Analysis and Solutions:

Questions 1–6:

For each number line, the task is to determine two fractions representing the marked points.

1. The number line is divided into 4 equal parts, so the fraction for the marked point is:

• 1/2 (as the point is halfway between 0 and 1).
• Equivalent fraction: 2/4.

2. The number line is divided into 5 equal parts, and the marked point is at 3 parts from 0:

• 3/5.
• Equivalent fraction: 6/10.

3. The number line is divided into 8 equal parts, and the marked point is at 5 parts from 0:

• 5/8.
• Equivalent fraction: 10/16.

4. The number line is divided into 6 equal parts, and the marked point is at 2 parts from 0:

• 2/6.
• Equivalent fraction: 1/3 (simplified).

5. The number line is divided into 3 equal parts, and the marked point is at 1 part from 0:

• 1/3.
• Equivalent fraction: 2/6.

6. The number line is divided into 8 equal parts, and the marked point is at 7 parts from 0:

• 7/8.
• Equivalent fraction: 14/16.

Question 7:

Are $\frac{3}{8}$ and $\frac{3}{4}$ equivalent fractions? Draw a number line to decide.

• To determine equivalence, compare their values:

  • $\frac{3}{8} = 0.375$
  • $\frac{3}{4} = 0.75$

• Since $0.375 \neq 0.75$, these are not equivalent fractions.

• Drawing a number line will show $\frac{3}{8}$ and $\frac{3}{4}$ at different locations, confirming they are not equivalent.

Question 8:

Draw a number line to show $\frac{2}{8}$ and $\frac{4}{16}$ are equivalent.

• Simplify:
  • $\frac{2}{8} = \frac{1}{4}$
  • $\frac{4}{16} = \frac{1}{4}$
• These fractions are equal because they simplify to the same value.
• On the number line, both $\frac{2}{8}$ and $\frac{4}{16}$ will occupy the same position, confirming equivalence.

Questions to Expand Understanding:

1. How can you verify if two fractions are equivalent without drawing a number line?
2. Why is it helpful to write fractions in their simplest form?
3. What is the significance of dividing the number line into equal parts when representing fractions?
4. Can you provide examples of two fractions that are not equivalent but close in value?
5. How does the denominator of a fraction affect its placement on a number line?

Tip:

To check for equivalent fractions, cross-multiply the two fractions. If the cross-products are equal, the fractions are equivalent!