Question

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In Target One Fractions, players choose three numbers to create a whole number and
a fraction that have a product close to 1. Their score is the difference between their
product and 1, and the lowest score wins the round.
1 Erica is playing Target One Fractions. She has these cards: 1, 2, 3, 4, 6.
a Which three cards should she choose to make a whole number and a fraction
that have a product close to 1?
62/3
b Write an expression for the problem Erica will solve.
2/3×4=4
c Solve the problem.
6=2₁b = 6₁ c=30r a=3,5=60-a
d What is Erica's score for this round?

Answer 1

Answer: a) Erica should choose 2, 3, and 6 to make a whole number and a fraction that have a product close to 1.

2 x 3 x 6 = 36, which is close to 1 when expressed as a fraction: 1/36.

b) (2/a) x (3/b) x (6/c) = 1

c) Multiplying both sides by a, b, and c, we get:

6bc = 2ac

3ac = ab

6ab = bc

Multiplying the three equations together, we get:

(6abc)^2 = (2ac) x (3ab) x (6bc)

216a^2 b^2 c^2 = 36a^2 b^2 c^2

a^2 b^2 c^2 = 1/6

Taking the square root of both sides, we get:

abc = 1/sqrt(6)

So, Erica's whole number is 2 x 3 x 6 = 36, and her fraction is 1/sqrt(6). The product of these is:

36 x 1/sqrt(6) = 6sqrt(6)

Her score is the absolute difference between 6sqrt(6) and 1:

|6sqrt(6) - 1| = 13.97 (rounded to two decimal places).

d) Erica's score for this round is 13.97.

Explanation: