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 $12 \frac{1}{2}$.

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 this problem, let's divide $1$ by $\frac{3}{4}$. The solution involves converting the division into a multiplication:

• Step 1: Recognize $\,1:\frac{3}{4}\,$ as the division $\frac{1}{\frac{3}{4}}$.

• Step 2: Convert division into multiplication: $\frac{1}{\frac{3}{4}} = 1 \times \frac{4}{3}$.

• Step 3: Compute the multiplication: $1 \times \frac{4}{3} = \frac{4}{3}$.

• Step 4: Convert $\frac{4}{3}$ into a mixed number: $1\frac{1}{3}$.

Therefore, the solution to the division $1 : \frac{3}{4}$ is $1\frac{1}{3}$

The correct answer is $(1 \frac{1}{3})$.

To solve the problem $3:\frac{3}{4}$, we must perform division of the whole number 3 by the fraction $\frac{3}{4}$. Here are the steps:

• Step 1: Recall the rule for dividing by a fraction. Dividing by $\frac{3}{4}$ is the same as multiplying by its reciprocal, $\frac{4}{3}$.
• Step 2: Rewrite the expression as a multiplication problem: $3 \times \frac{4}{3}$.
• Step 3: Perform the multiplication: $3 \times \frac{4}{3} = \frac{3 \times 4}{3} = \frac{12}{3}$.
• Step 4: Simplify the fraction: $\frac{12}{3} = 4$.

The solution to the division $3:\frac{3}{4}$ is $4$.

To solve the expression $2:\frac{2}{3}$, follow these steps:

• Step 1: Rewrite the expression as a division problem:
  This means $2 \div \frac{2}{3}$.
• Step 2: Convert the division to a multiplication by using the reciprocal:
  The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
• Step 3: Multiply by the reciprocal:
  $2 \times \frac{3}{2} = \frac{2 \cdot 3}{2 \cdot 1} = \frac{6}{2} = 3$.

Therefore, the solution to the problem is $3$.