# What are the ratios in 2:3=4:_____=8:____=_____:15?

Well, 2:3 expressed as a fraction is 2/3.  Problem 1: 2:3 = 4:x (your statement)  2/3 = 4/x (your statement - expressed as fractions)  2x = 12 (cross multiply: (2 * x) and (4 * 3))  2x/2 = 12/2 (divide by 2 on both sides)  x = 6 (simplify)  Therefore, 2:3 = 4:6  Problem 2: 2:3 = 8:x (your statement)  2/3 = 8/x (your statement - expressed as fractions)  2x = 24 (cross mulitply: (2 * x) and (8 * 3))  2x/2 = 24/2 (divide by 2 on both sides)  x = 12 (simplify)  Hence, 2:3 = 8:12  Problem 3: 2:3 = x:15 (your statement)  2/3 = x/15 (your statement - expressed as fractions)  3x = 30 (cross multiply: (2 * 15) and (3 * x))  3x/3 = 30/3 (divide by 3 on both sides)  x = 10 (simplify)  Thus, 2:3 = 10:15  Final answer: 2:3 = 4:6 = 8:12 = 10:15 (these are equivalent ratios)
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Oddman commented
Once again, "cross multiply" is a waste of time. In the case of 2/3=x/15, multiplying by 15 solves it: X=(2/3)*15. Your cross multiplying step introduces a factor of 3 that then must be divided out.
A ratio that is equivalent to 2:3 will be of the form
(2n):(3n)
where "n" is any number.

Each ratio gives you enough information to find the multiplier "n".
In the first case, 2n=4, so n=2 and the ratio is (2*2):(3*2) = 4:6.
In the next case, 2n=8, so n=4 and the ratio is (2*4):(3*4) = 8:12.
In the next case, 3n=15, so n=5 and the ratio is (2*5):(3*5) = 10:15.

2:3 = 4:6 = 8:12 = 10:15
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