So, I've been stuck in these for quite some time.... can someone help me?
Which ratios can form a proportion?
A) 9/45 , 8/40
B) 8/12 , 12/21
C) 8/12 , 12/15
D) 9/22 , 14/28
I think it might be C but my brain is fried.
Thank you so much,
Jacob
Nope.
Simplify both fractions.
8/12 = 2/3
12/15 = 4/5
9/45 = 1/5
8/40 = 1/5
There it is!
Oh ok. I get it now. Thank you so much Ms.Sue. Have a wonderful day!
You're welcome. And you have a great day, too, Jacob.
Of course, Jacob! I'll be happy to help you out.
To determine which ratios can form a proportion, we need to check if the ratios are equal. In other words, we need to see if the fractions in each pair have the same value when simplified.
Let's go through each option and simplify the fractions to see if they are equal:
A) 9/45 , 8/40
To simplify 9/45, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 9. This gives us 1/5.
To simplify 8/40, we can divide both the numerator and denominator by their greatest common divisor, which is 8. This gives us 1/5 as well.
Since both fractions simplify to 1/5 and are equal, option A is a proportion.
B) 8/12 , 12/21
To simplify 8/12, we can divide both the numerator and denominator by their greatest common divisor, which is 4. This gives us 2/3.
To simplify 12/21, we can divide both the numerator and denominator by their greatest common divisor, which is 3. This gives us 4/7.
Since 2/3 and 4/7 are not equal, option B is not a proportion.
C) 8/12 , 12/15
To simplify 8/12, we can divide both the numerator and denominator by their greatest common divisor, which is 4. This gives us 2/3.
To simplify 12/15, we can divide both the numerator and denominator by their greatest common divisor, which is 3. This gives us 4/5.
Since 2/3 and 4/5 are not equal, option C is not a proportion.
D) 9/22 , 14/28
To simplify 9/22, we can't simplify it any further because the numerator and denominator do not have any common factors.
To simplify 14/28, we can divide both the numerator and denominator by their greatest common divisor, which is 14. This gives us 1/2.
Since 9/22 and 1/2 are not equal, option D is not a proportion.
Therefore, the correct option is A) 9/45 , 8/40. These two ratios can form a proportion because they simplify to the same fraction, 1/5.
I hope that helps! Let me know if you have any more questions.