Basic Math Computation Problems

A basic understanding of addition, subtraction, multiplication, division, decimals and percentages is needed to solve various questions about animal nutrition in this course. The following are sample problems for you to use as an inventory of your skills and practice for the calculations expected in this course.

Decimals: Addition, Subtraction, Multiplication, and Division

The most important aspect of understanding decimals is knowing that numbers to the left of the decimal are whole units and the numbers to the right of the decimal indicate parts of a whole.

In the number 36.908, the 36 represents 36 whole units of whatever is being discussed and the .908 represents 908 thousandths of one whole unit.

The basic rule for adding numbers containing decimals is to line up the decimals vertically and add the columns as any addition problem retaining the decimal vertically in the answer.

For example: 134.6 + 66.305 + .0074 = ?

 would be written as: The problem can then be added in columns.
 1 3 4 . 6 1 3 4 . 6 6 6 . 3 0 5 6 6 . 3 0 5 + . 0 0 7 4 + . 0 0 7 4 . 2 0 0 . 9 1 2 4

Practice problems:

1. 54.69 + 103.9 = ?

2. .9876 + 35.07 = ?

3. 59.66 + 347 = ?

4. 3 + .9445 = ?

Subtraction with Decimals

The vertical alignment of the decimal points is also crucial to subtracting decimals. The number with the most whole units, the larger number left of the decimal, is placed on top and the smaller number placed beneath with the decimals vertically aligned.

46 - .7789 = ?

Set up the problem vertically. The 46 can be written 46.000 by inserting 0 to give the value of the places to the right of the decimal.

 4 6 . 0 0 0 0 - . 7 7 8 9 4 5 . 2 2 1 1

Practice problems:

1. 55 - 1.36 = ?

2. 1.988 - .9999 = ?

3. 40 - 31.754 = ?

4. .9077 - .644386 = ?

Multiplication with Decimals

Set up the multiplication of decimal numbers as any multiplication problem and complete the problem as though the decimals were not there. After the answer is listed place a decimal in the answer by by counting the number of digits to the right of the decimal in both numbers being multiplied. Count the same number of digits from right to left in the answer and place the decimal. Zero may be added in places to the left of the problem if needed to place the decimal.

In the problem: 45.6 x 139.55, set up the problem vertically and complete the multiplication.

 1 3 9. 5 5 x 4 5. 6 8 3 7 3 0 6 9 7 7 5 0 5 5 8 2 0 0 0 6 3 6 3 . 4 8 0

Practice problems:

1. 4.5 x 234.9 = ?

2. 26 x .0967 = ?

3. 4.67 x 318 = ?

4. .08896 x .558 = ?

Division with Decimals

Dividing numbers containing decimals requires dealing with the decimals first which is the opposite of multiplying numbers containing decimals. If the divisor contains a decimal, that decimal is moved to the right until it is completely to the right of the divisor. Count the number of digits the decimal passes to be completely beyond the number and move the decimal inside the division house the same number of places. If the number in the division house does not contain a decimal, place a decimal at the right of the number and add enough zeros to move the decimal to the right the number of places you moved the decimal in the divisor.

If the division problem only contains a decimal in the number within the division house, move the decimal straight up and place it there where the answer to the problem will be when the division process is completed.

In the problem: 41.5 ? 37 = ? the 37 is the divisor, 41.5 is the number within the division house. Since only the number in the division house contains a decimal, move the decimal up vertically and place it there where the answer will be placed.  Practice Problems

1. 736 ? .225 = ?

2. 3.122 ? .45 =?

3. 566.7 ? 39 =?

4. 53 ? .0449 =?

Calculating Percentages

Pencentages are always a comaprison of something with 100. Percent problems can all be done by identifying the 3 of the 4 elements below and solving for the fourth.

 % is = 1 0 0 of

For example: If a jacket is advertised as being 30% off of the original price of \$98, what is the sale price? Three of the the four components are given and you may solve for the fourth.

 30% missing element = 100% \$98

Cross multiply the 30 times \$98.00. Cross multiply the 100 times the missing element which can be noted as X and the problem will look like this.

30 multiplied by \$98.00 is equal to 100 multiplied by the missing element which we will call X.

\$2940 = 100 X.

Divide each side of the equal sign by 100 to determine X which stands for the amount to be taken off the original price.

\$29.40 = X

Subtract \$29.40 from \$98.00 to determine the sale price of \$68.60.

All percentage problems can be done in the same manner. For example: What percentage is 17 of 344?

The X is placed over the 100 because the percentage is the missing element. 17 is placed over the 344 as clearly indicated by the "is" and "of" statements.

 X 17 = 100% 344

Then X is cross multiplied by 344 to equal 100 times 17.

344X = 1700.

X = 4.9

So 17 is 4.9% of 344.

Practice Problems

1. What percentage is 5 of 41?

2. What is 49% of 221?

3. What is the total bill if a 7% tax is placed on \$199.50?

4. What is the sale price of an item originally costing \$89.00 if the item is advertised at 25% off?

The above math review will help you inventory the skills which will be needed to perform the various calculations needed in this course to calculate and convert yields to a common moisture content, determine the number of livestock that can be fed per acre and determine proper fertilizer and nutrient input amounts.