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Calculate the answer by following the correct order of operations.
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Calculate the answer by following the correct order of operations.
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Calculate the answer by following the correct order of operations.
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Calculate the answer by following the correct order of operations.
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The solution to the expression given below contains one error. Identify the error and present a correct solution.
The error occurs between the 3^{rd} and 4^{th} lines of the solution. The division needs to be done before the subtraction .
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Calculate the following.
Express your answer as a fraction in lowest terms.
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Calculate the following.
Express your answer as a fraction in lowest terms.
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Calculate the following.
Express your answer as a fraction in lowest terms.
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Calculate your answer.
Express your answer as a fraction in lowest terms.
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Convert the following fraction from mixed to improper.
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Convert the following fraction from improper to mixed.
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Calculate the following. Express your answer as a mixed fraction in lowest terms.
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Calculate the following. Express your answer as a mixed fraction in lowest terms.
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The solution to the expression given below contains one error. Identify the error and give the correct solution.
The error occurs between the 4^{th} and 5^{th} lines. The operation between the 9 and the 4 should be multiplication, not addition.
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Calculate the following:
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Calculate the following. Express your answer to the nearest hundredth.
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Calculate your answer. Express your answer to the nearest hundredth.
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Calculate the following. Express your answer to the nearest tenth.
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Calculate the following. Express your answer to the nearest hundredth.
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Calculate the following. Use the correct order of operations and the ‘rules’ for adding, subtracting, multiplying, and dividing decimals. Express your answer to the nearest tenth.
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Calculate the following. Use the correct order of operations and the ‘rules’ for adding, subtracting, multiplying, and dividing decimals. Express your answer to the nearest tenth.
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Fill in the blank spaces in the chart below. Use the first line as a guide.
Decimal | Fraction | Percent |
0.35 | 35/100 | 35% |
0.65 | ||
43/100 | ||
22.5% |
Decimal | Fraction | Percent |
0.35 | 35/100 | 35% |
0.65 | 65/100 | 65% |
0.43 | 43/100 | 43% |
0.225 | 225/1000 | 22.5% |
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At the start of the soccer season a player buys a new pair of shoes. The regular price of the shoes is $65.50. A discount of 35% is applied to the price before the 13% tax is added.
What is the total cost of the shoes?
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At the start of the soccer season a player buys a new pair of shoes. The regular price of the shoes is $65.50. A discount of 35% is applied to the price before the 13% tax is added.
If the discount was rounded to $22.93 instead of using 22.925, would the total cost of the shoes be greater or less than $48.11? By how much?
Rounding the discount up would make the total cost of the shoes decrease by $0.01.
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Convert the following Imperial measures into the units indicated.
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Convert the following metric measures into the units indicated.
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Fill in the blank spaces so that the total of the measurements equals 193 inches. Express your answer as a whole number.
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Determine whether or not a truck measuring 3.75 meters high is able to pass under a concrete bridge that is 12 feet above the surface of a road.
If the truck does fit, state the distance from the top of the truck to the bottom of the tunnel. If the truck does not fit, state how much shorter the truck needs to be to fit under the bridge.
Do not round any calculations for this question.
Answer: No, the truck is not able to pass under the bridge. The truck needs to be 0.30314961 feet shorter to fit under the bridge (or 0.0924 meters shorter).
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The solution to the conversion given below contains one error. Identify the error and present a correct solution.
Do not round any calculations for this question.
The conversion factor from centimeters to inches is reversed.
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Calculate the area and the perimeter of the object below. Be sure to include units of measure in your answer.
Do not round any calculations for this question.
Before we can find the length of the perimeter, the hypotenuse of the triangle must be calculated using the Pythagorean Theorem.
Answers: Area = 84 cm^{2}, Perimeter = 56 cm
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Calculate the area and the perimeter of the object below. Be sure to include units of measure in your answer.
Do not round any calculations for this question.
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Calculate the area and the perimeter of the object below. Be sure to include the unit of measure in your answer.
Area Calculations
The area of the square is:
The vertical leg of the triangle has a length of 4 cm because it is equal to the side length of the square.
The area of the triangle is:
The semi-circle has a diameter equal to the side length of the square. The radius is half the measure of the diameter.
The area of the semi-circle is:
The total area is:
Perimeter Calculations
The distance around the outside of the figure is the perimeter which will include two sides of the square, the two longer legs of the triangle, and half of the circumference of a circle with a radius of 2 cm.
Before we can find the length of the perimeter, the hypotenuse of the triangle must be calculated using the Pythagorean Theorem:
The circumference of the circle is:
The total perimeter is:
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A circle with a radius of 2 cm is inscribed in a square as shown in the diagram below. Calculate the area of the shaded region of the square. Be sure to include unit of measure in your answer.
The side length of the square is 4 m because it is twice the radius of the circle. The area of the shaded region of the square is calculated by subtracting the area of the circle from the area of the square.
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A rectangular box has a volume of 2.8 ft^{3}. The base of the rectangular box measures .
Determine the height of the box, measured in feet. Express your answer to the nearest hundredth.
Both the measurements of the base must be changed into feet.
Substituting the measurements into the formula for the volume of a rectangular solid gives:
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Solve the following equation for the variable x.
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Solve the following equation for the variable x.
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Solve the following equation for the variable x.
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The solution to the equation given below contains two errors. Identify the errors and give the correct solution.
