Section 1.3: Operations with Positive Fractions Worksheet 1.3
Remember that every number has a personality. And since fractions are numbers too, they're are no different.
When it comes to what they wear (how they present themselves), they're quite the minimalists!
They like to keep life as simple as possible, and prefer the easiest way to look at themselves in the mirror.
For example, consider the fraction $\frac{4}{6}$.
Example: Make $\frac{16}{24}$ 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?
When fractions "kiss": Multiplication
To multiply fractions, just multiply tops and bottoms. That is,
$$\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$$.
Question: What do we get when $\frac{2}{3}$ and $\frac{9}{5}$ kiss?
Hint:Multiply $\frac{2}{3}\cdot \frac{9}{5}$.
Question 1: How many quarters can we fit into one half?
Question 2: How do we represent the above question?
When fractions "break up": Division
To divide fractions, invert and multiply. That is,
$$\frac{a}{b} \div \frac{c}{d}=\frac{a}{b}\cdot \frac{d}{c}.$$
The one getting dumped gets turned upsidedown.
Question: What do we get when $\frac{2}{3}$ breaks up with $\frac{9}{5}$?
Hint:Divide $\frac{2}{3} \div \frac{9}{5}$.
When two fractions decide get married, each one has what the other needs.
For a proper marriage, each fraction must give the other exactly what it needs.
Question: What happens when $\frac{9}{20}$ gets married to $\frac{5}{12}$?
When two fractions divorce, they turn jealous and greedy, and must have what the other one has.
Question: What do we get when $\frac{9}{20}$ and $\frac{5}{12}$ divorce?
Hint:Subtract $\frac{9}{20}-\frac{5}{12}$
Application: A woman has 12 cups of rose
fertilizer. The fertilizer box recommends $\frac{1}{4}$ cup for each
rose bush. How many rose bushes can she fertilize with
the 12 cups?
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?