A, Show that the ration 10/20 and 30/60 form a proportion by finding a common multiplier.
B. Show that the ratios in part (A) are equal by writing them in the simplest form.
A.
10 / 20 = 10 ∙ 3 / 20 ∙ 3 = 30 / 60
So 10 / 20 is equivalent ratio of 30 / 60
B.
10 / 20
Divide the numerator and denominator by 10
10 : 10 / 20 : 10 = 1 / 2
30 / 60
Divide the numerator and denominator by 30
30 : 30 / 60 : 30 = 1 / 2
Both ratio are equal to 1 / 2 in simplest form.
Clarification for answer A
The ratio 10 / 20 from a proportion by common multipler 3 to get 30 / 60
Thank you!
No
A. Ah, proportions, those sneaky little fractions! Let's find a common multiplier to show that 10/20 and 30/60 form a proportion.
We can start by finding the greatest common divisor (GCD) of the two denominators, which are 20 and 60. Dividing both of these numbers by their GCD will give us the simplified form. The GCD of 20 and 60 is 20, so when we divide both numbers by 20, we get:
10/20 = 1/2
30/60 = 1/2
So, multiplying both sides of the equation by 3, we get:
3 * (1/2) = 3/2
3 * (1/2) = 3/2
Voila! We have found a common multiplier (3) that shows that 10/20 and 30/60 form a proportion.
B. Now, let's show that the ratios in part (A) are indeed equal by writing them in their simplest form.
We've already simplified the ratios in part (A) as 1/2 and 1/2. And guess what? They are the same! So, we can confidently say that the ratios in part (A) are equal, as they both simplify to the same fraction.
Hope that brings a proportionate amount of laughter to your math journey!
A. To show that the ratios 10/20 and 30/60 form a proportion by finding a common multiplier, we need to find a number that can be multiplied to both the numerator and denominator of one ratio to obtain the corresponding numerator and denominator of the other ratio.
For the ratio 10/20, we can see that both the numerator and denominator can be divided by 10 to simplify the ratio. Dividing both 10 and 20 by 10, we get:
10/10 = 1
20/10 = 2
So, the simplified form of the ratio 10/20 is 1/2.
Now, let's find a common multiplier for the ratio 30/60. We can simplify this ratio by dividing both the numerator and denominator by 30. Dividing both 30 and 60 by 30, we get:
30/30 = 1
60/30 = 2
So, the simplified form of the ratio 30/60 is also 1/2.
As we can see, both ratios have a common simplified form of 1/2. Hence, they form a proportion.
B. To show that the ratios in part A are equal by writing them in the simplest form, we have already simplified both ratios to 1/2.
Therefore, we can conclude that the ratios 10/20 and 30/60 are equal, as they both simplify to 1/2.