Question

When you multiply 2/3 by a fraction less than one, how does the product compare to the factors. Explain.

Answer 1

Answer: the product is smallr than either of the factors.

Step-by-step explanation:

1) Start seing some examples:

i) 2/3 × 1/2 = 1/3, which is less than 2/3 and less than 1/2

ii) 2/3 × 8/9 = 16 / 27, which is less than 2/3 and less than 8/9

iii) 2/3 × 1/10 = 2/30, which is less than 2/3 and less than 1/10.

2) Why does that happen?

Because 2/3 is a number less than 1, such as any proper fraction is. And, whenever a number is multiplied by a number less than 1, the result is a smaller number.

Then, since 2/3 is less than 1, the product will be less than the other fraction. And since the other fraction is less than 1 too, the product will also be less than 2/3.

Hence, you conclude that the product is a number smaller than 2/3 and than the other fraction, i.e. smaller than either of the factors.

Answer 2

The product is less than either of the factors. Multiplying a number < 1 with 2/3 another number < 1, will give a fraction of a fraction, and part of a fraction is an even smaller fraction. Another way of looking at it: Fractions less than one have numerators smaller than their denominators. When multiplying fractions, you multiply across, so multiplying two fractions that are both less than one will always give a numerator much smaller than the denominator, and a larger denominator makes for a smaller number. I hope this helps, but if you have questions, ask.