Multiplication of Integers by Fractions and Mixed Numbers Practice

To solve the problem $6 \times \frac{3}{4}$, we follow these steps:

• Step 1: Express the integer 6 as a fraction: $\frac{6}{1}$.
• Step 2: Multiply the fractions: $\frac{6}{1} \times \frac{3}{4}$.
• Step 3: Multiply the numerators: $6 \times 3 = 18$.
• Step 4: Multiply the denominators: $1 \times 4 = 4$.
• Step 5: Form the resulting fraction: $\frac{18}{4}$.
• Step 6: Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 2: $\frac{18}{4} \div \frac{2}{2} = \frac{9}{2}$.
• Step 7: Convert $\frac{9}{2}$ to a mixed number: Divide 9 by 2 to get 4 with a remainder of 1, thus $\frac{9}{2} = 4\frac{1}{2}$.

Therefore, the solution to the problem is $4\frac{1}{2}$.

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

• Multiply the numerator of the fraction by the integer.
• Keep the denominator unchanged.
• Convert the resulting improper fraction to a mixed number, if necessary.

Now, let's work through each step:
Step 1: Multiply the numerator of $\frac{1}{2}$, which is $1$, by $3$:
$1 \times 3 = 3$.

Step 2: Write the result over the original denominator:
$\frac{3}{2}$.

Step 3: Convert the improper fraction $\frac{3}{2}$ to a mixed number:
Divide $3$ by $2$. This gives $1$ as the quotient and $1$ as the remainder, so:
$\frac{3}{2} = 1\frac{1}{2}$.

Therefore, the solution to the problem is $1\frac{1}{2}$.

To solve this problem, we'll multiply the whole number 2 by the fraction $\frac{5}{7}$:

• Step 1: Multiply the numerator 5 by the whole number 2:

$2 \times 5 = 10$

• Step 2: Write the result over the original denominator 7:

$\frac{10}{7}$

• Step 3: Convert $\frac{10}{7}$ to a mixed number:

Since 10 divided by 7 is 1 with a remainder of 3, we can express this as:

$1\frac{3}{7}$

Therefore, the solution to the problem is $\textbf{1}\frac{\textbf{3}}{\textbf{7}}$.

To solve this problem, we'll multiply the whole number 4 by the fraction $\frac{2}{3}$ as follows:

• Step 1: Convert the whole number 4 into a fraction. This can be written as $\frac{4}{1}$.
• Step 2: Use fraction multiplication rules: multiply the numerators together and the denominators together.
• Step 3: So, multiply the numerators: $4 \times 2 = 8$.
• Step 4: Multiply the denominators: $1 \times 3 = 3$.
• Step 5: The result is $\frac{8}{3}$.
• Step 6: Since $\frac{8}{3}$ is an improper fraction, convert it to a mixed number.
  $8 \div 3 = 2$ with a remainder of 2.
  Thus, $\frac{8}{3} = 2\frac{2}{3}$.

Therefore, the solution to the problem is $2\frac{2}{3}$.

To solve the problem $7 \times \frac{2}{5}$, we will follow a structured approach:

• Step 1: Multiply the whole number by the numerator of the fraction.
• Step 2: Retain the denominator of the fraction.
• Step 3: Simplify the resulting fraction, if possible.

Let's work through each step:

Step 1: Multiply the whole number by the numerator.
We have $7 \times 2 = 14$.

Step 2: Keep the denominator the same.
The resulting fraction is $\frac{14}{5}$.

Step 3: Convert the improper fraction to a mixed number if possible.
Divide the numerator by the denominator: $14 \div 5 = 2$ with a remainder of $4$.
This results in the mixed number $2\frac{4}{5}$.

Therefore, the solution to the problem $7 \times \frac{2}{5}$ is $2\frac{4}{5}$, which corresponds to choice 3 in the provided options.