Mixed Numbers

To solve this problem, we will start by multiplying the whole number 7 by the fraction $\frac{3}{8}$ using the rule for multiplying a whole number by a fraction.

Calculate the product:

• $7 \times \frac{3}{8} = \frac{7 \times 3}{8}$
• $= \frac{21}{8}$

The fraction $\frac{21}{8}$ is an improper fraction, meaning the numerator is greater than the denominator. To convert it to a mixed number, we divide 21 by 8:

• 21 divided by 8 equals 2 with a remainder of 5.
• This gives us the mixed number: $2\frac{5}{8}$

The remainder becomes the numerator of the fraction part, and the denominator remains the same as in the original fraction.

Therefore, the solution to the problem is $2\frac{5}{8}$.

To solve the problem $10 \times \frac{7}{9}$, we follow these steps:

• Step 1: Multiply the whole number by the numerator. Calculate $10 \times 7 = 70$.
• Step 2: Divide this product by the denominator. Calculate $\frac{70}{9}$.
• Step 3: If the result is an improper fraction, convert it to a mixed number. Divide 70 by 9, which goes 7 times with a remainder of 7. This can be expressed as the mixed number $7\frac{7}{9}$.

Let's work through each step:
Step 1: Multiply 10 by 7 to get 70.
Step 2: Divide 70 by 9 to get 7 remainder 7.
Step 3: The proper whole number from the division is 7, with the remainder over the original fraction denominator giving us the final fraction $\frac{7}{9}$.

Thus, the product $10 \times \frac{7}{9}$ is $7\frac{7}{9}$.

To solve the division problem $1 : \frac{1}{4}$, we will follow these steps:

• Step 1: Express the division as a fraction operation: $1 \div \frac{1}{4}$.
• Step 2: Use the invert-and-multiply rule. Find the reciprocal of $\frac{1}{4}$, which is $4$.
• Step 3: Multiply the whole number by the reciprocal: $1 \times 4 = 4$.

Thus, after performing these operations, we find that the result of the division $1 : \frac{1}{4}$ is $4$.

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 $(1 \frac{1}{3})$.