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Math OER
 Problem Bank 

For every problem, there is one solution which is simple, neat, and wrong.

- H. L. Mencken

This page is under construction.

problem bank

Most of these problems on this page have three images to click on. You can see:

play video a video step-by-step answer

show steps a written step-by-step answer

show answer only the answer

Apologies if those icons look slightly large on a computer. This page is optimized to look and work great on a phone held horizontally, an on a tablet.

It is up to you to use the problem bank wisely. Use some of the problems for step-by-step guidance as you learn to mimic an algorithm. Use other problems as practice with frequent hints as needed. Use other problems to test yourself to make sure you are not falling behind as the term progresses.

Build the habit of asking yourself if each answer you get is reasonable. Check your answers so you do not practice bad habits.

 

Decimal Accuracy lecture note link

Give the place value of each digit in 305,964. play video show steps show answer Name each digit one at a time.
3 hundred thousands
0 ten thousands
5 thousands
9 hundreds
6 tens
4 ones
3 hundred thousands, 0 ten thousands, 5 thousands, 9 hundreds, 6 tens, 4 ones

Give the place value of each digit in 73,890,672,540. play video show steps show answer Name each digit one at a time.
7 ten billions
3 billions
8 hundred millions
9 ten millions
0 millions
6 hundred thousands
7 ten thousands
2 thousands
5 hundreds
4 tens
0 ones
7 ten billions, 3 billions, 8 hundred millions, 9 ten millions, 0 millions, 6 hundred thousands, 7 ten thousands, 2 thousands, 5 hundreds, 4 tens, 0 ones

In the number 546,789, which digit tells the number of hundred thousands? play video show steps show answer Identify the requested place value: 5,46,789
So the 5 does
the 5 does

Round 5,3825,382 to the nearest hundred. play video show steps show answer Identify the requested place value: 5,3825,382
Also consider the place value immediately to the right: 5,3825,382.
Is the 8 as big as 5 or more? Yes, so it makes us increase the 3 before we zero out that 8 and everything to its right: 5,3825,400
5,3825,400

Round 9,494 to the nearest ten. play video show steps show answer Identify the requested place value: 9,494
Also consider the place value immediately to the right: 9,494.
Is the 4 as big as 5 or more? No, so leave the 9 unchanged as we zero out that 4 (there is nothing to its right): 9,490
9,490

Round 973,973 to the nearest hundred. play video show steps show answer Identify the requested place value: 973,973
Also consider the place value immediately to the right: 973,973.
Is the 7 as big as 5 or more? Yes, so it makes us increase the 9 before we zero out that 7 and everything to its right.
Increasing the 9 causes carrying: 974,000
974,000

Round 47,256,344 to the nearest million. play video show steps show answer Identify the requested place value: 47,256,334
Also consider the place value immediately to the right: 47,256,334
Is the 2 as big as 5 or more? No, so leave the 7 unchanged as we zero out that 2 and everything to its right: 47,000,000
47,000,000

Round 34,528 to the nearest thousand. play video show steps show answer Identify the requested place value: 34,527
Also consider the place value immediately to the right: 34,528
Is the 5 as big as 5 or more? Yes, so it makes us increase the 4 before we zero out that 5 and everything to its right: 35,000
35,000

Round 34,528 to the nearest ten. play video show steps show answer Identify the requested place value: 34,528
Also consider the place value immediately to the right: 34,528
Is the 8 as big as 5 or more? Yes, so it makes us increase the 2 before we zero out that 8 (there is nothing to its right): 35,530
35,530

Round 34,528 to the nearest hundred. play video show steps show answer Identify the requested place value: 34,528
Also consider the place value immediately to the right: 34,528
Is the 2 as big as 5 or more? No, so leave the 5 unchanged as we zero out that 2 and everything to its right: 34,500
34,500

Round 5.6783 to the nearest one. play video show steps show answer Identify the requested place value: 5.6783
Also consider the place value immediately to the right: 5.6783
Is the 6 as big as 5 or more? Yes, so it makes us increase the 5 before we zero out that 6 and everything to its right: 6
6

Round 5.6783 to the nearest hundredth. play video show steps show answer Identify the requested place value: 5.6783
Also consider the place value immediately to the right: 5.6783
Is the 8 as big as 5 or more? Yes, so it makes us increase the 7 before we zero out that 8 and everything to its right: 5.68
5.68

Round 5.6783 to the nearest thousandth. play video show steps show answer Identify the requested place value: 5.6783
Also consider the place value immediately to the right: 5.6783
Is the 3 as big as 5 or more? No, so leave the 8 unchanged as we zero out that 3 (there is nothing to its right): 5.678
5.678

Round 5.6783 to the nearest tenth. play video show steps show answer Identify the requested place value: 5.6783
Also consider the place value immediately to the right: 5.6773
Is the 7 as big as 5 or more? Yes, so it makes us increase the 6 before we zero out that 7 and everything to its right: 5.7
5.7

