【People's Education Press】Junior High School English, Grade 7, Semester 1: Review & Reconnect: Embarking on the Advanced Journey of Rational Numbers

Imagine an explorer starting at the origin $O$. If he walks 10 meters east to point $A(10)$, and 10 meters west to point $B(-10)$, his final positions are completely different (opposite numbers). However, from the perspective of 'energy expenditure' or 'number of steps taken', both journeys have identical 'intensity'. This view—ignoring direction and focusing only on step count—is the key to unlocking our 'advanced journey'.

Observing Symmetry and Distance on the Number Line

This lesson serves as an introduction to 'rational number operations and comparisons'. Its core is using the number line—a visual tool—to transition from a static understanding of numbers to a dynamic grasp of their values.

By reviewing the three essential components of the number line, guide students to observe the symmetry of opposite numbers in spatial distribution. The sign determines which side of the origin we're on, while the 'value' determines how far we are from it. This separation of dual attributes is a crucial foundational concept for understanding later absolute value calculations and addition rules.

Numbers on the right side of the number line are always greater than those on the left; when comparing numerical size, absolute value describes the distance from a point to the origin—the pure numerical value without direction.

$|10| = |-10| = 10$

QUESTION 1

Write the absolute value of the number $-8$.

$-8$

$8$

$\pm 8$

$0$

QUESTION 2

Which of the following statements is correct? ( )

Numbers with opposite signs are opposites of each other

The larger the absolute value of a number, the further right its point lies on the number line

The larger the absolute value of a number, the farther its point is from the origin on the number line

When $a \neq 0$, $|a|$ may be less than 0

QUESTION 3

Inspect 5 volleyballs, where grams above standard are recorded as positive. Data: $+5, -3.5, +0.7, -2.5, -0.6$. Which ball is closest to standard?

$+5$

$-3.5$

$+0.7$

$-0.6$

QUESTION 4

Compare sizes: $-3.5$ vs. $-2$.

$-3.5 > -2$

$-3.5 < -2$

$-3.5 = -2$

Cannot compare

QUESTION 5

Calculate: $(-4) + 7$.

$11$

$-11$

$3$

$-3$

QUESTION 6

Calculate: $(-4) + (-6)$.

$-10$

$10$

$-2$

$2$

QUESTION 7

If $a < 0, b > 0$, and $|b| > |a|$, which of the following arrangements is correct? ( )

$a < -a < b < -b$

$-b < a < -a < b$

$-b < -a < a < b$

$a < -b < b < -a$

QUESTION 8

The result of $15 + (-22)$ is ( ).

$37$

$-37$

$7$

$-7$

QUESTION 9

Mental math: $(-4) + 4$.

$8$

$-8$

$0$

$1$

QUESTION 10

Among the following numbers, which has the smallest absolute value? ( )

$6$

$-8$

$0$

$100$