Answer :
We start by noting that the ratio
[tex]$$7:14$$[/tex]
can be simplified by dividing both terms by 7:
[tex]$$\frac{7}{14} = \frac{1}{2}.$$[/tex]
This means any ratio equivalent to [tex]$7:14$[/tex] must simplify to [tex]$\frac{1}{2}$[/tex] (or 0.5).
Now, let’s check each option:
1. For the ratio [tex]$21:42$[/tex], we have
[tex]$$\frac{21}{42} = \frac{1}{2}.$$[/tex]
This ratio is equivalent to [tex]$7:14$[/tex].
2. For [tex]$\frac{14}{30}$[/tex], note that
[tex]$$\frac{14}{30}$$[/tex]
does not simplify to [tex]$\frac{1}{2}$[/tex] (in decimal form it is approximately 0.4667).
This ratio is not equivalent.
3. For the ratio [tex]$4:8$[/tex], we compute
[tex]$$\frac{4}{8} = \frac{1}{2}.$$[/tex]
This ratio is equivalent.
4. For [tex]$\frac{14}{28}$[/tex], we find
[tex]$$\frac{14}{28} = \frac{1}{2}.$$[/tex]
This ratio is equivalent.
5. For [tex]$1:2$[/tex], we have directly
[tex]$$\frac{1}{2} = \frac{1}{2}.$$[/tex]
This ratio is equivalent.
6. For the ratio [tex]$7:10$[/tex], calculate
[tex]$$\frac{7}{10} = 0.7.$$[/tex]
Since [tex]$0.7 \neq 0.5$[/tex], this ratio is not equivalent.
Thus, the ratios that are equivalent to [tex]$7:14$[/tex] (i.e., simplify to [tex]$\frac{1}{2}$[/tex]) are:
[tex]$$21:42, \quad 4:8, \quad 14:28, \quad 1:2.$$[/tex]
[tex]$$7:14$$[/tex]
can be simplified by dividing both terms by 7:
[tex]$$\frac{7}{14} = \frac{1}{2}.$$[/tex]
This means any ratio equivalent to [tex]$7:14$[/tex] must simplify to [tex]$\frac{1}{2}$[/tex] (or 0.5).
Now, let’s check each option:
1. For the ratio [tex]$21:42$[/tex], we have
[tex]$$\frac{21}{42} = \frac{1}{2}.$$[/tex]
This ratio is equivalent to [tex]$7:14$[/tex].
2. For [tex]$\frac{14}{30}$[/tex], note that
[tex]$$\frac{14}{30}$$[/tex]
does not simplify to [tex]$\frac{1}{2}$[/tex] (in decimal form it is approximately 0.4667).
This ratio is not equivalent.
3. For the ratio [tex]$4:8$[/tex], we compute
[tex]$$\frac{4}{8} = \frac{1}{2}.$$[/tex]
This ratio is equivalent.
4. For [tex]$\frac{14}{28}$[/tex], we find
[tex]$$\frac{14}{28} = \frac{1}{2}.$$[/tex]
This ratio is equivalent.
5. For [tex]$1:2$[/tex], we have directly
[tex]$$\frac{1}{2} = \frac{1}{2}.$$[/tex]
This ratio is equivalent.
6. For the ratio [tex]$7:10$[/tex], calculate
[tex]$$\frac{7}{10} = 0.7.$$[/tex]
Since [tex]$0.7 \neq 0.5$[/tex], this ratio is not equivalent.
Thus, the ratios that are equivalent to [tex]$7:14$[/tex] (i.e., simplify to [tex]$\frac{1}{2}$[/tex]) are:
[tex]$$21:42, \quad 4:8, \quad 14:28, \quad 1:2.$$[/tex]
