Which is bigger, 4/7 or 7/12?

Question

Two close fractions, and you want the larger one fast. Solve in your head. Which is bigger, 	frac{4}{7} or 	frac{7}{12}? Aim: under 15 seconds.

Accepted Answer

Cross-multiply and compare the two products (the one sitting over the larger fraction wins): 4 	imes 12 = 48 \qquad	ext{vs}\qquad 7 	imes 7 = 49. Since 49 48, the side with the 7 	imes 7 product, namely 	frac{7}{12}, is larger. Confirm loosely: 	frac47 \approx 0.571 and 	frac{7}{12} \approx 0.583. Yes, 	frac{7}{12} wins. Takeaway. To compare 	frac{a}{b} and 	frac{c}{d}, compare a 	imes d against c 	imes b; whichever product is larger flags the larger fraction. It avoids finding a common denominator and beats converting to decimals when the fractions are close.

Which is bigger, 4/7 or 7/12?

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