WealthWiseGuys Practical Mathematics

Our number system is base ten. Each place is worth ten times the place to its right. Digits are grouped in threes, called periods: units, thousands, millions, billions. Commas separate the periods.

To read a number, read each period as a three-digit number and say the period name, except the units period. The word "and" is saved for the decimal point, so we never say it inside a whole number.

To round, find the place you are rounding to and look at the digit immediately to its right. If that digit is 5 or more, add 1 to the rounding digit. If it is 4 or less, leave the rounding digit alone. Every digit to the right becomes zero.

To add, line up the digits by place value and add right to left. When a column adds to 10 or more, write the ones digit and carry the tens digit to the next column.

To subtract, line up the larger number (minuend) on top. When a top digit is smaller than the one below it, borrow 1 from the next place to the left, which adds 10 to the current place.

Always check. Addition checks by adding the column in the opposite direction. Subtraction checks by adding the difference back to the subtrahend; you should get the minuend.

Multiplication is repeated addition. 24 cases of 36 bars means 36 added 24 times, which is 24 × 36.

Division splits a total into equal groups. When the total does not split evenly, the leftover is the remainder. In real life, decide whether the remainder is dropped (only full bags count), rounded up (you need another bus), or reported (14 bars left over).

The Blueprint. Before you calculate, write four things: (1) Facts given, (2) What you are solving for, (3) Steps to take, (4) Key points to watch. This keeps you from using the wrong numbers or answering the wrong question.

A trade discount reduces a supplier list price before the invoice amount is established. It may reflect a buyer category or order arrangement. A list price is a reference price, not necessarily the amount that any particular buyer pays.

For one discount, multiply list price by the discount rate and subtract that amount. The complementary rate, 1 minus the decimal discount rate, is the net price factor. Multiplying by this factor gives the same result before any rounding differences.

A discount series applies each discount to the price remaining after the previous discount. A 25% and 10% series does not mean 35% off. The second discount has a smaller base. On an $800 order, the discounts are $200 and $60, not $200 and $80.

The product of the net price factors gives the series net factor. Subtract it from 1 to find an equivalent single discount. This equivalent rate compares offers clearly, but actual invoices should follow the stated cent-rounding procedure for each discount. Freight and tax remain separate unless the contract says otherwise.

A cash discount rewards payment within an early-payment window. Terms 2/10, n/30 mean a 2% discount if payment meets the 10-day deadline; otherwise the full net amount is due within 30 days. This is different from a trade discount, which determines the invoice merchandise price before payment timing is considered.

For every example here, count the day after the invoice date as day 1, use calendar days, and assume payment is received on the stated date. Holidays and weekends do not extend deadlines in these hypothetical contracts. Real contracts may define receipt, mailing, or electronic settlement differently.

The discount base is the eligible merchandise balance after applicable returns and allowances. In these examples, freight is excluded from the cash discount and tax is omitted unless a problem explicitly supplies it. Apply the discount only to the eligible amount, then add the excluded charges.

Paying early reduces the amount paid but also uses cash sooner. A buyer should check that funds are actually available and compare any borrowing cost with the savings; a discount does not automatically justify borrowing. If payment misses the discount deadline, use the undiscounted balance rather than a partial discount.

A purchase return removes merchandise from an order and creates a credit for its agreed invoice value. An allowance reduces the price of goods the buyer keeps, perhaps because of minor damage. Subtract these credits before calculating a cash discount when the contract makes only the adjusted balance eligible.

Freight is part of acquiring goods even when it is not eligible for a cash discount. For these problems, delivered cost means adjusted merchandise minus any qualifying cash discount plus freight and any stated tax. No tax is assumed when it is not supplied.

Purchasing comparisons should use the same quantity and quality. Cost per usable unit divides complete delivered cost by units actually retained and usable. Returned or unusable units do not belong in that denominator, even if the original order was larger.

The lowest unit cost is a mathematical comparison, not the entire purchasing decision. Delivery reliability, storage capacity, quality, and the cash needed for a large order also matter. State which costs and assumptions the comparison includes rather than presenting a low sticker price as the complete answer.