# Stretching the Line: How to Multiply Fractions by Whole Numbers with Number Lines

Number lines offer a visual way to understand the multiplication of fractions by whole numbers.

By representing fractions and whole numbers on a number line, we can visually see the product and gain a deeper understanding of the multiplication process. In this guide, we’ll explore how to use number lines to multiply fractions by whole numbers.

## Step-by-step Guide:

**1. Setting Up the Number Line:**

Draw a number line and mark it with appropriate intervals. If you’re multiplying a fraction by a whole number, the number line should extend at least up to that whole number.

**2. Plotting the Fraction: **

Mark the fraction you’re working with on the number line. For instance, if you’re multiplying \(\frac{1}{3}\), mark a point one-third of the way between 0 and 1.

**3. Multiplying Using Jumps:**

To multiply the fraction by a whole number, make “jumps” on the number line equal to the size of the fraction. The number of jumps should be equal to the whole number you’re multiplying by.

**4. Determining the Product: **

The point where you land after making all the jumps represents the product of the fraction and the whole number.

**5. Converting Improper Fractions:**

If the result is an improper fraction (i.e., the numerator is greater than the denominator), convert it to a mixed number.

### Example 1:

Multiply \(\frac{1}{2}\) by 3 using a number line.

**Solution: **

– Draw a number line from 0 to 3.

– Mark the point \(\frac{1}{2}\) between 0 and 1.

– Make 3 jumps of size \(\frac{1}{2}\).

After 3 jumps, you’ll land on the point 1.5 or \(1 \frac{1}{2}\).

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### Example 2:

Multiply \(\frac{2}{3}\) by 4 using a number line.

**Solution:**

– Draw a number line from 0 to 4.

– Mark the point \(\frac{2}{3}\) between 0 and 1.

– Make 4 jumps of size \(\frac{2}{3}\).

After 4 jumps, you’ll land on the point \(2 \frac{2}{3}\).

### Practice Questions:

1. Multiply \(\frac{1}{4}\) by 4 using a number line.

2. Multiply \(\frac{3}{5}\) by 3 using a number line.

3. Multiply \(\frac{2}{6}\) by 5 using a number line.

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**Answers: **

1. 1

2. \(1 \frac{4}{5}\) or 1.8

3. \(1 \frac{2}{3}\) or 1.67

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