Question

Decide if each pair of ratios create an equivalent unit rate or not.
Ratio
Equivalent
Not equivalent
1
4

a
n
d

3
12
4
1
​
and
12
3
​



1
4

a
n
d

4
16
4
1
​
and
16
4
​



1
2

a
n
d

5
8
2
1
​
and
8
5
​

Answer 1

To determine if each pair of ratios creates equivalent unit rates, we can simplify each ratio to see if they yield the same value.

1. **For the first pair:**
- Ratios: \( \frac{4}{1} \) and \( \frac{12}{3} \)
- Simplifying \( \frac{12}{3} = 4 \)
- Since \( \frac{4}{1} = 4 \), they are equivalent.

**Answer:** Equivalent

2. **For the second pair:**
- Ratios: \( \frac{4}{1} \) and \( \frac{16}{4} \)
- Simplifying \( \frac{16}{4} = 4 \)
- Since \( \frac{4}{1} = 4 \), they are equivalent.

**Answer:** Equivalent

3. **For the third pair:**
- Ratios: \( \frac{1}{2} \) and \( \frac{5}{8} \)
- To compare, convert to decimals or find a common denominator.
- \( \frac{1}{2} = 0.5 \) and \( \frac{5}{8} = 0.625 \)
- Since \( 0.5 \neq 0.625 \), they are not equivalent.

**Answer:** Not equivalent

To summarize:

1. \( \frac{4}{1} \) and \( \frac{12}{3} \) - **Equivalent**
2. \( \frac{4}{1} \) and \( \frac{16}{4} \) - **Equivalent**
3. \( \frac{1}{2} \) and \( \frac{5}{8} \) - **Not equivalent**