ratios- which pairs could form a proportion? 1. 10/24, 7/18 2. 6/9,10/15, 3. 3/4, 18/24
also g/5 = 6/10 solve
why don't you reduce to lowest terms ?
by doing that I found 2 pairs very quickly.
as for g/5 = 6/10
the simplest way to handle these is to cross-multiply, so ...
10g = 30
g = 3
To determine which pairs can form a proportion, we need to compare the ratios of the numerators to the ratios of the denominators. If the ratios are equal, then the pairs can form a proportion.
1. 10/24 and 7/18:
To compare the ratios, we can simplify both fractions:
10/24 can be simplified to 5/12 (by dividing both numerator and denominator by 2).
7/18 is already simplified.
5/12 and 7/18 cannot form a proportion because the ratios are not equal.
Therefore, pair 1 cannot form a proportion.
2. 6/9, 10/15:
For the first pair, 6/9 simplifies to 2/3.
For the second pair, 10/15 simplifies to 2/3.
The ratios are equal (2/3 = 2/3).
Therefore, pair 2 can form a proportion.
3. 3/4, 18/24:
For the first pair, 3/4 is already simplified.
For the second pair, 18/24 simplifies to 3/4 (by dividing both numerator and denominator by 6).
The ratios are equal (3/4 = 3/4).
Therefore, pair 3 can form a proportion.
So, the pairs that can form a proportion are pair 2 (6/9, 10/15) and pair 3 (3/4, 18/24).
Now, let's solve the equation g/5 = 6/10 to find the value of g:
To solve this, we can cross-multiply:
10g = 5 * 6
10g = 30
Now, divide both sides of the equation by 10 to isolate g:
g = 30/10
g = 3
Therefore, g is equal to 3.
To determine which pairs could form a proportion, we need to check if the ratios are equal. A proportion is formed when the cross products of the ratios are equal. Let's go through each option:
1. To find out if 10/24 is in proportion with 7/18, we cross multiply:
10 x 18 = 24 x 7
180 = 168
Since 180 is not equal to 168, this pair does not form a proportion.
2. For 6/9 and 10/15, we cross multiply:
6 x 15 = 9 x 10
90 = 90
The cross products are equal, so this pair does form a proportion.
3. Similarly, we cross multiply for 3/4 and 18/24:
3 x 24 = 4 x 18
72 = 72
As the cross products are equal, this pair also forms a proportion.
Therefore, option 2 (6/9, 10/15) and option 3 (3/4, 18/24) could form proportions.
Now, let's solve the equation g/5 = 6/10:
To isolate g, we can cross multiply:
g x 10 = 5 x 6
10g = 30
To solve for g, divide both sides of the equation by 10:
g = 30/10
g = 3
Therefore, the solution to the equation g/5 = 6/10 is g = 3.