Don’t use a calculator for this question.

Calculate the answer by following the correct order of operations.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the answer by following the correct order of operations.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the answer by following the correct order of operations.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the answer by following the correct order of operations.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

The solution to the expression  DMA - Image 13 given below contains one error. Identify the error and present a correct solution.

Question
Solution

The error occurs between the 3rd and 4th lines of the solution. The division DMA - Image 15 needs to be done before the subtraction DMA - Image 16.

Workbook PDF

Don’t use a calculator for this question.

Calculate the following.

Express your answer as a fraction in lowest terms.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the following.

Express your answer as a fraction in lowest terms.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the following.

Express your answer as a fraction in lowest terms.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate your answer.

Express your answer as a fraction in lowest terms.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Convert the following fraction from mixed to improper.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Convert the following fraction from improper to mixed.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the following. Express your answer as a mixed fraction in lowest terms.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the following. Express your answer as a mixed fraction in lowest terms.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

The solution to the expression DMA - Image 42 given below contains one error. Identify the error and give the correct solution.

DMA - Image 43

Solution

The error occurs between the 4th and 5th lines. The operation between the 9 and the 4 should be multiplication, not addition.

Workbook PDF

Don’t use a calculator for this question.

Calculate the following:

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the following. Express your answer to the nearest hundredth.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate your answer. Express your answer to the nearest hundredth.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the following. Express your answer to the nearest tenth.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Calculate the following. Express your answer to the nearest hundredth.

Question
Solution
Answer
Workbook PDF

You can use a calculator for this question.

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.

Question
Solution
Answer
Workbook PDF

You can use a calculator for this question.

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.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

 

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%
Workbook PDF

You can use a calculator for this question.

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?

Question
Solution
Answer
Workbook PDF

You can use a calculator for the following question.

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?

Solution

Rounding the discount up would make the total cost of the shoes decrease by $0.01.

Workbook PDF

Don’t use a calculator for this question.

Convert the following Imperial measures into the units indicated.

 

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Convert the following metric measures into the units indicated.

Question
Solution
Answer
Workbook PDF

You can use a calculator for this question.

Fill in the blank spaces so that the total of the measurements equals 193 inches. Express your answer as a whole number.

Question
Solution
Answer
Workbook PDF

You can use a calculator for this question.

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.

Solution

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).

Workbook PDF

You can use a calculator for this question.

The solution to the conversion DMA - Image 78 given below contains one error. Identify the error and present a correct solution.
Do not round any calculations for this question.

Question
Solution

The conversion factor from centimeters to inches is reversed.

Workbook PDF

You can use a calculator for this question.

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.

Question

DMA - Image 81

 

Before we can find the length of the perimeter, the hypotenuse of the triangle must be calculated using the Pythagorean Theorem.

DMA - Image 142c.gif

DMA - Image 82

 

Answers: Area = 84 cm2, Perimeter = 56 cm

 

Workbook PDF

You can use a calculator for this question.

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.

Question

DMA - Image 83b

 

DMA - Image 84b

 

 

Answers: Area = 63.585 in2, Perimeter = 28.26 in

Workbook PDF

You can use a calculator for this question.

Calculate the area and the perimeter of the object below. Be sure to include the unit of measure in your answer.

Question

Area Calculations

The area of the square is:

DMA - Image 85

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:

DMA - Image 86

 

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:

DMA - Image 87

 

The total area is:

DMA - Image 88b.gif

 

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:DMA - Image 89

DMA - Image 90b

The circumference of the circle is:

DMA - Image 91

 

The total perimeter is:

DMA - Image 92

Workbook PDF

You can use a calculator for this question.

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.

Question

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.

DMA - Image 93b

Answer
Workbook PDF

You can use a calculator for this question.

 

A rectangular box has a volume of 2.8 ft3. The base of the rectangular box measures DMA - Image 94.

Determine the height of the box, measured in feet. Express your answer to the nearest hundredth.

 

Solution

Both the measurements of the base must be changed into feet.

DMA - Image 95b

 

Substituting the measurements into the formula for the volume of a rectangular solid gives:

Answer
Workbook PDF

Don’t use a calculator for this question.

Solve the following equation for the variable x.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Solve the following equation for the variable x.

 

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Solve the following equation for the variable x.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

The solution to the equationDMA - Image 106 given below contains two errors. Identify the errors and give the correct solution.

 

Question
Solution

The first error is on line 3 where the double negative was missed. The term DMA - Image 108 really should be DMA - Image 109. The second error is in collecting like terms on line 5. The constant terms were collected correctly, but the variable terms were not. When theDMA - Image 108 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.

 

 

 

Workbook PDF

Don’t use a calculator for this question.

Find the value of x that makes the proportion true.

Question
Solution
Answer
Workbook PDF

Don’t use a calculator for this question.

Find the value of x that makes the proportion true.

Question
Solution
Answer
Workbook PDF

You can use a calculator for this question.

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 5th math test to increase her overall test score average by 5%?

The average on her first 4 tests is:

DMA - Image 116

 

An increase of 5% would be an overall test average of

DMA - Image 117

 

DMA - Image 118b

 

Susanne would need to score DMA - Image 119 on her 5th math test to increase her overall test score average by 5%.

 

Answer
Workbook PDF

You can use a calculator for this question.

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.

Workbook PDF

You can use a calculator for this question.

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.

Solution
Answer
Workbook PDF

Describe the order of operations required to correctly calculate the value of

DMA - Image 120

 

 

Answer:

The multiplication and division need to be done first.
Next, the two results are added together.

 

 

 

Workbook PDF

Don’t use a calculator for this question.

Calculate the value of DMA - Image 120.

Solution
Answer
Workbook PDF

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.

 

 

Workbook PDF

Don’t use a calculator for this question.

Give a numeric example that supports your explanation given in the previous question (28a).

A sample response is:

DMA - Image 123b

Therefore, the common denominator of the two fractions is 20 and the numerators are added together to get the final answer of DMA - Image 144.

Workbook PDF

Don’t use a calculator for this question.

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 (=)
Solution

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.

Workbook PDF

You can use a calculator for this question.

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:DMA - Image 127d.gif

The volume of each storage bin is: DMA - Image 124

The volume of the shelving unit divided by the volume of each bin is: DMA - Image 128

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 m3, from feet to meters, is:

DMA - Image 139c.gif

The volume of the shelving unit isDMA - Image 140.

The volume of the shelving unit divided by the volume of each bin is DMA - Image 141b.gif.

Since you cannot have a partial bin, 423 storage bins will fit onto the shelf. This is a theoretical calculation based on total volume.

Workbook PDF

You can use a calculator for this question.

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  DMA - Image 131 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 DMA - Image 133b.gif 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 sinceDMA - Image 130b.gif.

This would give a total number of DMA - Image 135 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.

Workbook PDF

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.