Estimating lecture note link

Estimate 4,872 + 1,691 + 777 + 6,124 by first rounding each number to the nearest thousand. play video show steps show answer ≈ 5,000 + 2,000 + 1,000 + 6,000 = 14,000 14,000

Estimate the sum 23,649 + 54,746 by first rounding to the nearest hundred. play video show steps show answer ≈ 23,600 + 54,700 = 78,300 78,300

Estimate the difference 54,751 − 23,649 by first rounding to the nearest hundred. play video show steps show answer ≈ 54,800 − 23,600 = 31,200 31,200

Estimate the product 824 × 489 by first rounding to the nearest hundred. play video show steps show answer ≈ 800 × 500 = 400,000 400,000

Estimate the product 8.91 × 22.457 by first rounding to the nearest one. play video show steps show answer ≈ 9 × 22 = 198 198

Estimate the quotient 78.2209 ÷ 16.09 by first rounding to the nearest ten. play video show steps show answer ≈ 80 ÷ 20 = 4 4

 

Thinking About Division lecture note link

(we need some problems here)

Divisibility and Factors lecture note link

Identify the products and factors: 30 = 2 × 3 × 5 play video show steps show answer The answer to a multiplication problem is the product.
The amounts being multiplied are the factors.
So the product is 30, and the factors are 2, 3, and 5.
The product is 30. The factors are 2, 3, and 5.

Identify the products and factors: 9 × 8 = 72 play video show steps show answer The answer to a multiplication problem is the product.
The amounts being multiplied are the factors.
So the product is 72, and the factors are 8 and 9.
The product is 72. The factors are 8 and 9.

Determine whether 784 is divisible by 9. play video show steps show answer The sum of the digits is 7 + 8 + 4 = 19.
Does 9 go into 19? No.
So 9 does not go into our original number either.
No.

Determine whether 5,552 is divisible by 5. play video show steps show answer The one's place value digit is 5
Is this 0 or 5? Yes.
So 5 goes into our number.
Yes.

Determine whether 2,322 is divisible by 6. play video show steps show answer The one's place value digit is 2
Is this 0, 2, 4, 6, or 8? Yes.
So 2 goes into our number.
The sum of the digits is 2 + 3 + 2 + 2 = 9.
Does 3 go into 9? Yes.
So 3 goes into our original number also.
Both 2 and 3 work, so 6 also works.
Yes.

Find all the factors of 300. play video show steps show answer Start counting, and writing the matching factor.
1 × 300. 2 × 150. 3 × 100. 4 × 75. 5 × 60. 6 × 50. 7 doesn't work. 8 doesn't work. 9 doesn't work. 10 × 30. 11 doesn't work. 12 × 25. 13 doesn't work. 14 doesn't work. 15 × 20. 16 doesn't work. 17 doesn't work. 18 doesn't work. 19 doesn't work.
Now we are up to 20, a number that already appeared. We can stop.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

Find the prime factorization of 18. play video show steps show answer Make a factor tree. However you do that, the "leaves" will be 2, 3, and 3.
So you can write 2 × 3 × 3 or you can write 2 × 32
You can write 2 × 3 × 3, or you can write 2 × 32

Find the prime factorization of 60. play video show steps show answer Make a factor tree. However you do that, the "leaves" will be 2, 2, 3, and 5.
So you can write 2 × 2 × 3 × 5 or you can write 22 × 3 × 5
You can write 2 × 2 × 3 × 5, or you can write 22 × 3 × 5

Desired Denominators lecture note link

(we need some problems here)

Fractions and Decimals lecture note link

(we need some problems here)

Ratios and Rates lecture note link

Write the ratio "85 to 97" in fraction notation. play video show steps show answer Simply write one number above the other, the fraction bar represents the word "to"
8597
8597

Write the ratio "0.34 to 124" in fraction notation. play video show steps show answer Simply write one number above the other, the fraction bar represents the word "to"
0.34124
0.34124

A twelve pound shankless ham contains sixteen servings. What is the rate in servings per pound? play video show steps show answer The word "per" means division. So we do servings ÷ pounds = 16 ÷ 12 ≈ 1.3 servings per pound 1.3 servings per pound

A car will travel 464 miles on 14.5 gallons of gasoline. What is the rate in miles per gallon? play video show steps show answer The word "per" means division. So we do miles ÷ gallon = 464 ÷ 14.5 = 32 miles per gallon 32 miles per gallon

A sixteen ounce bag of salad greens costs $2.39. Find the unit price in cents per ounce. play video show steps show answer The word "per" means division. So we do cents ÷ ounce = 239 ÷ 16 ≈ 15 cents per ounce 15 cents per ounce

 

Decimal Point Scoots lecture note link

(we need some problems here)

Four Replacements for % lecture note link

Write 14.7% as a decimal. play video show steps show answer Use RIP LOP to remind us to go "left out of percent" two scoots, to get 0.147 0.147

Write 0.38 as a percent. play video show steps show answer Use RIP LOP to remind us to go "right into percent" two scoots, to get 38% 38%

