Subjects algebra

Number Line Placement

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Number Line Placement


1. The problem asks us to place the given numbers from the box onto the number line at the positions marked with a "+". 2. First, let's convert all boxed numbers to decimal form to understand their relative sizes clearly: - $-\frac{8}{4} = -2$ - $0.4 = 0.4$ - $1 \frac{2}{5} = 1 + \frac{2}{5} = 1 + 0.4 = 1.4$ - $1.8 = 1.8$ - $-2.2 = -2.2$ 3. Analyzing the number line tick marks from left to right: $-3$, (unknown tick), $-1$, $0$, $1$, $2$. 4. The unknown tick is between $-3$ and $-1$. Since $-2.2$ and $-2$ are between $-3$ and $-1$, these fit into the unknown tick positions. 5. We have an arrow pointing to $-\frac{8}{4} = -2$ near the unknown tick labeled with a question mark, indicating the unknown tick corresponds to $-2$. 6. The other unknown tick before $-2$ must be $-2.2$, which is slightly less than $-2$, so it fits to the left of $-2$. 7. The positive ticks to the right of 0 are $0.4$, $1.4$, and $1.8$. We can assign them from left to right as 0.4 is between 0 and 1, 1.4 and 1.8 are between 1 and 2. 8. Therefore, the number line placements are: - Leftmost unknown tick: $-2.2$ - Next unknown tick: $-2$ - Positive ticks: $0.4$, $1.4$, $1.8$ in ascending order after 0 Final answer: On the number line, tick marks correspond to $-2.2$, $-2$, $0.4$, $1.4$, and $1.8$ as described.