Question
Find the number that makes the ratio equivalent to \( 16: 2 \).
Ask by Chan Pena. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The number that makes the ratio equivalent to 16:2 is 8.
Solution
The ratio 16:2 can be simplified by dividing both numbers by their greatest common divisor. Since 16 and 2 share a common divisor of 2, we have
16 ÷ 2 = 8 and 2 ÷ 2 = 1.
So, 16:2 is equivalent to 8:1.
Thus, if you were asked for the number that "completes" the ratio, it depends on the context. For example, if you want a ratio with the first term 8 (that is, 8:?), to be equivalent to 16:2 you need to have
8/? = 8/1 ⇒ ? = 1.
Alternatively, if you want a ratio with the second term 1 (that is, ? : 1) to match 16:2, then
?/1 = 8 ⇒ ? = 8.
Often, the problem is interpreted as finding the simplified ratio. In that case, 16:2 simplifies to 8:1, and the key number is 8.
So, the answer is 8.
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Simplify this solution The Deep Dive
To find a number that makes the ratio equivalent to \( 16: 2 \), we can understand that this ratio simplifies to \( 8: 1 \). This means we need a number \( x \) such that \( \frac{x}{1} = 8 \), which clearly gives us \( x = 8 \). Alternatively, if you want to keep the original ratio intact, any equivalent ratio can be formed by multiplying both sides of \( 16:2 \) by the same positive integer. For example, if we multiply by 3, we get \( 48:6 \), which is also equivalent to \( 16:2 \). So, 8 is one simple answer, and there are infinitely many other equivalent pairs!