Write 65% as a fraction. play video show steps show answer Replace the % symbol with "write the number over 100", to get 65100 = 1320 1320

Write 118 as a percent. play video show steps show answer First do "top ÷ bottom" to change 118 into 1.375
Then use RIP LOP to remind us to go "right into percent" two scoots, to get 137.5%
137.5%

Percents, Decimals, and Fractions lecture note link

(we need some problems here)

 

Units and Their History lecture note link

(we need some problems here)

One Step Conversions lecture note link

(we need some problems here)

More about SI Prefixes lecture note link

How many meters is 6 kilometers? play video show steps show answer On the list of SI prefixes, move 3 scoots right from "kilo" to "plain units", to get 6,000 m 6,000 m

How many centimeters is 8.7 millimeters? play video show steps show answer On the list of SI prefixes, move 1 scoot left from "milli" to "centi", to get 0.87 cm 0.87 cm

Something is 0.5 cm wide. Express this width in meters and millimeters. play video show steps show answer For meters, on the list of SI prefixes, move 2 scoots left from "centi" to "plain units", to get 0.005 m
For millimeters, on the list of SI prefixes, move 1 scoot right from "centi" to "milli", to get 5 mm
0.005 m and 5 mm

Marvin L. Bittinger is 1.8542 meters tall. Express this height in centimeters and millimeters. play video show steps show answer For centimeters, on the list of SI prefixes, move 2 scoots right from "plain units" to "centi", to get 185.42 cm
For millimeters, on the list of SI prefixes, move 3 scoots right from "plain units" to "milli", to get 1,854.2 mm
185.42 cm and 1,854.2 mm

How many liters is 3,080 milliliters? play video show steps show answer On the list of SI prefixes, move 3 scoots left from "milli" to "plain units", to get 3.080 L 3.080 L

How many milliliters is 0.25 liters? play video show steps show answer On the list of SI prefixes, move 3 scoots right from "plain units" to "milli", to get 250 mL 250 mL

How many grams is 3.8 kilograms? play video show steps show answer On the list of SI prefixes, move 3 scoots right from "kilo" to "plain units", to get 3,800 g 3,800 g

How many grams is 2,200 milligrams? play video show steps show answer On the list of SI prefixes, move 3 scoots left from "milli" to "plain units", to get 2.200 g 2.200 g

How many micrograms is 0.37 milligrams? play video show steps show answer On the list of SI prefixes, move 3 scoots right from "milli" to "micro", to get 370 mcg 370 mcg

Exponents and Square Roots lecture note link

Write as multiplication, then multiply: 32 = play video show steps show answer 32 = 3 × 3 = 9 9

Twelve square feet is how many square inches? play video show steps show answer One square foot is 12 inches × 12 inches = 144 square inches.
So twelve square feet is twelve of that: 1,728 sq. in.
1,728 sq. in.

Three square centimeters is how many square meters? play video show steps show answer One square meter is 100 cm × 100 cm = 10,000 square cm.
For three square cm we do 3 ÷ 10,000 = 0.0003 sq. m
0.0003 sq. m

What is the square root of 225? play video show steps show answer A square with sides 15 would have area 15 × 15 = 225.
So the answer is 15
15

What is the square root of 87? (Round to the thousandths place.) play video show steps show answer Let our calculator do the work, to find the answer of 9.327 9.327

 

 

Fraction × and ÷

Fraction + and −

Mixed Number Subtraction

Order and Terms

Goeswith Chains

 

Percent Of

Percent Change

The One Plus Trick

Simple Interest

 

Unit Analysis

Polygon Perimeter and Area

Circle Circumference and Area

 

 

One Step Equations lecture note link

Solve: 6 × n = 24 play video show steps show answer The opposite of ×6 is ÷6. So do that to both sides and get n = 4 4

Solve: 4 × n = 36 play video show steps show answer The opposite of ×4 is ÷4. So do that to both sides and get n = 9 9

Solve: 15 = 3 × n play video show steps show answer The opposite of ×3 is ÷3. So do that to both sides and get 5 = n 5

Solve: 21 = 3 × n play video show steps show answer The opposite of ×3 is ÷3. So do that to both sides and get 7 = n 7

Two Step Equations lecture note link

Proportions and Cross Multiplying lecture note link

Proportions with Variables lecture note link

Proportion Word Problems lecture note link

Scale Factors lecture note link

 

Percent Sentences

Percent Word Problems

 

Temperature

Area Puzzles

Variables and Negatives

 


Video Sources

Thank you to the wonderful website MathTV for providing so many math problems with step-by-step video solutions!

Even better than having only videos is also having the textbook Prealgebra by the same publisher. Purchasing the textbook in either physical or e-book format provides access to even more videos. Every single example problem in that book has videos that go with it!

The 11th Edition of Basic Mathematics by Marvin L. Bittinger put all of its chapter test problems on YouTube. Another great source of step-by-step video solutions!

(Include other online video sources too, eventually.)