Which pair of ratios can form a true proportion?
A. 3/4 and 6/9
B. 4/5 and 8/10
C. 5/6 and 10/12
D. 7/8 and 14/16
Answer: D. 7/8 and 14/16
To determine the pair of ratios that can form a true proportion, you need to understand what a proportion is. A proportion is an equation that states that two ratios are equal. It can be written in the form a/b = c/d.
To check if a pair of ratios forms a true proportion, you need to cross-multiply and see if the product of the means (ac) equals the product of the extremes (bd). If they are equal, then the ratios form a true proportion.
Let's consider an example to illustrate this process:
Example:
Ratios: 2/3 and 4/6
To check if these ratios form a true proportion, cross-multiply:
2 x 6 = 3 x 4
12 = 12
Since the products of the means (12) and the products of the extremes (12) are equal, the pair of ratios 2/3 and 4/6 form a true proportion.
Therefore, in this case, the pair of ratios that form a true proportion is 2/3 and 4/6.
To determine if a pair of ratios can form a true proportion, we need to check if their cross products are equal. Let's consider the ratios:
Ratio 1: a/b
Ratio 2: c/d
To form a true proportion, the cross products should be equal. The cross products are obtained by multiplying the numerator of one ratio by the denominator of the other ratio. In this case,
Cross product 1: (a/b) * d = ad/b
Cross product 2: (c/d) * b = cb/d
For the pair of ratios to form a true proportion, Cross product 1 should be equal to Cross product 2:
ad/b = cb/d
To simplify, we can cross multiply and get:
ad = cb
Therefore, for a pair of ratios to form a true proportion, the product of the means (ad) should be equal to the product of the extremes (cb).