Use diagram or the description of equivalent ratios to show that the ratios 2: 3,4: 6,and 8: 12 are equivalent

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Use diagram or the description of equivalent ratios to show that the ratios 2: 3,4: 6,and 8: 12 are equivalent

4:6 and 8:12 are equivalent ratios to 2:3 as you can see in the diagram below

4:6

_2_ _2_

_2_ _2_ _2_

8:12

_4_ _4_

_4_ _4_ _4_

Step-by-step explanation:

The diagrams of equivalent ratios represent the initial relation, in the image you can see each value is in a box so as the initial relation is 2:3 we have two boxes in the first row and three on the second. Now we have to find a number that added the times of the box, give us the other ratios 4:6 and 8:12

4:6

_2_ _2_ = 4

_2_ _2_ _2_ = 6

As 4 is 2 times 2 and 6 is 3 times 2, 4:6 is an equivalent ratio to 2:3 where 2 is the constant.

8:12

_4_ _4_ = 8

_4_ _4_ _4_ =12

As 8 is 2 times 4 and 6 is 3 times 4, 8:12 is an equivalent ratio to 2:3 where 4 is the constant.

To calculate the constant you may divide each of the corresponding values for example 4 divided by 2 is 2 and 6 divided by 3 is 2 then the constant for 4:6 is 2.

In the case of 8:12, 8 divided by 2 is 4 and 12 divided by 6 is 4 then the constan for 8:12 is 4

[tex]Use diagrams or the description of equivalent ratios to show that the ratios 2: 3, 4: 6, and 8: 1[/tex]

they are not equivalent because,2×2 is 4, 4×2 is 6, and 8×2 is 16.so they are not equivalent.

to be an equivalent all of them needs to be able to be multiplied by 2.

Taking 2:3 as a reference, you can get an equivalent ratio multiplying each member by some constant, for example multiplying by 2 we get:

2:3 = 2*2:3*2 = 4:6

Multiplying by 4 we get:

2:3 = = 2*4:3*4 = 8:12

Then, 2:3 4:6 and 8:12 are equivalent

9:24, 10:48, 11:56 you just go up one number on the left side of the semicolon and you multiply the right side by 2

If you multiply 2 by 2 and 3 by 2, you get 4:6. If you multiply 4 by 2 and 6 by 2, you get 8:12. As long as you are able to multiply the numerator and denominator by the same amount, the ratios are equivalent.

So

lets say we have

a/b=2a/2b

we know that if we invert one and multiply it by the other (divide them), we get 1 because a/a=1 where a=a

so

2/3 and 4/6 are equivelent because if you divide them we get 12/12=1

2/3 and 8/12 are equivilent because if you divide them we get 24/24=1

and sinde 2/3=4/6 and 2/3=8/12, 2/3=4/6=8/12

they are equivlent