/tex], the ratios are not equivalent.
Among the given options, only [tex]\(\frac{50}{45}\)[/tex] simplifies to [tex]\(\frac{10}{9}\)[/tex].
Thus, the ratio that is equivalent to [tex]\(\frac{10}{9}\)[/tex] is:
Option B: [tex]\(\frac{50}{45}\)[/tex]
To find the answer we would need to find what would be the same answer as 10/9 so that simplifies to 1.11….
we would do A first. So 50 divided by 36 is 1.38 and that can’t be it
B. 50 divided by 45 would equal 1.11…
C. 15 divided by 14 would equal 1.071
So B is the correct answer because it matches
we would do A first. So 50 divided by 36 is 1.38 and that can’t be it
B. 50 divided by 45 would equal 1.11…
C. 15 divided by 14 would equal 1.071
So B is the correct answer because it matches
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