1.
What is one hundred and seven thousandths in standards form?
Correct Answer
B. 100.007
Explanation
one hundred, and means . 0(tenths)0(hundredths)7(thousandths)
2.
Which value is NOT between 3.6 and 3.75?
Correct Answer
D. 3.8
Explanation
3.8 is more than 3.75
3.
Yvonne earns $38.25 in one week by baby-sitting. She earns $4.75 per hour. Estimate the number of hours she works.
Correct Answer
A. 8
Explanation
Yvonne earns $4.75 per hour by babysitting and earns a total of $38.25 in one week. To estimate the number of hours she works, we can divide the total amount earned by the amount earned per hour. In this case, $38.25 divided by $4.75 equals approximately 8. Therefore, Yvonne works approximately 8 hours in one week.
4.
Replacing the box with which number will make 0.22+ 0.☐8 > 0.5 true?
Correct Answer
D. 3
Explanation
Replacing the box with the number 3 will make the inequality 0.22 + 0.38 > 0.5 true. This is because when we replace the box with 3, the expression becomes 0.22 + 0.38 = 0.60, which is greater than 0.5.
5.
In 9 minutes it will be 11:06. What time is it now?
Correct Answer
D. 10:57
Explanation
The question states that in 9 minutes, it will be 11:06. This means that currently, it is 9 minutes before 11:06. Therefore, the current time is 10:57.
6.
4 × 0.2 × 1000
Correct Answer
C. 800
Explanation
The expression 4 × 0.2 × 1000 can be simplified by multiplying 4 and 0.2 to get 0.8, and then multiplying the result by 1000 to get 800. Therefore, the answer is 800.
7.
Which quotient is greatest?
Correct Answer
C. 83.1 ÷ 10
Explanation
The quotient 83.1 ÷ 10 is the greatest because when dividing 83.1 by 10, the result is 8.31. The other quotients are smaller: 8.31 ÷ 10 equals 0.831, 83.1 ÷ 100 equals 0.831, and 831 ÷ 1000 equals 0.831. Therefore, 83.1 ÷ 10 is the greatest quotient among the options given.
8.
The quotient 1.35 ÷ 0.4 is nearest which value?
Correct Answer
B. 3
Explanation
The quotient of 1.35 ÷ 0.4 is closest to the value 3. This can be determined by dividing 1.35 by 0.4, which equals 3.375. Since we are looking for the nearest value, we round down to the nearest whole number, which is 3. Therefore, the correct answer is 3.
9.
Use the order of operations to solve.
36 ÷ 3 −1 × 7
Correct Answer
A. 5
Explanation
To solve this expression, we need to follow the order of operations, which states that we should perform multiplication and division before addition and subtraction. First, we divide 36 by 3, which equals 12. Then, we subtract 1 from 12, resulting in 11. Finally, we multiply 11 by 7, giving us the final answer of 77. Therefore, the given answer of 5 is incorrect.
10.
What is the fifth term in the number pattern? 1; 20; 400; 8000;...
Correct Answer
B. 16,000
Explanation
The pattern in the given number sequence is that each term is obtained by multiplying the previous term by 20. Starting with 1, we get 1 x 20 = 20, then 20 x 20 = 400, and so on. To find the fifth term, we multiply the fourth term (8000) by 20, which gives us 160,000. Therefore, the fifth term in the number pattern is 160,000.
11.
What is the value of 3p+6 when p=7?
Correct Answer
C. 27
Explanation
When p is equal to 7, we can substitute this value into the expression 3p+6. This gives us 3(7)+6, which simplifies to 21+6. Therefore, the value of 3p+6 when p=7 is 27.
12.
Which of the following does NOT describe the expression x-36?
Correct Answer
B. X less than 36
Explanation
The expression "x less than 36" does not describe the expression x-36. The expression x-36 represents subtracting 36 from x, not comparing x to 36.
13.
What is the value of 8x−6 when x=4?
Correct Answer
B. 26
Explanation
When x is equal to 4, we can substitute this value into the expression 8x - 6. Therefore, the calculation becomes 8(4) - 6 = 32 - 6 = 26. Hence, the value of 8x - 6 when x is equal to 4 is 26.
14.
What is the solution of 60 ÷ n = 4?
Correct Answer
B. 15
Explanation
The solution to the equation 60 ÷ n = 4 can be found by dividing 60 by 4, which equals 15. Therefore, the correct answer is 15.
15.
What is the solution of z − 2.71 = 5?
