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Updated on Jul 5, 2011
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 d. The product is the result of multiplication. To solve this problem, you need to multiply 4 by 3. The product (and the answer) is 12, choice d. Answer choice a, 1, is the difference. Choice b, 1, is the quotient. Choice c, 7, is the sum.
 c. Millimeters is a smaller unit of measurement than centimeters. Therefore, you need to use multiplication to convert from centimeters to millimeters. To convert from centimeters to millimeters, you need to multiply by 10. 30 centimeters = 30 × 10 millimeters, or 300 millimeters, choice c.
 c. To add unlike fractions, you need to find a common denominator. The lowest common denominator or and is 12. To convert so that it has a denominator of 12,multiply the numerator and denominator by 3: . To convert so it has a denominator of 12,multiply the numerator and denominator by 4: . Once the fractions have like denominators, you can add them by simply adding the numerators: .
 a. Remember that the decimal value of a percent can be found by moving the decimal point two places to the left. So 50% is equivalent to 0.50. The student should not have multiplied 80 by 50, but instead should have multiplied 80 by 0.50, choice a.
 d. To solve for the value of an exponent, multiply the base times itself the number of times in the power. So, to solve for 33, you need to multiply 3 by itself 3 times. The product of 3 × 3 × 3 is 27, so choice d is correct.
 a. To find the area of a rectangle, a student needs to multiply the length of the rectangle by its width. The expression in answer choice a shows this solution correctly.
 b. There are 100 cents in 1 dollar. Therefore, there are 200 cents in 2 dollars. The only answer choice that has a value equal to 2 dollars is choice b, 200 cents.
 c. There are 200 students in the middle school. The circle graph shows that 20% of the students in the middle school are 12 years old. To find the total number of 12yearold students in the school, you need to multiply the percent by the total number of students. To multiply a percent, first convert it to a decimal by moving the decimal to places to the left. Because 200 × 0.20 = 40, answer choice c is correct.
 d. The value of the decimal 0.1 is onetenth, because there is a 1 in the tenth column. It does not matter if there are zeros at the end of a decimal; the value does not change. The number 0.1 is equivalent to 0.10, 0.100, or 0.1000. However, 0.01 has a value of onehundredth, so choice d does not represent onetenth.
 a. Remember that the symbol > means is more than and the symbol < means is less than. If you solve for the addition and subtraction on either side of the symbols, only 8 + 8 > 17 – 2 (which is 16 > 15) is correct.
 c. To find an estimate, you do not need to find an actual answer. You can choose numbers that are easier to work with. Instead of multiplying the 12 boxes of crayons times the 18 crayons in each box, you can round each number to the nearest 10. You can then multiply 10 boxes of crayons by 20 crayons in each box to find an approximate total number of crayons that the teacher ordered. The best estimate for the total number of crayons ordered is 200, choice c.
 b. The small box in the bottomleft corner of the triangle means that the angle is a right angle. Because the triangle has a right angle, it is a right triangle, choice b. The triangle has three sides of different lengths, so it is neither equilateral, choice a, or isosceles, choice c. It does not have an obtuse angle, so it is not an obtuse triangle either.
 d. The trick to setting up this kind of addition problem is to align the digits properly when stacking them. Make sure to regroup the ten ones to form one more ten, and then regroup the ten hundreds to form one more thousand. The sum is 4,023, answer choice d.
 a. This question asks for the approximate value, which means that you to not need to find an exact answer. Because the problem gives you decimals, it would be easier to round each number to a whole number. Instead of dividing 6.13 by 2.03, divide 6 by 2.Now the correct answer, choice a, becomes clearer.
 d. Several steps are required to solve this problem. First, you need to figure out how many minutes a teacher has with a group of students per week. Because the teacher has the group for three classes, and each class is 40 minutes, the amount of time the teacher has each week is 3 × 40 minutes, or 120 minutes. 120 minutes can be converted to two hours because there are 60 minutes in one hour—or 120 minutes in two hours. Last, you need to remember that the question asks for the total number of hours that the teacher has with the group of students during a fourweek period. If the teacher has the students for two hours each week for four hours, then the answer is 2 hours × 4 weeks = 8 hours in total.
 d. The tricky part of this problem is identifying the pattern. If you don't see the pattern right away, try to figure out how to get from the first number (5) to the second number (16). You could multiply by 5 and add 1. Or you could add 11. To go from 16 to 27, however, multiplying by 5 and adding 1 does not work. The number 27 is 11 more than 16, so adding 11 must be the way that the pattern increases. Therefore, the number after 38 will be 49. However, that is only the fifth number in the pattern. The sixth number in the pattern will be 11 more than 49, which is 60, choice d.
