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

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

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

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

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

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

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

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

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

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

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

To solve this problem, we'll follow these steps:

• Step 1: Identify the original fraction, which is $\frac{3}{7}$.
• Step 2: Multiply both the numerator and denominator by 3 to increase the fraction by a factor of 3.
• Step 3: Calculate the new fraction.

Now, let's work through each step:
Step 1: The original fraction is $\frac{3}{7}$.
Step 2: Multiply the numerator (3) by 3 to get 9, and multiply the denominator (7) by 3 to get 21.
So, the new fraction becomes $\frac{9}{21}$.

Therefore, the solution to the problem is $\frac{9}{21}$.

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, 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, we'll follow these steps:

• Step 1: Multiply the numerator by 6.
• Step 2: Multiply the denominator by 6.
• Step 3: Write down the result as a new fraction.

Now, let's work through each step:
Step 1: The original fraction is $\frac{2}{3}$. Multiply the numerator 2 by 6, which gives $2 \times 6 = 12$.
Step 2: Multiply the denominator 3 by 6, which gives $3 \times 6 = 18$.
Step 3: The resulting fraction after multiplying both numerator and denominator by 6 is $\frac{12}{18}$.

Therefore, the solution to the problem is $\frac{12}{18}$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given fraction $\frac{2}{15}$.
• Step 2: Multiply both the numerator and the denominator by the factor 3.
• Step 3: Write the new fraction.

Now, let's work through each step:

Step 1: The given fraction is $\frac{2}{15}$.

Step 2: We need to enlarge this fraction by a factor of 3.
Multiply the numerator: $2 \times 3 = 6$.
Multiply the denominator: $15 \times 3 = 45$.

Step 3: The enlarged fraction is $\frac{6}{45}$.

Therefore, the solution to the problem is $\frac{6}{45}$.