Question

write the subtraction sentence that is shown on the number line. do not reduce the fractions. a number line from 0/5 to 10/5 with a blue dot at 3/5 and a purple arrow from 3/5 to 2/5 labeled 4/10. below the number line, there are three boxes with a minus sign and an equals sign between them, each box has a numerator and a denominator line.

Explanation:

Step1: Identify the starting point

The blue dot is at $\frac{4}{5}$. We can convert $\frac{4}{5}$ to tenths: $\frac{4}{5}=\frac{8}{10}$.

Step2: Identify the amount subtracted

The purple arrow shows a subtraction of $\frac{4}{10}$.

Step3: Perform the subtraction

We start with $\frac{8}{10}$ and subtract $\frac{4}{10}$. So the subtraction sentence is $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. But we can also use fifths. Wait, $\frac{4}{5}$ is the starting point, and we subtract $\frac{4}{10}$ (which is $\frac{2}{5}$). Wait, let's check the number line. The starting point is at $\frac{4}{5}$, and we move left by $\frac{4}{10}$. Let's convert $\frac{4}{5}$ to tenths: $\frac{4}{5}=\frac{8}{10}$. Then subtract $\frac{4}{10}$: $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. Alternatively, in fifths, $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$, but the problem says do not reduce the fractions, and the arrow is labeled $\frac{4}{10}$. So let's use tenths. Wait, the starting point is $\frac{4}{5}$, which is $\frac{8}{10}$, subtract $\frac{4}{10}$, so the sentence is $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. But maybe in fifths? Wait, $\frac{4}{5}$ is the starting point, and the subtraction is $\frac{4}{10}$ which is $\frac{2}{5}$. Wait, no, the number line has marks at $\frac{0}{5},\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5},...$ So the blue dot is at $\frac{4}{5}$, and we move left by $\frac{4}{10}$ (which is $\frac{2}{5}$? Wait, no, the distance between $\frac{3}{5}$ and $\frac{4}{5}$ is $\frac{1}{5}$, which is $\frac{2}{10}$. So moving left by 2 units of $\frac{2}{10}$? Wait, the purple arrow is labeled $\frac{4}{10}$, so from $\frac{4}{5}$ (which is $\frac{8}{10}$) subtract $\frac{4}{10}$, so $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. But let's check the fractions. The starting point is $\frac{4}{5}$, the subtracted amount is $\frac{4}{10}$, and the result is $\frac{4}{10}$ (or $\frac{2}{5}$ but we don't reduce). Wait, the problem has boxes for numerator and denominator. So let's write the starting fraction as $\frac{4}{5}$? No, wait, $\frac{4}{5}$ is equal to $\frac{8}{10}$, but maybe the problem expects using the fractions as per the number line. Wait, the number line is in fifths, but the arrow is labeled $\frac{4}{10}$. So let's convert $\frac{4}{5}$ to tenths: $\frac{4}{5}=\frac{8}{10}$, subtract $\frac{4}{10}$, so the subtraction sentence is $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. Alternatively, in fifths, $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$, but $\frac{4}{10}$ is $\frac{2}{5}$, so maybe the problem wants $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$, but the arrow is labeled $\frac{4}{10}$. Wait, the arrow is labeled $\frac{4}{10}$, so the subtracted amount is $\frac{4}{10}$, so the starting point is $\frac{8}{10}$ (which is $\frac{4}{5}$), subtract $\frac{4}{10}$, so $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. So the subtraction sentence is $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. But let's check the number line again. The blue dot is at $\frac{4}{5}$, the arrow goes from $\frac{4}{5}$ to $\frac{2}{5}$ (since $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$), and $\frac{2}{5}$ is $\frac{4}{10}$. Wait, $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$, and $\frac{2}{5}=\frac{4}{10}$. But the arrow is labeled $\frac{4}{10}$, so maybe we should use tenths. So starting at $\frac{8}{10}$ (which is $\frac{4}{5}$), subtract $\frac{4}{10}$, get $\frac{4}{10}$ (which is $\frac{2}{5}$). So the subtraction sentence is $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. But let's confirm with the number line. The marks are at $\frac{0}{5},\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5},...$ So $\frac{4}{5}$ is the starting point, subtract $\frac{4}{10}$ (which is $\frac{2}{5}$), so $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$, but $\frac{2}{5}$ is $\frac{4}{10}$. So if we don't reduce, we can write $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$ or $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$, but the arrow is labeled $\frac{4}{10}$, so maybe the first term is $\frac{8}{10}$, second is $\frac{4}{10}$, result is $\frac{4}{10}$. Wait, the problem has three boxes: first fraction, second fraction, result. So let's fill them as $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. But let's check the number line again. The blue dot is at $\frac{4}{5}$, which is $\frac{8}{10}$, the arrow is $\frac{4}{10}$, so subtraction is $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$. Alternatively, in fifths, $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$, but $\frac{2}{5}$ is $\frac{4}{10}$, so maybe the problem expects $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$, but the arrow is labeled $\frac{4}{10}$, so perhaps we should use tenths. So the subtraction sentence is $\frac{8}{10}-\frac{4}{10}=\frac{4}{10}$.

Answer:

$\frac{8}{10} - \frac{4}{10} = \frac{4}{10}$ (or alternatively, if using fifths: $\frac{4}{5} - \frac{2}{5} = \frac{2}{5}$, but since the arrow is labeled $\frac{4}{10}$, the first form is more accurate as per the label)