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Answer :
Sure! Let's determine which ratios are equivalent to 12:36 and which are not.
First, let's simplify the ratio 12:36:
1. Simplify 12:36:
- Find the greatest common divisor (GCD) of 12 and 36, which is 12.
- Divide both numbers by their GCD:
[tex]\[
\frac{12}{12} : \frac{36}{12} = 1:3
\][/tex]
Now we have the simplified form of 12:36, which is 1:3. We need to find out which of the given ratios simplify to 1:3.
2. Check each ratio:
- 10 to 30:
- Find the GCD of 10 and 30, which is 10.
- Simplify the ratio:
[tex]\[
\frac{10}{10} : \frac{30}{10} = 1:3
\][/tex]
- This ratio is equivalent to 12:36.
- 6:15:
- Find the GCD of 6 and 15, which is 3.
- Simplify the ratio:
[tex]\[
\frac{6}{3} : \frac{15}{3} = 2:5
\][/tex]
- This ratio is not equivalent to 12:36.
- [tex]\(\frac{9}{24}\)[/tex]:
- Find the GCD of 9 and 24, which is 3.
- Simplify the ratio:
[tex]\[
\frac{9}{3} : \frac{24}{3} = 3:8
\][/tex]
- This ratio is not equivalent to 12:36.
- 8 out of 24:
- Find the GCD of 8 and 24, which is 8.
- Simplify the ratio:
[tex]\[
\frac{8}{8} : \frac{24}{8} = 1:3
\][/tex]
- This ratio is equivalent to 12:36.
Conclusion:
- Ratios equivalent to 12:36:
- 10 to 30
- 8 out of 24
- Ratios not equivalent to 12:36:
- 6:15
- [tex]\(\frac{9}{24}\)[/tex]
By simplifying each ratio, we can see which ones match the simplified form of 12:36, which is 1:3.
First, let's simplify the ratio 12:36:
1. Simplify 12:36:
- Find the greatest common divisor (GCD) of 12 and 36, which is 12.
- Divide both numbers by their GCD:
[tex]\[
\frac{12}{12} : \frac{36}{12} = 1:3
\][/tex]
Now we have the simplified form of 12:36, which is 1:3. We need to find out which of the given ratios simplify to 1:3.
2. Check each ratio:
- 10 to 30:
- Find the GCD of 10 and 30, which is 10.
- Simplify the ratio:
[tex]\[
\frac{10}{10} : \frac{30}{10} = 1:3
\][/tex]
- This ratio is equivalent to 12:36.
- 6:15:
- Find the GCD of 6 and 15, which is 3.
- Simplify the ratio:
[tex]\[
\frac{6}{3} : \frac{15}{3} = 2:5
\][/tex]
- This ratio is not equivalent to 12:36.
- [tex]\(\frac{9}{24}\)[/tex]:
- Find the GCD of 9 and 24, which is 3.
- Simplify the ratio:
[tex]\[
\frac{9}{3} : \frac{24}{3} = 3:8
\][/tex]
- This ratio is not equivalent to 12:36.
- 8 out of 24:
- Find the GCD of 8 and 24, which is 8.
- Simplify the ratio:
[tex]\[
\frac{8}{8} : \frac{24}{8} = 1:3
\][/tex]
- This ratio is equivalent to 12:36.
Conclusion:
- Ratios equivalent to 12:36:
- 10 to 30
- 8 out of 24
- Ratios not equivalent to 12:36:
- 6:15
- [tex]\(\frac{9}{24}\)[/tex]
By simplifying each ratio, we can see which ones match the simplified form of 12:36, which is 1:3.
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