Math Problem Statement

How are fractions and mixed numbers placed correctly on a number line?

Solution

This is a number line that appears to show fractions and mixed numbers placed at appropriate intervals.

Explanation of Key Points:

  1. Fractions and Mixed Numbers:

    • Fractions like 54\frac{5}{4}, 168\frac{16}{8}, and mixed numbers like 2122 \frac{1}{2} are placed along the number line.
    • 11 is equivalent to 44\frac{4}{4}, and 168\frac{16}{8} is equal to 22, so these fractions/mixed numbers are aligned correctly on the number line.
  2. Intervals:

    • The intervals between whole numbers 11, 22, 33, etc., are divided into smaller, equal parts, representing the fractions.
  3. Placement:

    • 54=114\frac{5}{4} = 1 \frac{1}{4} is between 11 and 22.
    • 2122 \frac{1}{2} is halfway between 22 and 33.
    • 72=312\frac{7}{2} = 3 \frac{1}{2} is between 33 and 44.

Let me know if you'd like further breakdown or clarification!


Related Questions:

  1. How do you convert improper fractions to mixed numbers?
  2. What are the steps to find the equivalent decimal value of these fractions?
  3. How are intervals on the number line divided to accommodate fractions?
  4. Why is 168\frac{16}{8} equal to 22?
  5. How can fractions be simplified when placed on a number line?

Tip:

When working with fractions on a number line, always simplify them first or convert them to mixed numbers for clarity!

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Math Problem Analysis

Mathematical Concepts

Number Lines
Fractions
Mixed Numbers
Simplification of Fractions

Formulas

Improper fraction to mixed number: \( \text{Mixed Number} = \frac{\text{Numerator}}{\text{Denominator}} \)
Simplification: \( \frac{a}{b} = c \text{ if } a = b \cdot c \)

Theorems

Equality of Fractions: \( \frac{16}{8} = 2 \) based on \( a = b \cdot c \)

Suitable Grade Level

Grades 4-6