Multiplying fractions by whole numbers - Fraction and Decimal ... - Free Printable

Problem Analysis:

The worksheet focuses on multiplying fractions by whole numbers. The task involves understanding how to multiply a fraction by a whole number and expressing the result as an improper fraction or a mixed number. Let's solve each part step by step.

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Step 1: Understanding the Example

The example provided is:
$$
3 \times \frac{3}{4}
$$
- The bars show that multiplying \(3\) by \(\frac{3}{4}\) means taking \(\frac{3}{4}\) three times.
- Mathematically:
$$
3 \times \frac{3}{4} = \frac{3 \times 3}{4} = \frac{9}{4}
$$
- Converting \(\frac{9}{4}\) to a mixed number:
$$
\frac{9}{4} = 2 \frac{1}{4}
$$

So, the result is:
$$
\frac{9}{4} = 2 \frac{1}{4}
$$

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Step 2: Solving Problem 2

The problem is:
$$
3 \times \frac{2}{5}
$$
- Multiply the whole number \(3\) by the numerator of the fraction:
$$
3 \times \frac{2}{5} = \frac{3 \times 2}{5} = \frac{6}{5}
$$
- Convert \(\frac{6}{5}\) to a mixed number:
$$
\frac{6}{5} = 1 \frac{1}{5}
$$

So, the result is:
$$
\frac{6}{5} = 1 \frac{1}{5}
$$

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Step 3: Solving Problem 3

The problem is:
$$
4 \times \frac{4}{7}
$$
- Multiply the whole number \(4\) by the numerator of the fraction:
$$
4 \times \frac{4}{7} = \frac{4 \times 4}{7} = \frac{16}{7}
$$
- Convert \(\frac{16}{7}\) to a mixed number:
$$
\frac{16}{7} = 2 \frac{2}{7}
$$

So, the result is:
$$
\frac{16}{7} = 2 \frac{2}{7}
$$

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Step 4: Solving Problems 4 to 7

These problems involve multiplying fractions by whole numbers without visual aids. We follow the same method: multiply the whole number by the numerator of the fraction, keeping the denominator the same.

#### Problem 4:
$$
3 \times \frac{2}{7}
$$
- Multiply:
$$
3 \times \frac{2}{7} = \frac{3 \times 2}{7} = \frac{6}{7}
$$
- The result is already in simplest form:
$$
\frac{6}{7}
$$

#### Problem 5:
$$
4 \times \frac{3}{5}
$$
- Multiply:
$$
4 \times \frac{3}{5} = \frac{4 \times 3}{5} = \frac{12}{5}
$$
- Convert to a mixed number:
$$
\frac{12}{5} = 2 \frac{2}{5}
$$

#### Problem 6:
$$
5 \times \frac{5}{8}
$$
- Multiply:
$$
5 \times \frac{5}{8} = \frac{5 \times 5}{8} = \frac{25}{8}
$$
- Convert to a mixed number:
$$
\frac{25}{8} = 3 \frac{1}{8}
$$

#### Problem 7:
$$
6 \times \frac{7}{10}
$$
- Multiply:
$$
6 \times \frac{7}{10} = \frac{6 \times 7}{10} = \frac{42}{10}
$$
- Simplify the fraction:
$$
\frac{42}{10} = \frac{21}{5}
$$
- Convert to a mixed number:
$$
\frac{21}{5} = 4 \frac{1}{5}
$$

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Final Answers:

1. What do you notice?
When multiplying a fraction by a whole number, the whole number multiplies the numerator of the fraction, while the denominator remains the same. The result can be expressed as an improper fraction or a mixed number.

2. \( 3 \times \frac{2}{5} = \boxed{\frac{6}{5} = 1 \frac{1}{5}} \)

3. \( 4 \times \frac{4}{7} = \boxed{\frac{16}{7} = 2 \frac{2}{7}} \)

4. \( 3 \times \frac{2}{7} = \boxed{\frac{6}{7}} \)

5. \( 4 \times \frac{3}{5} = \boxed{\frac{12}{5} = 2 \frac{2}{5}} \)

6. \( 5 \times \frac{5}{8} = \boxed{\frac{25}{8} = 3 \frac{1}{8}} \)

7. \( 6 \times \frac{7}{10} = \boxed{\frac{21}{5} = 4 \frac{1}{5}} \)

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Boxed Final Answer:

$$
\boxed{\frac{6}{5} = 1 \frac{1}{5}, \frac{16}{7} = 2 \frac{2}{7}, \frac{6}{7}, \frac{12}{5} = 2 \frac{2}{5}, \frac{25}{8} = 3 \frac{1}{8}, \frac{21}{5} = 4 \frac{1}{5}}
$$