Decimal arithmetic will be an important component of this course.
However, I will assume that you can do decimal arithmetic by hand well enough
to justify using a basic calculator.
On the other hand, fractions and percentages are also common in the food-service industry.
Therefore, we will spend some time with both fraction arithmetic and percentages.
Consider the fraction $\frac{4}{6}.$
Example: Make $\frac{18}{24}$ happy by expressing it in lowest terms.
Question 1: What is one half of a half?
Question 2: How do we represent the above question?
Multiplication
To multiply fractions, just multiply tops and bottoms. That is,
$$\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}.$$
Example: Multiply $\frac{2}{3}\cdot 1\frac{4}{5}.$
Question 1: How many quarters can we fit into one half?
Question 2: How do we represent the above question?
Division
To divide fractions, invert and multiply. That is,
$$\frac{a}{b} \div \frac{c}{d}=\frac{a}{b}\cdot \frac{d}{c}.$$
Example: Divide $\frac{2}{3} \div 1 \frac{4}{5}.$
Fraction Addition: Just remember that fractions get greedy and jealous of each other's denominators when we add them together.
We must must make sure every fraction has what every other fraction has.
Example: $\frac{9}{20}+\frac{5}{12}?$
Fraction Subtraction: The Greedy Fraction Principle applies here as well.
Example: $\frac{9}{20}-\frac{5}{12}$
Application: A chef is using a recipe which calls for $\frac{1}{4}$ cup of flour.
How many times can she make the recipe with $12\frac{1}{2}$ cups of flour ?
Application: A recipe calls for $\frac{5}{8}$ of a cup of sugar. If there is already
$\frac{1}{3}$ cup of sugar in the mix, how much more sugar is needed?
Percent
A percent expresses how many parts per $100.$
So, for example, $0.79$ expresses $79$ parts per $100.$ That is, $0.79=\frac{79}{100}=79\%.$
To convert any decimal to a percent, simply move the decimal place two places to the right.
Percent
On the other hand, we generally don't do calculations with raw percentages.
We do calculations with regular decimals. So we need to know how to convert percentages into
decimals as well.
Example: $134\%$ expresses 134 parts per 100. That is, $134\%=\frac{134}{100}=1.34.$
To convert any percent to a decimal, simply move the decimal place two places to the left.
Example: What is $21\%$ of $78$?
Example: What is $134\%$ of $78?$
Example: $78$ is what percent of $92?$
Example: $78$ is what percent of $25?$