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Chapter 4: Problem 90

Plot the fraction on the number line. $$-\frac{5}{6}$$

Short Answer

Expert verified
\(-\frac{5}{6}\) is located 5/6 of a step to the left of 0 on the number line.

Step by step solution

01

Understand the Fraction

The fraction is \(-\frac{5}{6}\). The negative sign indicates that it is to the left of zero on the number line.
02

Divide the Number Line

Mark the number line with whole numbers and divide the segment between 0 and -1 into 6 equal parts since the denominator is 6.
03

Locate the Fraction

Starting from 0, move left 5 steps out of the 6 equal parts you divided. This is where \(-\frac{5}{6}\) will be located on the number line.
04

Final Position

Place a point and label it as \(-\frac{5}{6}\) on the number line where you reached after moving 5 steps to the left from 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

number line
A number line is a visual representation of numbers in a straight line. It helps us understand the position and order of numbers. The center of the number line is typically 0.
Positive numbers are to the right of 0, and negative numbers are to the left. When plotting fractions, the number line is divided into equal parts based on the denominator of the fraction.
For example, if the fraction is \(-\frac{5}{6}\), we divide the segment between 0 and -1 into 6 equal parts. Each part is \(-\frac{1}{6}\). So, \(-\frac{5}{6}\) would be 5 parts to the left of 0.
negative fractions
Negative fractions can seem tricky, but they follow the same principles as positive fractions, just in the opposite direction. If a fraction is negative, it means the value is less than zero.
When plotting a negative fraction on a number line, you move to the left of zero. The farther left the value is, the smaller it becomes.
For our fraction \(-\frac{5}{6}\), the negative sign tells us to move left from zero. By dividing the segment between 0 and -1 into 6 equal parts, each part represents \(-\frac{1}{6}\).
Moving 5 parts left, we reach \(-\frac{5}{6}\).
fraction division
Fraction division involves dividing a whole into smaller parts. The denominator tells us how many equal parts the whole is divided into.
For instance, in \(-\frac{5}{6}\), the denominator is 6, indicating that the segment from 0 to -1 is divided into 6 equal sections. Each section is \(-\frac{1}{6}\).
The numerator tells us how many of these sections we need to count. With \(-\frac{5}{6}\), start at 0, divide the segment into 6 parts, and count 5 parts to the left.
This way, we find our final position at \(-\frac{5}{6}\) on the number line.

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Most popular questions from this chapter

Determine whether the factorization represents the prime factorization. If not, explain why. $$126=3 \cdot 7 \cdot 3 \cdot 2$$

Solve the equations by first clearing fractions. $$\frac{x}{3}+\frac{7}{6}=\frac{x}{2}$$

Divide. Write the quotient as a mixed number. $$8913 \div 11$$

Multiply or divide the mixed numbers. Write the answer as a mixed number or whole number. $$12 \frac{4}{5} \div\left(-2 \frac{3}{5}\right)$$

Find the LCM. 18 and 24
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