Question

Which addition equation matches the number line

Answer 1

Answer:

$\frac{2}{3}+(-2\frac{1}{3})=-1 \frac{2}{3}$ is correct.

Step-by-step explanation:

The number line between two consecutive integers is divided into 3 intervals. This means each of these intervals is 1/3. For example, starting from 0 towards right the first small line is at 1/3, the next at 2/3 and then at 3/3 = 1.

Similarly, towards the left of 0, we have -1/3, -2/3 and then-1. Based on this data, we can find the end points of the given line

• The location of right end point is 2/3
• The location of left end point is $(-1\frac{2}{3} )$

The distance between two endpoints can be calculated as:

Right End point - Left End point

$=\frac{2}{3} - (-1\frac{2}{3})\\\\ =\frac{2}{3} + 1\frac{2}{3}\\\\ =\frac{2}{3}+\frac{5}{3}\\\\ =\frac{7}{3}\\\\ =2\frac{1}{3}$

So, the equation can be set up as:

$\frac{1}{3}-(-1\frac{2}{3})=2\frac{1}{3}\\\\ \frac{1}{3}= 2\frac{1}{3}+(-1\frac{2}{3})\\\\ \frac{1}{3}-2\frac{1}{3}=-1\frac{2}{3}\\\\ \frac{1}{3}+(-2\frac{1}{3})=-1\frac{2}{3}$

Which matches with the final option.

Keywords: addition, graph, number line

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Answer 2

Answer:

The answer is 2nd equation

Step-by-step explanation:

Since, this line goes from $\frac{2}{3}$ till $-1-\frac{1}{3}$, therefore,

$\frac{2}{3} + (-1-\frac{1}{3})$

$\frac{2}{3} + (-\frac{4}{3})$

$\frac{-2}{3}$

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

and this is equal to right hand side of the equation in option two, i.e.

$\frac{2}{3} + (-2) = -1\frac{1}{3}$

Hence, 2nd equation is the answer.