Question

n7.3, & n7.4 use benchmarks and a number line to order this set of numbers from least to greatest a) \\(\frac{11}{12}\\), \\(\frac{1}{3}\\), \\(\frac{7}{6}\\), \\(\frac{5}{4}\\) from least to greatest: \\(\frac{1}{3}\\) \\(\frac{11}{12}\\) \\(\frac{7}{6}\\) \\(\frac{5}{4}\\)

Explanation:

Step1: Find a common denominator

The fractions are $\frac{1}{3}$, $\frac{11}{12}$, $\frac{7}{6}$, $\frac{5}{4}$. The least common denominator (LCD) of 3, 12, 6, 4 is 12.

• $\frac{1}{3}=\frac{1\times4}{3\times4}=\frac{4}{12}$
• $\frac{11}{12}=\frac{11}{12}$
• $\frac{7}{6}=\frac{7\times2}{6\times2}=\frac{14}{12}$
• $\frac{5}{4}=\frac{5\times3}{4\times3}=\frac{15}{12}$

Step2: Compare the numerators

Now that all fractions have the same denominator (12), we compare the numerators:

• $4 < 11 < 14 < 15$

Step3: Order the original fractions

Using the equivalent fractions with denominator 12, we can order the original fractions:

• $\frac{4}{12}$ (which is $\frac{1}{3}$) $< \frac{11}{12} < \frac{14}{12}$ (which is $\frac{7}{6}$) $< \frac{15}{12}$ (which is $\frac{5}{4}$)

Answer:

$\frac{1}{3}$, $\frac{11}{12}$, $\frac{7}{6}$, $\frac{5}{4}$