Rational Numbers and Numerical Expressions Practice

Vocabulary and concept flashcards covering properties of rational numbers, order of fractions on a number line, length overlap problems, and expression evaluations.

Inequality Condition for Same Denominator Rational Numbers ($\frac{p}{k} > \frac{q}{k}$, $k > 0$)

$$p > q$$

Condition for Positive Rational Number Strictly Less Than 1 ($\frac{x}{y} < 1$, $x > 0$, $y > 0$)

The numerator is smaller than the denominator ($x < y$).

Ordering Rational Numbers with Same Numerator ($X = \frac{7}{k}$, $Y = \frac{7}{k+3}$, $Z = \frac{7}{k+5}$ for $k > 0$)

$$Z < Y < X$$

Total Length of Joined Overlapping Pipes

For two pipes of lengths $0.7\,\text{m}$ and $1.6\,\text{m}$ with an overlapping segment of $\frac{1}{5}\,\text{m}$ ($0.2\,\text{m}$), the total length is $0.7 + 1.6 - 0.2 = 2.1\,\text{m}$.

Value of Expression $E = \frac{2}{7} - \left(5\frac{1}{3} - 4\right) + \frac{5}{7}$

$$-\frac{1}{3}$$