State if each pair of ratios forms a proportion.
1) 4/2 20 6 and
2) a and 18 8
1) The pair of ratios 4/2 and 20/6 forms a proportion because when you simplify both ratios, you get 2/1 and 10/3, which are equivalent.
2) The pair of ratios a/18 and 8/18 does not form a proportion because the denominators are the same, but the numerators are different. So, the ratios are not equivalent.
3/2 and 18/8 State if each pair of ratios forms a proportion.
The pair of ratios 3/2 and 18/8 forms a proportion because when you simplify both ratios, you get 1.5 and 2.25, which are equivalent.
To determine if a pair of ratios forms a proportion, we need to check if their cross products are equal.
1) 4/2 = 20/6
To find the cross products, we multiply the numerator of the first ratio with the denominator of the second ratio and vice versa. In this case:
4 * 6 = 24
2 * 20 = 40
Since the cross products of this pair of ratios are not equal (24 ≠ 40), they do not form a proportion.
2) a/18 = 8/6
Again, we find the cross products:
a * 6 = 8 * 18
6a = 144
Divide both sides by 6 to solve for 'a':
a = 24
So, the second pair of ratios forms a proportion if a = 24.