Select all ratios equivalent to 14:21.
no choices listed
14/7 / 21/7 = 2/3
so factor the others (whatever they are) and see if they come out to 2/3
To find all ratios equivalent to 14:21, you can multiply or divide both numbers by the same nonzero whole number. This will give you different ratios that have the same ratio value as 14:21.
Let's list some ratios equivalent to 14:21:
1) 14:21 (the original ratio)
2) 2:3 (divided both numbers by 7)
3) 4:6 (divided both numbers by 3)
4) 7:10 (divided both numbers by 3)
So, the ratios equivalent to 14:21 are 2:3, 4:6, and 7:10.
To find all the ratios equivalent to 14:21, we need to simplify the given ratio by dividing both numbers by their greatest common divisor (GCD).
Step 1: Find the GCD of 14 and 21
The factors of 14 are 1, 2, 7, and 14.
The factors of 21 are 1, 3, 7, and 21.
The common factors are 1 and 7, so the GCD of 14 and 21 is 7.
Step 2: Divide both numbers by the GCD
Dividing 14 by 7 gives us 2.
Dividing 21 by 7 gives us 3.
Therefore, the simplified ratio is 2:3.
Any ratio that can be obtained by multiplying both numbers of the simplified ratio by the same non-zero integer is equivalent to the original ratio.
Here are a few examples of equivalent ratios:
- Multiplying both numbers of the simplified ratio (2:3) by 2 gives us the ratio 4:6.
- Multiplying both numbers of the simplified ratio by 3 gives us the ratio 6:9.
- Multiplying both numbers of the simplified ratio by 4 gives us the ratio 8:12.
- Multiplying both numbers of the simplified ratio by any other non-zero integer will also yield an equivalent ratio.