Solution: 532.
Because we want the largest result possible, you should try
to do two things: make the denominator of the fraction as small as possible,
and make the numerator as large as possible.
To make the denominator as small as possible, you can use
subtraction and division. The smallest possible denominator can be obtained
with 1 – 8 ÷ 9, which has a value of 1/9, and dividing by 1/9 is the
same as multiplying by 9. That’s a good start. Then, to make the numerator
as large as possible, take the three greatest remaining digits 5, 6, and 7, and
combine them with the remaining operations, + and ×. The largest expression that
can be formed in the numerator using these digits and operations is 6 × 7 + 5.
Luckily, the result with this numerator and denominator contains the remaining
three digits, 2, 3, and 4:
(6×7+5) ÷ (1-8÷9) = 47×9 = 423
This is a very good answer, and if this is the answer you
obtained, you should be very proud!
However, there is a better answer. If you compromise just a
little on the size of the denominator, you can increase the size of the
numerator, which will yield a greater result. In the denominator, use 1 – 6 ÷
7, which has a value of 1/7. Dividing by 1/7 is the same as multiplying by 7,
which isn’t as good as multiplying by 9, but it’s still pretty good. The
benefit of doing this is that it leaves the largest digits, 8 and 9, to be used
in the numerator. You can then make the expression 8 × 9 + 4 for the numerator,
which will yield a final result on the right containing the digits 2, 3, and 5
that is greater than 423:
(8×9+4) ÷ (1-6÷7) = 76×7 = 532
