Question

Divide Fractions and Whole Numbers Quick Check

Answer 1

Dividing fractions by whole numbers involves a few straightforward steps. Here’s a quick guide to help you understand the process:

### Steps to Divide Fractions by Whole Numbers

1. **Write the Whole Number as a Fraction**:
Convert the whole number into a fraction. For example, if you want to divide 1/2 by 3, rewrite 3 as 3/1.

2. **Reciprocate the Whole Number**:
Find the reciprocal of the whole number (now in fraction form). The reciprocal of 3/1 is 1/3.

3. **Multiply the Fractions**:
Multiply the original fraction by the reciprocal of the whole number:
\[
\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3}
\]

4. **Multiply the Numerators and Denominators**:
Perform the multiplication:
\[
\frac{1 \times 1}{2 \times 3} = \frac{1}{6}
\]

### Example Problems

1. **Dividing a Fraction by a Whole Number**:
- **Problem**: \( \frac{3}{4} \div 2 \)
- **Solution**:
1. Rewrite 2 as \( \frac{2}{1} \).
2. Find the reciprocal: \( \frac{1}{2} \).
3. Multiply: \( \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8} \).

2. **Dividing a Fraction by Another Whole Number**:
- **Problem**: \( \frac{5}{8} \div 4 \)
- **Solution**:
1. Rewrite 4 as \( \frac{4}{1} \).
2. Find the reciprocal: \( \frac{1}{4} \).
3. Multiply: \( \frac{5}{8} \times \frac{1}{4} = \frac{5 \times 1}{8 \times 4} = \frac{5}{32} \).

### Practice Problems
Try these on your own:
1. \( \frac{1}{3} \div 5 \)
2. \( \frac{2}{5} \div 3 \)
3. \( \frac{7}{10} \div 2 \)

### Answers to Practice Problems
1. \( \frac{1}{15} \)
2. \( \frac{2}{15} \)
3. \( \frac{7}{20} \)

Feel free to ask if you have any questions or need further explanations!