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

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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.
The number that makes the ratio equivalent to $$10:70$$ is $$10$$.

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

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