what ratios are equivalent to 21:6 and 7:2
To find ratios that are equivalent to 21:6, we can simplify this ratio by dividing both terms by their greatest common divisor, which is 3.
21 ÷ 3 = 7
6 ÷ 3 = 2
So, the simplified ratio is 7:2.
Therefore, the ratio 7:2 is equivalent to 21:6.
Similarly, to find ratios that are equivalent to 7:2, we can simplify this ratio by dividing both terms by their greatest common divisor, which is 1 (since 7 and 2 are already relatively prime).
So, the simplified ratio is 7:2.
Therefore, the ratio 7:2 is equivalent to itself.
To find ratios that are equivalent to 21:6 and 7:2, we need to multiply or divide both numbers in the ratio by the same value.
For ratio 21:6:
To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD). The GCD of 21 and 6 is 3.
Dividing both numbers by 3 gives us the simplified ratio:
21 ÷ 3 : 6 ÷ 3
= 7 : 2
So, the ratio 7:2 is equivalent to 21:6.
For ratio 7:2:
To find additional ratios equivalent to 7:2, we can multiply both numbers by the same value.
Let's multiply both numbers by 3:
7 × 3 : 2 × 3
= 21 : 6
So, the ratio 21:6 is equivalent to 7:2.
In summary, the ratios equivalent to 21:6 are 7:2 and 21:6 itself.
To find ratios that are equivalent to 21:6 and 7:2, you need to find a common multiplier that can be applied to both the numerator and denominator of each ratio.
For the ratio 21:6, we can simplify it by finding the greatest common divisor (GCD) of 21 and 6, which is 3. Divide both the numerator and denominator by 3 to get the simplified ratio: 21 ÷ 3 : 6 ÷ 3, which is 7:2.
To find equivalent ratios, you can multiply or divide both the numerator and denominator of a ratio by the same number.
To obtain a ratio that is equivalent to 21:6, you can multiply both sides of the ratio by a common multiplier, such as 2, to get 42:12.
Similarly, to find ratios equivalent to 7:2, you can multiply both sides by a common multiplier. Here are a few examples:
- Multiply both sides by 3: 7 * 3 : 2 * 3, which gives 21:6 (same as the original ratio).
- Multiply both sides by 4: 7 * 4 : 2 * 4, which gives 28:8.
- Multiply both sides by 5: 7 * 5 : 2 * 5, which gives 35:10.
- Multiply both sides by 6: 7 * 6 : 2 * 6, which gives 42:12 (same as the simplified ratio above).
So, the ratios equivalent to 21:6 are 42:12, 28:8, 35:10, and any other ratios that can be obtained by multiplying both sides by the same number.