Which number line shows a negative mixed number graphed correctly?
Check the final answer first, then review the worked steps.
Problem
Which number line shows a negative mixed number graphed correctly?
Answer
The third number line.
Step-by-step solution
- Understand the number to be graphed: The number to be graphed is $-2\frac{1}{6}$. This is a negative mixed number. It means it is 2 whole units to the left of zero, plus an additional $\frac{1}{6}$ of a unit further to the left.
- Convert the mixed number to an improper fraction: To better understand its position, convert $-2\frac{1}{6}$ to an improper fraction. Multiply the whole number (2) by the denominator (6) and add the numerator (1): $2 \times 6 + 1 = 12 + 1 = 13$. So, $-2\frac{1}{6} = -\frac{13}{6}$.
- Determine the approximate location: Since the number is negative, it will be on the left side of zero on the number line. The whole number part is -2, so the number will be between -2 and -3. To be more precise, we can divide 13 by 6: $13 \div 6 = 2$ with a remainder of 1. This confirms it is 2 whole units and $\frac{1}{6}$ of the next unit.
- Analyze the fraction part: The fraction part is $\frac{1}{6}$. This means we need to divide the interval between -2 and -3 into 6 equal parts. The number $-2\frac{1}{6}$ will be located one-sixth of the way from -2 towards -3.
- Examine the number line options: Look at each number line provided. We are looking for a point located between -2 and -3, closer to -2. Specifically, it should be one-sixth of the distance between -2 and -3. The interval between -2 and -3 is divided into 6 smaller tick marks in the correct option.
- Identify the correct graph: The third number line shows a point located between -2 and -3. This interval is divided into 6 equal segments. The blue dot is placed on the first tick mark to the left of -2, which represents $-2\frac{1}{6}$. The other number lines show points at -2.5 (between -2 and -3, but in the middle), -4, and -2, none of which match $-2\frac{1}{6}$.