Find 3 equivalent ratios for the following fractions:
1. [tex]\frac{4}{3}[/tex]
2. [tex]\frac{12}{14}[/tex]
3. [tex]\frac{6}{9}[/tex]
Answer (3)
So the question is what are three equivalent ratios for 4/3, 12/14 and 6/9. The simplest way to get the equivalent ratio of some other ratio is to either multiply the nominator and the denominator by the same number or to divide the nominator and the denominator with the same number. I need to point out that it's not always possible to divide them and get a whole number. First: (4/3) (2/2)=8/6, (4/3) (3/3)=12/9 and (4/3) (4/4)=16/12. Second: (12/14)/(2/2)=6/7, (12/14) (2/2)=24/28 and (12/14) (3/3)=36/42. Third: (6/9)/(3/3)=2/3, (6/9) (2/2)=12/18 and finally (6/9)*(3/3)=18/27.
Equivalent ratios for 4/3, 12/14, and 6/9 are obtained by multiplying or dividing both terms of the ratio by the same number. Examples include 8/6, 12/9, and 16/12 for 4/3; 24/28, 6/7, and 36/42 for 12/14; and 12/18, 2/3, and 24/36 for 6/9.
Equivalent ratios can be found by multiplying or dividing the numerator and denominator of the original ratio by the same number. For the ratio 4/3, we can multiply both the numerator (4) and the denominator (3) by a constant to find equivalent ratios. For example:
Multiplying by 2 gives us 8/6.
Multiplying by 3 gives us 12/9.
Multiplying by 4 gives us 16/12.
Similarly, for the ratio 12/14, equivalent ratios can be found by:
Multiplying by 2 gives us 24/28.
Dividing by 2 gives us 6/7.
Multiplying by 3 gives us 36/42.
And lastly, for the ratio 6/9:
Multiplying by 2 gives us 12/18.
Dividing by 3 gives us 2/3.
Multiplying by 4 gives us 24/36.
To find equivalent ratios for the fractions 3 4 , 14 12 , and 9 6 , we can multiply the numerator and denominator by the same number or simplify them. For 3 4 , we get 6 8 , 9 12 , and 12 16 . For 14 12 , we find 28 24 , 7 6 , and 42 36 , and for 9 6 , we have 3 2 , 18 12 , and 27 18 .
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