Question

Number 68. Fill in box to make a true equation?

Answer 1

`color(blue)(6)/color(blue)(3) + color(blue)(5)/color(blue)(4) = 3 1/4`

Explanation:

We want to place `3, 4, 5, 6` into the template:

`?/? + ?/? = 3 1/4`

in order that the equation holds.

Note that if close numbers are chosen as the numerator and denominator of a fraction then the resulting fraction will tend to be close to `1` and `1+1=2` is somewhat less than the target `3 1/4`.

We can maximise one of the fractions by choosing `6` and `3` to give:

`6/3 = 2`

Then the remaining fraction we need is:

`3 1/4 - 2 = 1 1/4 = 5/4`

So one solution is:

`color(blue)(6)/color(blue)(3) + color(blue)(5)/color(blue)(4) = 3 1/4`

The only other solution is:

`color(blue)(5)/color(blue)(4) + color(blue)(6)/color(blue)(3) = 3 1/4`