Question

n7.3, & n7.4
use benchmarks and a number line to order this set of numbers from lea
a) $\frac{11}{12}$, $\frac{1}{3}$, $\frac{7}{6}$, $\frac{5}{4}$
0 $\frac{1}{2}$ 1 $1\frac{1}{2}$

Explanation:

Step1: Find a common denominator

To compare the fractions, we find the least common denominator (LCD) of 12, 3, 6, and 4. The LCD of these numbers is 12.

Step2: Convert each fraction to twelfths

• For $\frac{1}{3}$: Multiply numerator and denominator by 4: $\frac{1\times4}{3\times4}=\frac{4}{12}$
• For $\frac{7}{6}$: Multiply numerator and denominator by 2: $\frac{7\times2}{6\times2}=\frac{14}{12}$
• For $\frac{5}{4}$: Multiply numerator and denominator by 3: $\frac{5\times3}{4\times3}=\frac{15}{12}$
• $\frac{11}{12}$ remains as $\frac{11}{12}$

Step3: Order the fractions by numerator

Now that all fractions have the same denominator, we order them by their numerators:
$\frac{4}{12} < \frac{11}{12} < \frac{14}{12} < \frac{15}{12}$

Step4: Substitute back the original fractions

Substituting back, we get:
$\frac{1}{3} < \frac{11}{12} < \frac{7}{6} < \frac{5}{4}$

Answer:

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