The first error is on line 3 where the double negative was missed. The term really should be . The second error is in collecting like terms on line 5. The constant terms were collected correctly, but the variable terms were not. When the is moved to the left side, it must become positive. Even though two errors were made, one ‘undid’ the other and in turn, the answer is correct. Unfortunately, this answer was achieved using two incorrect procedures.
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Find the value of x that makes the proportion true.
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Find the value of x that makes the proportion true.
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Susanne achieved the following test scores on her first 4 math tests:
Test 1: 67%
Test 2: 81%
Test 3: 71%
Test 4: 56%
What percentage does Susanne need to get on her 5^{th} math test to increase her overall test score average by 5%?
The average on her first 4 tests is:
An increase of 5% would be an overall test average of
Susanne would need to score on her 5^{th} math test to increase her overall test score average by 5%.
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One way Max can calculate the final price of a television, in Manitoba, is to multiply the before-tax price by 1.13.
There is a second method that Max could use to calculate the final price of the television. This method involves two steps rather than just the one step of multiplying by 1.13.
Explain this second method.
To get the final price of the television, Max could multiply the before-tax price by 0.13 and then add the result to the before-tax price.
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Using your answer from the previous question (26a) calculate the final price of a television, purchased in Manitoba, that has a before-tax price of $485.00.
Answer:
The multiplication and division need to be done first.
Next, the two results are added together.
Explain the necessary steps to perform the addition of two simple fractions by finding a common denominator.
A common denominator may be found by multiplying together the denominators of the two simple fractions. The result will be the common denominator and will be the denominator of the answer.
Once the common denominator is found, each fraction must be multiplied by the other fraction’s denominator in order to balance out the fractions.
Lastly, the numerators of the fraction are added together. This number becomes the numerator of the answer and is written over the common denominator. This fraction is the answer.
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Give a numeric example that supports your explanation given in the previous question (28a).
A sample response is:
Therefore, the common denominator of the two fractions is 20 and the numerators are added together to get the final answer of .
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Construct an algebraic equation that, when solved, is equal to 7. Your equation must have the following characteristics:
- a binomial (two terms) enclosed in one set of brackets that contains the variable ‘x’ and a subtraction sign. [ex. (2x-3)]
- one addition sign (+)
- one equal sign (=)
The solutions to this question will vary and the possibilities are endless. One example is shown above but any algebraic equation with an answer of 7 and satisfying the characteristics outlined in the question would be considered correct.
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Part 1: A shop owner has a large number of rectangular storage bins that measure 1 ft by 0.75 foot by 0.75 ft.
He needs to place these bins on a shelf that measures 3 meters by 1.5 meters by 1.5 meters.
By comparing the total volume of the bins to the volume of the shelf, determine the number of bins that can fit on the shelf.
Do not round any calculations for this question.
Convert the units of measure from either Imperial to metric or vice versa. The metric to Imperial version is shown in Solution 1 and the Imperial to metric version is shown in Solution 2. Either calculation will yield the same number of boxes.
Solution 1:
Calculate the volume of the shelving unit and the volume of each storage bin. Then, divide the volume of the shelving unit by the volume of each storage bin.
The conversion for the shelving unit, from meters to feet, is:
The volume of each storage bin is:
The volume of the shelving unit divided by the volume of each bin is:
Since you cannot have a partial bin, 423 storage bins will fit onto the shelf. This is a theoretical calculation based on total volume.
Solution 2:
Calculate the volume of the shelving unit and the volume of each storage bin. Then, divide the volume of the shelving unit by the volume of each storage bin.
The conversion for the volume of each storage bin, measured in m^{3}, from feet to meters, is:
The volume of the shelving unit is.
The volume of the shelving unit divided by the volume of each bin is .
Since you cannot have a partial bin, 423 storage bins will fit onto the shelf. This is a theoretical calculation based on total volume.
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Part 2: Taking into consideration the physical limits of the bins to be stored, and not just based on volume, do you think the actual number of bins that will fit on the shelf will be exactly 423? Fully explain your answer.
In theory, taking into consideration the physical limits of the shelf and the bins, there will be fewer than 423 bins that can be stored on the shelf.
Solution:
Considering the physical geometry of the shelving unit and of the storage bins, there are two possibilities by which the bins can be arranged on the shelves.
The first possible arrangement is given below.
Nine storage bins (9 ft x 1 ft = 9 ft) can fit across the side of the shelving unit measuring 9.842519685 feet.
Six storage bins (6 ft x 0.75 ft = 4.5 ft) can fit across the shelving unit where the side measures 4.921259843 feet.
After rounding the numbers down to the nearest whole number (since you cannot have part of a box) the result is an actual number of boxes.
The other possible arrangement is to put the 0.75 ft sides of the box along the 9.842519685 ft. length of the shelf. This would yield boxes across.
Four of the 1 ft sides can fit along the width of the shelf (since 4.921259843 is slightly less than 5) and the boxes could be stacked 6 boxes high since.
This would give a total number of boxes.
The first arrangement results in the largest number of boxes on the shelf so the answer is 324 boxes.
The difference in the number of boxes is due to the fact that it is impossible to have part of a box, or part of a box’s dimension.
The answer to the question in theory is 423 boxes, but the physical number of boxes that will fit based on the geometric shapes is 324 boxes.
You’ve reached the end of the Numeracy @ Work Self-Assessment.
We hope this assessment has given you a better understanding of the numeracy skills you have and the skills you need.
Don’t forget: you can use the workbooks for more practice!
It’s Workplace Education Manitoba’s goal that Manitoba employers have a workforce that’s efficient, effective and adaptable, while workers have the skills they need for success in the workplace.