Find two ratios that are equivalent to each given ratio.

1) 7/14

2) 9/12

3) 21/35

Divide both the numerator and the denominator by the same number.

7/14 = 1/7

9/12 = 3/4

21/35 = ?

1) To find two ratios that are equivalent to 7/14, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 7 and 14 is 7. Dividing both numbers by 7, we get:

7 ÷ 7 = 1
14 ÷ 7 = 2

So, the simplified fraction is 1/2.

Two ratios that are equivalent to 7/14 are:

2/4
3/6

2) To find two ratios that are equivalent to 9/12, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 9 and 12 is 3. Dividing both numbers by 3, we get:

9 ÷ 3 = 3
12 ÷ 3 = 4

So, the simplified fraction is 3/4.

Two ratios that are equivalent to 9/12 are:

6/8
15/20

3) To find two ratios that are equivalent to 21/35, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 21 and 35 is 7. Dividing both numbers by 7, we get:

21 ÷ 7 = 3
35 ÷ 7 = 5

So, the simplified fraction is 3/5.

Two ratios that are equivalent to 21/35 are:

6/10
9/15

To find two ratios that are equivalent to a given ratio, we need to multiply or divide both the numerator and denominator of the given ratio by the same number. This is because multiplying or dividing both parts of a ratio by the same number does not change the ratio itself.

1) 7/14:
To find two ratios equivalent to 7/14, we can multiply both the numerator and denominator by the same number. Let's multiply both by 2:
7/14 * 2/2 = 14/28
The ratio 14/28 is now equivalent to 7/14.

We can also divide both the numerator and denominator by the same number. Let's divide both by 7:
7/14 ÷ 7/7 = 1/2
The ratio 1/2 is also equivalent to 7/14.

So, two ratios equivalent to 7/14 are 14/28 and 1/2.

2) 9/12:
To find two ratios equivalent to 9/12, we can also multiply or divide both the numerator and denominator by the same number.
Multiplying by 2:
9/12 * 2/2 = 18/24

Dividing by 3:
9/12 ÷ 3/3 = 3/4

So, two ratios equivalent to 9/12 are 18/24 and 3/4.

3) 21/35:
We can use the same method to find two ratios equivalent to 21/35.

Dividing both by 7:
21/35 ÷ 7/7 = 3/5

Multiplying by 2:
21/35 * 2/2 = 42/70

So, two ratios equivalent to 21/35 are 3/5 and 42/70.