equivalent ratios
write two equivalent ratios.
1)

2)

4)

5)

determine whether the ratios are equivalent.
7) (\frac{7}{9}) and (\frac{49}{63})
8) (\frac{3}{7}) and (\frac{5}{2})
10) (\frac{9}{2}) and (\frac{45}{10})
11) (\frac{2}{9}) and (\frac{9}{5})

Question

equivalent ratios
write two equivalent ratios.
1)

2)

4)

5)

determine whether the ratios are equivalent.
7) (\frac{7}{9}) and (\frac{49}{63})
8) (\frac{3}{7}) and (\frac{5}{2})
10) (\frac{9}{2}) and (\frac{45}{10})
11) (\frac{2}{9}) and (\frac{9}{5})

Accepted Answer

### Problem 1: Write two equivalent ratios for $ \frac{5}{9} $
# Explanation:
## Step 1: Multiply numerator and denominator by 2
To find an equivalent ratio, we can multiply both the numerator and the denominator of the ratio $ \frac{5}{9} $ by the same non - zero number. Let's multiply by 2.
$ \frac{5\times2}{9\times2}=\frac{10}{18} $
## Step 2: Multiply numerator and denominator by 3
Now, multiply the numerator and denominator of $ \frac{5}{9} $ by 3.
$ \frac{5\times3}{9\times3}=\frac{15}{27} $
# Answer:
Two equivalent ratios for $ \frac{5}{9} $ are $ \frac{10}{18} $ and $ \frac{15}{27} $

### Problem 2: Write two equivalent ratios for $ \frac{4}{9} $
# Explanation:
## Step 1: Multiply numerator and denominator by 2
Multiply both the numerator and denominator of $ \frac{4}{9} $ by 2.
$ \frac{4\times2}{9\times2}=\frac{8}{18} $
## Step 2: Multiply numerator and denominator by 3
Multiply the numerator and denominator of $ \frac{4}{9} $ by 3.
$ \frac{4\times3}{9\times3}=\frac{12}{27} $
# Answer:
Two equivalent ratios for $ \frac{4}{9} $ are $ \frac{8}{18} $ and $ \frac{12}{27} $

### Problem 4: Write two equivalent ratios for $ \frac{9}{11} $
# Explanation:
## Step 1: Multiply numerator and denominator by 2
Multiply both the numerator and denominator of $ \frac{9}{11} $ by 2.
$ \frac{9\times2}{11\times2}=\frac{18}{22} $
## Step 2: Multiply numerator and denominator by 3
Multiply the numerator and denominator of $ \frac{9}{11} $ by 3.
$ \frac{9\times3}{11\times3}=\frac{27}{33} $
# Answer:
Two equivalent ratios for $ \frac{9}{11} $ are $ \frac{18}{22} $ and $ \frac{27}{33} $

### Problem 5: Write two equivalent ratios for $ \frac{2}{7} $
# Explanation:
## Step 1: Multiply numerator and denominator by 2
Multiply both the numerator and denominator of $ \frac{2}{7} $ by 2.
$ \frac{2\times2}{7\times2}=\frac{4}{14} $
## Step 2: Multiply numerator and denominator by 3
Multiply the numerator and denominator of $ \frac{2}{7} $ by 3.
$ \frac{2\times3}{7\times3}=\frac{6}{21} $
# Answer:
Two equivalent ratios for $ \frac{2}{7} $ are $ \frac{4}{14} $ and $ \frac{6}{21} $

### Problem 7: Determine if $ \frac{7}{9} $ and $ \frac{49}{63} $ are equivalent
# Explanation:
## Step 1: Simplify $ \frac{49}{63} $
We can simplify $ \frac{49}{63} $ by dividing both the numerator and the denominator by their greatest common divisor, which is 7.
$ \frac{49\div7}{63\div7}=\frac{7}{9} $
## Step 2: Compare with $ \frac{7}{9} $
Since $ \frac{49}{63} $ simplifies to $ \frac{7}{9} $, the two ratios are equivalent.
# Answer:
Yes

### Problem 8: Determine if $ \frac{3}{7} $ and $ \frac{5}{2} $ are equivalent
# Explanation:
## Step 1: Cross - multiply
For two ratios $ \frac{a}{b} $ and $ \frac{c}{d} $, if $ ad = bc $, then they are equivalent. Here, $ a = 3$, $ b = 7$, $ c = 5$, $ d = 2 $.
Calculate $ ad=3\times2 = 6 $ and $ bc = 7\times5=35 $
## Step 2: Compare the products
Since $ 6
eq35 $, the two ratios are not equivalent.
# Answer:
No

### Problem 10: Determine if $ \frac{9}{2} $ and $ \frac{45}{10} $ are equivalent
# Explanation:
## Step 1: Simplify $ \frac{45}{10} $
Divide both the numerator and denominator of $ \frac{45}{10} $ by 5.
$ \frac{45\div5}{10\div5}=\frac{9}{2} $
## Step 2: Compare with $ \frac{9}{2} $
Since $ \frac{45}{10} $ simplifies to $ \frac{9}{2} $, the two ratios are equivalent.
# Answer:
Yes

### Problem 11: Determine if $ \frac{2}{9} $ and $ \frac{9}{5} $ are equivalent
# Explanation:
## Step 1: Cross - multiply
For $ \frac{2}{9} $ and $ \frac{9}{5} $, $ a = 2$, $ b = 9$, $ c = 9$, $ d = 5 $.
Calculate $ ad=2\times5 = 10 $ and $ bc=9\times9 = 81 $
## Step 2: Compare the products
Since $ 10
eq81 $, the two ratios are not equivalent.
# Answer:
No

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QUESTION IMAGE

Question

Explanation:

Problem 1: Write two equivalent ratios for \( \frac{5}{9} \)

Step 1: Multiply numerator and denominator by 2

Step 2: Multiply numerator and denominator by 3

Step 1: Multiply numerator and denominator by 2

Step 2: Multiply numerator and denominator by 3

Step 1: Multiply numerator and denominator by 2

Step 2: Multiply numerator and denominator by 3

Answer:

Problem 2: Write two equivalent ratios for \( \frac{4}{9} \)