Is 5/4 times 6, 11/8 times 6, and 3/8 times 6 products greater than 6?

Here were are dealing only with positive numbers and positive fractions whose numerators and denominators are positive integers.

If you multiply a number by 1, you get that number.

For example, 1 * 5 = 5; 1 * 8 = 8

If you multiply a number by a positive number less than one, the result is smaller than the number you started with.

For example, 1/2 * 6 = 3. Since 1/2 is less than 1, multiplying 1/2 by 6 gives a result smaller than 6. 3 is smaller than 6.

If you multiply a number by a number greater than 1, the result is greater than the number you started with.

For example, 2 * 6 = 12. Since you multiplied 6 by a number greater than 1, which 2 is, you get 12 which is greater than 6.  5/4 * 20 = 25. Since 20 was multiplied by 5/4, and 5/4 is greater than 1, the result, 25, is greater than 20.

It's easy to tell if a fraction is greater than or less than 1. If the numerator is less than the denominator, the fraction is less than 1.

Examples of fractions less then 1: 1/3, 1/6, 5/6, 11/12, 18/121. In every case to the left, the numerator is less than the denominator, so all fractions are lees than 1.

If the numerator is greater than the denominator, then the fraction is greater than 1.

Examples of fractions that are greater than 1: 4/3, 11/8, 3/2, 121/100, 17/18.

5/4 is greater than 1, so 5/4 * 6 is greater than 6.

11/8 is greater than 1, so 11/8 * 6 is greater than 6.

3/8 is less than 1, so 3/8 * 6 is less than 6.

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step-by-step explanation: