Mixed Numbers

To solve this problem, we'll perform the division $5 \div \frac{2}{5}$ by converting it into multiplication:

• Step 1: Recognize that dividing by a fraction is the same as multiplying by its reciprocal.
• Step 2: Convert the division into multiplication: $5 \div \frac{2}{5} = 5 \times \frac{5}{2}$.
• Step 3: Multiply the whole number by the reciprocal of the fraction: $5 \times \frac{5}{2} = \frac{25}{2}$.
• Step 4: Convert the improper fraction to a mixed number: $\frac{25}{2} = 12 \frac{1}{2}$.

Through these steps, we find that the solution to the division problem is $12 \frac{1}{2}$.

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 $\textbf{1}\frac{\textbf{3}}{\textbf{7}}$.

We need to evaluate the expression $1 \div \frac{2}{3}$.

To do this, we use the principle that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, the expression becomes:

$1 \times \frac{3}{2}$.

Next, we multiply the whole number by the reciprocal:

$1 \times \frac{3}{2} = \frac{3}{2}$.

To express $\frac{3}{2}$ as a mixed number, we write it as:

$1\frac{1}{2}$.

Thus, the solution to the problem is $1\frac{1}{2}$, which matches choice 3 from the options provided.

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.

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

• Convert the whole number into a fraction.
• Multiply the fractions.
• Simplify the result.

Now, let's work through each step:

Step 1: Convert the whole number 3 into a fraction:
3 becomes $\frac{3}{1}$.

Step 2: Multiply the fraction $\frac{3}{1}$ by $\frac{6}{7}$:
The numerators are $3 \times 6 = 18$.
The denominators are $1 \times 7 = 7$.
The result is $\frac{18}{7}$.

Step 3: Convert $\frac{18}{7}$ to a mixed number:
Divide the numerator by the denominator: 18 divided by 7 is 2 with a remainder of 4.
Thus, $\frac{18}{7} = 2\frac{4}{7}$.

Therefore, the solution to the problem is $2\frac{4}{7}$.