Correct Answer
D. 7.71
Explanation
The solution of the equation z - 2.71 = 5 can be found by adding 2.71 to both sides of the equation. This will eliminate the -2.71 on the left side, leaving us with z = 7.71. Therefore, the correct answer is 7.71.
16.
What is the value of 2^{3}×3^{2}?
Correct Answer
A. 72
Explanation
The value of 23 multiplied by 32 is 72.
17.
What is the value of 5 + 6^{2} − 1?
Correct Answer
C. 40
Explanation
The value of 5 + 62 is 67. Subtracting 1 from 67 gives us 66. Therefore, the correct answer is 66, not 40.
18.
Which number is divisible by both 2 and 3?
Correct Answer
C. 1, 230
Explanation
The number 1,230 is divisible by both 2 and 3 because it ends with a 0, which means it is divisible by 2, and the sum of its digits (1 + 2 + 3 + 0) is 6, which is divisible by 3.
19.
What is the prime factorization for 48?
Correct Answer
D. 3 ∙ 2^4
Explanation
The prime factorization of 48 can be found by breaking down the number into its prime factors. Starting with the smallest prime number, which is 2, we divide 48 by 2 to get 24. We continue dividing by 2 until we can no longer divide evenly, which gives us 24 ÷ 2 = 12. Next, we divide 12 by the next smallest prime number, which is 3, to get 12 ÷ 3 = 4. Finally, we divide 4 by 2 to get 4 ÷ 2 = 2. Therefore, the prime factorization of 48 is 2^4 × 3, which can be written as 3 ∙ 2^4.
20.
What is the GCF of 56 and 84?
Correct Answer
D. 28
Explanation
The GCF (Greatest Common Factor) is the largest number that can evenly divide both 56 and 84. To find the GCF, we can list the factors of each number and find the largest common factor. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The largest common factor between the two numbers is 28, so it is the GCF.
21.
The length of a segment is 3/8 inch. How do you write the length as a fraction with a 16 as its denominator?
Correct Answer
B. 6/16
Explanation
To write the length of a segment as a fraction with a denominator of 16, we need to find an equivalent fraction. Since 16 is a multiple of 8, we can multiply both the numerator and denominator of 3/8 by 2 to get the equivalent fraction. This gives us 6/16, which is the correct answer.
22.
The largest pearl ever found was in the Philippines. Its diameter measures 5 1/2 inches. What is the diameter of the pearl as an improper fraction?
Correct Answer
C. 11/2 inches
Explanation
The given diameter of the pearl is 5 1/2 inches. To convert this mixed number into an improper fraction, we multiply the whole number (5) by the denominator (2) and then add the numerator (1). This gives us 11. The denominator remains the same (2). Therefore, the diameter of the pearl as an improper fraction is 11/2 inches.
23.
What is the LCM of 24 and 28?
Correct Answer
C. 168
Explanation
The LCM (Least Common Multiple) of two numbers is the smallest multiple that is divisible by both numbers. To find the LCM of 24 and 28, we can list their multiples and find the smallest common multiple. The multiples of 24 are 24, 48, 72, 96, 120, 144, 168, ... and the multiples of 28 are 28, 56, 84, 112, 140, 168, .... The smallest common multiple is 168, which is divisible by both 24 and 28. Therefore, 168 is the LCM of 24 and 28.
24.
Which of these fractions is NOT in order from least to greatest?
Correct Answer
A. 3/8, 3/9, 5/12
Explanation
The fractions in the first option are 3/8, 3/9, and 5/12. To determine if they are in order from least to greatest, we can convert them to have the same denominator. The least common multiple of 8, 9, and 12 is 72. Converting the fractions, we get 27/72, 24/72, and 30/72. Comparing the numerators, we can see that 24/72 is the smallest, followed by 27/72, and then 30/72. Therefore, the fractions in the first option are not in order from least to greatest.
25.
What decimal is equivalent to 8/15?
Correct Answer
B. 0.53333...
Explanation
The decimal equivalent to 8/15 is 0.53333... because when we divide 8 by 15, we get a repeating decimal pattern of 0.53333... The number 0.53333... means that the digit 3 repeats infinitely.
26.
What is 0.24 as a fraction in simplest form?
Correct Answer
B. 6/25
Explanation
The decimal 0.24 can be written as the fraction 24/100. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 24 by 4 gives us 6, and dividing 100 by 4 gives us 25. Therefore, the simplest form of 0.24 as a fraction is 6/25.