1. D: The smallest negative integers are those that have the largest absolute value. Therefore, the negative integers, written in order from least to greatest, are -8,-7 4/5,-3/4. The percent, 18%, can be written as the decimal, 0.18; 0.18 is less than 0.25. The decimal, 2.5, is the greatest rational number given. Thus, the values, -8,-7 4/5,-3/4,18%,0.25,2.5, are written in order from least to greatest.
2. B: The fraction, 2 1/4, can be written as the decimal,2.25. The fraction, 2 2/5, can be written as the decimal, 2.40. The fraction, 2 3/8, can be written as the decimal, 2.375; 2.375 is larger than 2.25 but smaller than 2.40.
3. A: Jason's number can be determined by writing the following expression: ?(2x-4), where x represents Amy's number. Substitution of 20 for x gives ?(2(20)-4), which simplifies to ?36, or 6. Thus, Jason's number is 6. Jason's number can also be determined by working backwards. If Jason's number is the square root of 4 less than 2 times Amy's number, Amy's number should first be multiplied by 2 with 4 subtracted from that product and the square root taken of the resulting difference.
4. A: The square root of a square is equal to the length of one of the sides, or the number of unit squares comprising a side. For example, a square representing 7 squared will have 7 unit squares on each side; 7^2=49, and 7 is the square root of 49. The square will contain 49 unit squares, with 7 unit squares comprising each side.
5. B: In order to determine the total number of cups of sugar used while baking, the product of 5 and 3/4 should be calculated: 5?3/4=15/4, which can be simplified to 3 3/4. Thus, she used 3 3/4 cups in all.
6. B: In order to determine the number of manuscripts each editor will review, the total number of manuscripts should be divided by the number of editors; 29 / 8 can be written as 29/8, which simplifies to the mixed fraction 3 5/8. Notice that the quotient is 3 with a remainder of 5.
7. C: The 80% means 80 out of 100, which can be written as 80/100 . This fraction can be written in lowest terms by dividing both the numerator and denominator by the greatest common factor of 20, to get the fraction, 4/5.
8. D: By adding all of the dimes, we find that there are a total of 100 dimes in the bag. 10 of them were minted in 1945. The probability, then, of choosing a dime minted in 1945 is 10 out of 100, which is equivalent to the fraction 1/10.
9. B: 15/4 . The value of 3 is equivalent to 12/4. Therefore, 3 3/4=12/4+3/4=15/4. Another way of of finding this is sometimes called the "C" method. 3 3/4 equals (4x3+3)/4=15/4 .
10. E: . When you take the square root of a number, the answer is the positive and negative values of the root. Therefore, and x=-7. Only -7 is an answer choice.
