To find the ratio equivalent to 1:4 where the second part of the ratio is 6, you can set up a proportion.
Starting with the ratio \(1:4\), we want to find the first part (let's call it \(x\)) such that:
\[ \frac{x}{6} = \frac{1}{4} \]
To solve for \(x\), cross-multiply:
\[ x \cdot 4 = 1 \cdot 6 \]
This simplifies to:
\[ 4x = 6 \]
Now, divide both sides by 4:
\[ x = \frac{6}{4} = \frac{3}{2} \]
So the ratio equivalent to \(1:4\) when the second part is 6 is:
\(\frac{3}{2}:6\) or \(3:8\) (by multiplying both sides by 4).
Thus, the answer is:
3:6 is equivalent, meaning the blank is 3.
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