You have a wire that is 42 inches long. You want to cut it into 2 pieces. You want one piece to be 2/5 the length of the other. How long should the 2 pieces be?

x = one piece
(2/5)x = other piece {one is 2/5 the length of the other}

x + (2/5)x = 42 {added together to make wire length, 42}
(7/5)x = 42 {combined like terms}
x = 42(5/7) {divided both sides by 7/5, multiplying by reciprocal, 5/7}
x = 30 {cancelled and multiplied what's left}
(2/5)x = 12 {substituted 30, in for x, into (2/5)x}

30 in. and 12 in. are the lengths

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