by Bill Graham

The answer is [4 - (4÷7)] × 7. (The grouping symbols are used only for clarity.)

If you’re like most people, you will do the division on a calculator using decimals. (Who likes long division?) On most inexpensive calculators when you divide four by seven, you will get the answer 0.5714285 . . ., a repeating decimal. When you do the rest of the calculation, the result will be 23.999999 (close enough for government work) or 24 if your calculator rounds off.

But that’s not the best way to think about this solution. There is no difference between a fraction and a division problem. Four divided by seven is the same as the fraction 4/7. If you work out the above solution remembering your fractions from seventh-grade math, 4 - 4/7 = 3 3/7. Then change 3 3/7 to the improper fraction 24/7 and multiply by 7 and zowie, exactly 24.

The important step in finding this answer is using fractions. Here, you may have a fraction with a denominator of 7 or 4. Realizing that 4 is the same as 28/7 gets you close. Subtract 4 from the numerator to get 24/7, and multiply by 7 to get 24.