Sure, let's find which of the given ratios are equivalent to the ratio 4:6.
To check if two ratios are equivalent, we can use the concept of cross multiplication. If the product of the means equals the product of the extremes, then the ratios are equivalent. In other words, the ratio [tex]\( \frac{a}{b} \)[/tex] is equivalent to [tex]\( \frac{c}{d} \)[/tex] if and only if [tex]\( a \cdot d = b \cdot c \)[/tex].
Let's proceed with checking each of the given ratios:
1. 16:12
- Cross multiply: [tex]\( 4 \cdot 12 = 48 \)[/tex]
- Cross multiply: [tex]\( 6 \cdot 16 = 96 \)[/tex]
- Since [tex]\( 48 \neq 96 \)[/tex], the ratio 16:12 is not equivalent to 4:6.
2. 2:3
- Cross multiply: [tex]\( 4 \cdot 3 = 12 \)[/tex]
- Cross multiply: [tex]\( 6 \cdot 2 = 12 \)[/tex]
- Since [tex]\( 12 = 12 \)[/tex], the ratio 2:3 is equivalent to 4:6.
3. 20:30
- Cross multiply: [tex]\( 4 \cdot 30 = 120 \)[/tex]
- Cross multiply: [tex]\( 6 \cdot 20 = 120 \)[/tex]
- Since [tex]\( 120 = 120 \)[/tex], the ratio 20:30 is equivalent to 4:6.
4. 24:36
- Cross multiply: [tex]\( 4 \cdot 36 = 144 \)[/tex]
- Cross multiply: [tex]\( 6 \cdot 24 = 144 \)[/tex]
- Since [tex]\( 144 = 144 \)[/tex], the ratio 24:36 is equivalent to 4:6.
5. 40:60
- Cross multiply: [tex]\( 4 \cdot 60 = 240 \)[/tex]
- Cross multiply: [tex]\( 6 \cdot 40 = 240 \)[/tex]
- Since [tex]\( 240 = 240 \)[/tex], the ratio 40:60 is equivalent to 4:6.
Therefore, the equivalent ratios to 4:6 are:
- 2:3
- 20:30
- 24:36
- 40:60
