An infinite number of ratios are equivalent to 3: 8.how can that be possible, when the multiplication table only goes to 9?

Certainly, you know how to multiply by numbers larger than 9. If you're doing it by hand (not using a calculator), you make use of place value and partial products. The numbers in the multiplication table, together with appropriate procedures, let you multiply by any number you like.

If we want to multiply this ratio by 85, we have

... 3×85 : 8×85

... = 3×(8×10 +5) : 8×(8×10 + 5)

... = (3×8×10 +3×5) : (8×8×10 + 8×5)

... = (24×10 + 15) : (64×10 + 40)

... = (240 + 15) : (640 +40)

... = 255 : 680 . . . . . without using multiplcation table values beyond 9

The factor of 85 that we arbitrariy chose could have been any of an infinite number of factors, including negative and fractional values.

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step-by-step explanation: