4.2: What are Fractions?

									\(\dfrac{\text { Part }}{\text { Whole }} \rightarrow \dfrac{\text { Numerator }}{\text { Denominator }}\)	\(\text { Denominator } \sqrt{\text { Numerator }}\)	Fractions are just Division!

Figure 4.2.1

Example \(\PageIndex{1}\)

Explain the meaning of \(\dfrac{1}{4}\)

Figure 4.2.2

Example \(\PageIndex{2}\)

Show \(3 \dfrac{5}{8}\)

Figure 4.2.3

Example \(\PageIndex{3}\)

Which is bigger? \(\dfrac{1}{3}\) OR \(\dfrac{1}{4}\)

Figure 4.2.4

Example \(\PageIndex{4}\)

Which is bigger? \(\dfrac{4}{9}\) OR \(\dfrac{5}{8}\)

Solution

Use the LCM to make the common denominator. The LCM (9, 8) = 72.

Figure 4.2.4

\(\begin{array}{l}
\dfrac{4}{9}=\dfrac{4 \times 8}{9 \times 8}=\dfrac{32}{72} \\
\dfrac{5}{8}=\dfrac{5 \times 9}{8 \times 9}=\dfrac{45}{72}
\end{array} \)

Since \(\dfrac{45}{72}>\dfrac{32}{72}\), then \(\dfrac{5}{8}>\dfrac{4}{9}\)

Example \(\PageIndex{5}\)

Equivalent Fractions. Show that \(\dfrac{1}{2}=\dfrac{4}{8}\).

Figure 4.2.5

Example \(\PageIndex{6}\)

Create Equivalent Fractions for \(\dfrac{2}{3}\).

Solution

\(\dfrac{2}{3}=\dfrac{2 \times 4}{3 \times 4}=\dfrac{8}{12} \)

OR

\(\dfrac{2}{3}=\dfrac{2 \times 11}{3 \times 11}=\dfrac{22}{33} \)

Example \(\PageIndex{7}\)

A 5th grade class has 11 girls and 13 boys. What fraction of the class has boys?

Solution

1. Find the total (whole): 11 + 13 = 24 students
2. Write your fraction: \(\dfrac{\text { boys }}{\text { class }}=\dfrac{13}{24}\)

Partner Activity 1

Describe ways of telling when a fraction is close to…

1. zero
2. One
3. one-half
4. one-third

Partner Activity 2

Organize the fractions by which it is closest to zero, one-half or one.

\(\dfrac{3}{8} \quad \dfrac{5}{4} \quad \dfrac{2}{9} \quad \dfrac{4}{7} \quad \dfrac{1}{3}\)

Practice Problems

1. Explain the meaning of \(3 \dfrac{1}{2}\) two different ways.
2. Put the following fractions in order from least to greatest: \(\dfrac{4}{7}, \dfrac{2}{5}, \dfrac{1}{9}, \dfrac{12}{13}, \dfrac{3}{8}\)