Question

ordering rational numbers

concept(s): i can order rational numbers
sample question: write the following numbers in order from least to greatest?
\\3.25 \quad -4.75 \quad -\frac{3}{4} \quad \frac{15}{4} \quad -\frac{11}{4} \quad 3.5\\

practice and consolidation:

1. write the mixed number and improper fraction that corresponds with these pictures.

a)
b)

Explanation:

Convert numbers to decimals

To compare the rational numbers, we convert all fractions to decimal form.

$$ -\frac{3}{4} = -0.75 $$

$$ \frac{15}{4} = 3.75 $$

$$ -\frac{11}{4} = -2.75 $$

Order the rational numbers

We arrange the numbers from least (most negative) to greatest.

$$ -4.75 < -2.75 < -0.75 < 3.25 < 3.5 < 3.75 $$

Replacing them with their original forms:

$$ -4.75, -\frac{11}{4}, -\frac{3}{4}, 3.25, 3.5, \frac{15}{4} $$

Analyze circle diagrams for 1a

We count the fully shaded circles and the fraction of the partially shaded circle.

• There are \(2\) fully shaded circles.
• The third circle has \(3\) out of \(4\) parts shaded, which is \(\frac{3}{4}\).
• Mixed Number: \(2\frac{3}{4}\)
• Improper Fraction: \(\frac{2 \times 4 + 3}{4} = \frac{11}{4}\)

Analyze rectangle diagrams for 1b

We count the fully shaded rectangles and the fraction of the partially shaded rectangle.

• There are \(3\) fully shaded rectangles, each divided into \(6\) equal horizontal bars.
• The fourth rectangle has \(2\) out of \(6\) bars shaded, which simplifies to \(\frac{2}{6} = \frac{1}{3}\).
• Mixed Number: \(3\frac{2}{6}\) (or \(3\frac{1}{3}\))
• Improper Fraction: \(\frac{3 \times 6 + 2}{6} = \frac{20}{6}\) (or \(\frac{10}{3}\))

Answer:

Sample Question

The numbers ordered from least to greatest:

$$-4.75, -\frac{11}{4}, -\frac{3}{4}, 3.25, 3.5, \frac{15}{4}$$

Question 1a

• Mixed Number: \(2\frac{3}{4}\)
• Improper Fraction: \(\frac{11}{4}\)

Question 1b

• Mixed Number: \(3\frac{2}{6}\) (or \(3\frac{1}{3}\))
• Improper Fraction: \(\frac{20}{6}\) (or \(\frac{10}{3}\))