Sixth grade ? 5.6 Write an equivalent ratio NEA Find the number that makes the ratio equivalent to 10:70. Submit

To find a number that makes the ratio equivalent to \(10:70\), we can set up a proportion. 1. **Understanding Ratios**: The ratio \(10:70\) can be simplified. To do this, we can divide both numbers by their greatest common divisor (GCD). The GCD of \(10\) and \(70\) is \(10\). \[ \frac{10}{10} : \frac{70}{10} = 1 : 7 \] So, the simplified ratio is \(1:7\). 2. **Finding an Equivalent Ratio**: We want to find a number \(x\) such that the ratio \(x:70\) is equivalent to \(10:70\). This means we can set up the equation: \[ \frac{x}{70} = \frac{10}{70} \] 3. **Cross-Multiplying**: To solve for \(x\), we can cross-multiply: \[ x \cdot 70 = 10 \cdot 70 \] Simplifying this gives: \[ x = 10 \] Thus, the number that makes the ratio equivalent to \(10:70\) is \(10\). If you need to find another equivalent ratio, you can multiply both sides of the simplified ratio \(1:7\) by any positive integer. For example, multiplying by \(2\) gives \(2:14\), or multiplying by \(3\) gives \(3:21\), and so on.