Consider each answer separately. What happens when we multiply a number by 0? What happens when we multiply a number by a proper fraction? An mixed number?
D
Practice makes perfect
In this exercise, we want to determine which of the given numbers gives a product between 34 and 1 when multiplied by 34. Let's take a look at the first option, 0. Recall that when 0 is multiplied by any number, the result is always 0. Since 0 is not between 34 and 1, answer A is not correct.
cclc
A:&0 * 3/4 =0& 0 < 3/4& *Now let's consider answers B and C together because they both contain values that are proper fractions. Proper fractions are less than 1. When we multiply a number by such a fraction, the result has to be less than the original value. Since our other factor is 34, both products have to be less than 34. Therefore, options B and C are also incorrect.
cclc
B:&3/4 * 3/4 = 9/16 & 9/16 < 3/4& * [1em]
C:&1/4 * 3/4 = 3/16 & 3/16 < 3/4& *
This would suggest that option D is correct, but let's check it anyway. The number 1 14 is a mixed number that can be also written as 54. This value is greater than 1, so when it is multiplied by 34, the result will be greater than 34. Let's multiply 54 by 34 to see if the result is also less than 1.
cclc
D:&5/4 * 3/4 = 15/16 & 3/4 < 15/16 < 1 & ✓
The result of the multiplication of the number from option D and 34 is between 34 and 1. Therefore, option D is the correct answer.
