Simplification and Expansion of Simple Fractions - Examples, Exercises and Solutions

Let's reduce as follows, divide the numerator by 4 and the denominator by 4:

$\frac{12:4}{4:4}=\frac{3}{1}$

Let's reduce as follows, we'll divide both the numerator and denominator by 1:

$\frac{1:1}{1:1}=\frac{1}{1}$

Let's reduce as follows, we'll divide both the numerator and denominator by 5:

$\frac{15:5}{10:5}=\frac{3}{2}$

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

$\frac{12:2}{8:2}=\frac{6}{4}$

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

$\frac{16:2}{8:2}=\frac{8}{4}$

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

$\frac{2:2}{10:2}=\frac{1}{5}$

Let's simplify as follows, we'll divide both the numerator by 4 and the denominator by 4:

$\frac{4:4}{8:4}=\frac{1}{2}$

We will reduce as follows, divide the numerator by 3 and the denominator by 3:

$\frac{3:3}{6:3}=\frac{1}{2}$

We will reduce in the following way, divide the numerator by 1 and the denominator by 1:

$\frac{3:1}{10:1}=\frac{3}{10}$

We will reduce in the following way, divide the numerator by 4 and the denominator by 4:

$\frac{4:4}{16:4}=\frac{1}{4}$

To solve the problem of enlarging the fraction $\frac{1}{3}$ by a factor of 4, we will follow these steps:

• Step 1: Identify the given fraction and enlargement factor. The fraction is $\frac{1}{3}$ and the factor is 4.
• Step 2: Multiply both the numerator and denominator of the fraction by the enlargement factor. This means we calculate:

$\frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Step 3: Check if the fraction can be simplified. Here, $\frac{4}{12}$ can be simplified to $\frac{1}{3}$, but since we aim to express it in an "enlarged" form, $\frac{4}{12}$ is a correct representation when enlarged by the given factor.

Step 4: Verify against answer choices if applicable. In our list of choices, $\frac{4}{12}$ is listed as choice 3, which matches our calculated answer.

Therefore, the solution to the problem is $\frac{4}{12}$.

To solve the problem of increasing the fraction $\frac{2}{5}$ by a factor of 8, we follow these steps:

• Multiply the numerator of the fraction by the factor of 8.
• Multiply the denominator of the fraction by the same factor of 8 to preserve the value relation.
• Check the result against the options provided, especially since this is a multiple-choice question.

Following these steps:

Step 1: Multiply the numerator:

The numerator is 2. Multiplying 2 by 8 gives $2 \times 8 = 16$.

Step 2: Multiply the denominator:

The denominator is 5. Multiplying 5 by 8 gives $5 \times 8 = 40$.

Thus, the fraction becomes $\frac{16}{40}$ after being increased by a factor of 8.

The correct answer among the provided choices is:

$\frac{16}{40}$

To solve the problem of increasing the fraction $\frac{3}{10}$ by a factor of 5, follow these steps:

• Step 1: Multiply the numerator by 5.
  The original numerator is 3, so $3 \times 5 = 15$.
• Step 2: Multiply the denominator by 5.
  The original denominator is 10, so $10 \times 5 = 50$.
• Step 3: Write the new fraction.
  The resulting fraction after applying the factor is $\frac{15}{50}$.

Thus, when we increase the fraction $\frac{3}{10}$ by a factor of 5, we get $\frac{15}{50}$.

Therefore, the correct answer is $\frac{15}{50}$.

To solve the problem, we need to increase the fraction $\frac{6}{7}$ by a factor of 5. This involves multiplying both the numerator and denominator by 5.

• Step 1: Multiply the numerator of the fraction: $6 \times 5 = 30$.
• Step 2: Multiply the denominator of the fraction: $7 \times 5 = 35$.
• Step 3: Form the new fraction: $\frac{30}{35}$.

Thus, when you increase the fraction $\frac{6}{7}$ by a factor of 5, the result is $\frac{30}{35}$.

To solve this problem, follow these steps:

• Step 1: Identify the given fraction as $\frac{8}{11}$.
• Step 2: Determine the factor to increase by, which is 6.
• Step 3: Multiply the numerator by the factor: $8 \times 6 = 48$.
• Step 4: Multiply the denominator by the factor: $11 \times 6 = 66$.

Now, let's perform the calculation to expand the fraction:

Starting with the original fraction:

$\frac{8}{11}$

We need to multiply both the numerator and the denominator by the factor of 6:

The new numerator is:

$8 \times 6 = 48$

The new denominator is:

$11 \times 6 = 66$

Thus, the fraction increased by a factor of 6 is:

$\frac{48}{66}$

Therefore, the solution to the problem is $\frac{48}{66}$.