One of the things I love about teaching applied math topics in our culinary arts programs is that this math often requires the learner to step outside of the “rules” of math and consider the reality of the situation. The standard rules of rounding do not always make sense in foodservice applications. I like to describe these standard rules as making sense on the Island of Math, but not always trustworthy where we live and work.

What our students know about rounding
For the most part, our students learn the standard rounding rules in elementary school:

• Round up if the digit after the place value you are rounding to is five or greater.
• Round down if the digit after the place value you are rounding to is less than five.

These rules work with numbers in general. However, we have to support our students as they realize that some problems require further scrutiny when the numbers are attached to real-world situations. Treating this sort of rounding differently often throws students off since they are taught these are the rules of rounding – period! Below are a few examples of situations that challenge those rules and often our students.

Standard Rounding vs. Reality Rounding - Example 1
Basic Math Problem: The problem specifies the student’s answer should be rounded to the whole number. The student’s preliminary answer is 14.65.

• Basic Math Solution: Based on standard rounding rules, the student rounds 14.65 up to 15 because the digit after the whole number (14) is a 6, and that is greater than 5.

Culinary Math Problem: The problem asks how many people can be served specified portions of a house-made soup from a given amount. After performing the calculations, the student’s preliminary answer is 14.65.

• Culinary Math Solution: In general, when we ask our culinary students how many people can be served it goes without saying the portions being served are whole, not partial. Even though rounding rules dictate when rounding 14.65 to the whole number, the answer is 15. In this case, we have to help our students resist the urge to follow the rules. We do not want to short the guest (which I always announce will be me!). Rounding down to 14 makes more sense when asked how many people can be served the soup.

Standard Rounding vs. Reality Rounding – Example 2
Basic Math Problem: Round 10.234 to the hundredth place.

• Basic Math Solution: Based on standard rounding rules, 10.234 rounds down to 10.23 because the digit after the hundredth place (3) is a 4, and that is less than 5.

Culinary Math Situation: The problem asks to find the total cost of an ingredient on a food cost form. After performing the calculations, the student’s preliminary answer is $10.234.

• Culinary Math Solution: When students calculate the cost of ingredients on a food cost form, I encourage them not to round the calculation answers until they get to the total cost column of the ingredient, the final calculation. Not rounding along the way keeps the total cost more accurate. When the total cost is calculated, it is best to round up to the next higher cent in a foodservice operation. Rounding up makes sure that no partial pennies are “given away.” It may be hard to see this on a food cost form when determining the cost of a few portions. However, over time the partial pennies add up to a lot of lost revenue.

Standard Rounding vs. Reality Rounding - Example 3
Basic Math Problem: Round 7.312 to the whole number.

• Basic Math Solution: Based on standard rounding rules, 7.312 rounds down to 7 because the digit after the tenth place is a 3, and that is less than five.

Culinary Math Problem: The problem asks how many whole pounds of potatoes should be ordered. After performing the calculations, the student’s preliminary answer is 7.312 lbs.

• Culinary Math Solution: Undoubtedly, many factors need to be considered when determining how much of a particular vegetable to order in a foodservice operation. However, for this example, we are simply considering the amount to order based on the student’s answer and the fact the question requires the answer to be rounded to a whole number. While standard rounding rules suggest that 7.312 should be rounded to 7 pounds, that would short the amount of potatoes needed. It is important to instruct our students to round any partial pound up to the next higher pound when ordering to ensure there is enough.

Standard Rounding vs. Reality Rounding - Example 4
Basic Math Problem: Round 76.65% to a whole percent.

• Basic Math Solution: Based on standard rounding rules, 76.65% rounds up to 77% because the digit in the tenth place is a 6, and that is greater than 5.

Culinary Math Problem: The problem asks the student to find the yield percent for pears given the edible portion quantity and the as purchased quantity. After performing the calculations, the student’s preliminary answer is 76.65%. Since the problem specifies that the answer should be given as a whole percent, the student rounds to 77%.

• Culinary Math Solution: While the student’s answer makes sense in a standard math world, it is a concern in a foodservice application. We teach our students that yield percent is the percent of purchase quantity that is usable after the trim loss is removed. Rounding 76.65% up to 77% would slightly overpredict the amount of edible portion quantity available when pears are fabricated. This is particularly an issue when calculating a large amount of pears to order. It is best to round yield percent down to 76% if the student must round at all.

Next month I will discuss the basics of unit conversion within weight measures and within volume measures.

Click here for last month’s Culinary Math Teaching Series: Recipe Costing Basic Math Concepts.