 c. The tenths place is the first place directly to the right of the decimal point. In the number 219.74, the digit 7, choice c, is in the tenths place.
 a. A negative number will be to the left of 0 on a number line. The number –3.5 is also smaller than –3, so it will be to the left of –3 on the number line. It will be between –3 and –4, choice a.
 b. Point F is one unit to the left of the origin (the point where the xaxis and yaxis cross). That means its xcoordinate is –1. The point is also 4 units down from the origin. That means its ycoordinate is –4. The ordered pair for point F should be (–1, –4). If you picked choice d, you confused the order of the x and y coordinates in an ordered pair. The xcoordinate will always go first.
 b. To solve this onestep linear equation, a student needs to isolate the variable, x, on one side of the equation. Because the left side of the equation has 4x, which is the same as 4 times x, the student must "undo" the multiplication. To do that, he or she must divide by the number in front of the variable. Whatever is done to one side of the equation must be done to both sides, however. Therefore, the student should divide both sides of the equation by 4, choice b.
 d. The student buys two slices of pizza, which are $0.90 each, one apple, which is $0.35, and one milk, which is $0.45. To solve this problem, add up the prices of each of the items (being sure to count the cost of the pizza twice). $0.90 + $0.90 + $0.35 + $0.45 = 2.60, choice d. Be sure to regroup the ten hundredths in your addition, or you may get choice c instead.
 b. You need to remember the order of operations to solve this problem. Multiplication and division always get solved before addition or subtraction (unless there are parentheses). Therefore, the first step is to perform the multiplication:
 23 – 3 × 5 + 2 =
 23 – 15 + 2 =
 a. To find the perimeter of any polygon, you must add the lengths of all its sides. If the pentagon were regular, you could multiply the length of one side by 5. But because the pentagon is irregular, the only way to determine its perimeter is to use addition, choice a.
 c. If you follow the line on the graph, you can tell that the population of the city goes up a few thousand every year. The population is a little less than 32,000 in 2010. The question asks for the best prediction for the population of the city in 2020. Therefore, it will most likely be more than 32,000, eliminating choices a and b. It would be a huge jump for the population to reach 40,000—a jump too great for the trend of the line. 35,000, choice c, is the best prediction.
 c. The decimals 1.59, 1.8, and 1.88 all have the digit 1 in the ones place. But because 1.59 has the digit 5 in the tenths place, it is smaller than the other two decimals. The decimals 1.8 and 1.88 both have an 8 in the tenths place. To compare 1.8 and 1.88, it may be helpful to add a zero to the right of 1.8. Changing 1.8 to 1.80 does not change its value. Now you can compare the digits in the hundredths place. Because 8 is greater than 0, 1.88 is greater than 1.8. That means 1.88 is the largest decimal, followed by 1.8, and then 1.59, choice c.
 a. Set up this subtraction problem by aligning the numbers by their decimal points, as shown:
 4.05
 – 1.34
 d. Converting from kilograms to grams involves converting from a larger unit to a smaller unit. That means you must use multiplication to solve. One kilogram is equal to 1,000 grams. Therefore, 2.5 kilograms is equivalent to 2.5 × 1,000 grams per kilogram = 2,500 grams, choice d.
 b. The numbers in the addition problem are aligned to the right. However, decimals must always be added and subtracted with their decimal points aligned. (When multiplying, it is not essential to align by decimal point.) The student found an incorrect sum because he or she failed to align by the decimal point, choice b.
 a. Adding a negative integer is the same as subtracting a positive integer. Therefore, –25 + (–10) is equivalent to –25 – 10. The difference will be smaller (or more negative) than –25. The correct answer is –35, choice a.
 c. To find the median of any data set, you need to put the values in order. Th3.e number in the middle will be the median. In the table shown in this problem, the heights are 62, 63, 66, 67, and 67 inches in order from shortest to tallest. The value in the middle of the set is 66 inches, choice c. Remember that the values need to be in order. The number 62, choice a, may be in the middle of the table, but it is not in the middle when the numbers are in order. The mode is 67 inches, choice d, because it appears more often than any other number. The mean of the data set is 65 inches, choice b.
Now only subtraction and addition remain. You perform those operations in order from left to right. So subtract the 15 first:
 23 – 15 + 2 =
 8 + 2 =
And finally you can perform the addition:
 8 + 2 = 10
The answer is 10, choice b.
To subtract in the tenths place, you need to regroup from the ones place.
Now you can subtract from right to left, and the difference will be 2.71, choice a.
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