Final answer:
The ratios 12:16 and 72:96 are equivalent as they both simplify to the ratio 3:4. So, the statement that they are equivalent is true. A ratio is usually expressed with the symbol ‘:’. The comparison or simplified form of two quantities of the same kind is referred to as ratio.
Step-by-step explanation:
The question asked is whether the ratios 12:16 and 72:96 are equivalent. To determine if two ratios are equivalent, we simplify both to see if they reduce to the same ratio. Simplifying the first ratio 12:16 by dividing both numbers by their greatest common divisor, which is 4, we get 12 ÷ 4 = 3 and 16 ÷ 4 = 4. So, the reduced form of 12:16 is 3:4.
Next, we simplify the second ratio 72:96 in the same way. The greatest common divisor for these numbers is 24. Dividing both by 24, 72 ÷ 24 = 3, and 96 ÷ 24 = 4, getting 3:4 as well.
Since both ratios simplify to 3:4, we can conclude that 12:16 and 72:96 are indeed equivalent ratios. Therefore, the correct answer is A. True.
In Mathematics, a ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
A ratio is usually expressed with the symbol ‘:’. The comparison or simplified form of two quantities of the same kind is referred to as ratio.