Mixed Fractions - Examples, Exercises and Solutions

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

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 $3$.

To solve this problem, we will follow these steps:

• Step 1: Find the reciprocal of the fraction $\frac{2}{5}$.
• Step 2: Multiply the whole number 2 by this reciprocal.
• Step 3: Simplify the result, if necessary.

Now, let's work through each step:
Step 1: The reciprocal of the fraction $\frac{2}{5}$ is $\frac{5}{2}$.
Step 2: Multiply the whole number 2 by $\frac{5}{2}$:

$2 \times \frac{5}{2} = \frac{2 \times 5}{2} = \frac{10}{2}$

Step 3: Simplify $\frac{10}{2}$:
Divide 10 by 2, which gives us 5.

Therefore, the solution to the problem is $5$.

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 follow these steps:

• Step 1: Identify the reciprocal of the divisor.
• Step 2: Multiply the dividend by the reciprocal.

Now, let's work through each step:
Step 1: The divisor is $\frac{1}{2}$. The reciprocal of $\frac{1}{2}$ is 2.

Step 2: Multiply the dividend, which is 3, by the reciprocal of the divisor:
$3 \times 2 = 6$

Therefore, the solution to the problem is $6$.

We need to find the value of $3:\frac{2}{3}$, which means dividing 3 by $\frac{2}{3}$.

To solve this, follow these steps:

• Step 1: Find the reciprocal of $\frac{2}{3}$. The reciprocal is obtained by swapping the numerator and the denominator, thus the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
• Step 2: Multiply 3 by the reciprocal $\frac{3}{2}$.
• Step 3: Perform the multiplication: $3 \times \frac{3}{2}$.

Let's execute these steps:

Step 2: Since multiplying a whole number by a fraction gives:

$3 \times \frac{3}{2} = \frac{3 \times 3}{2} = \frac{9}{2}$

Step 3: Convert the improper fraction $\frac{9}{2}$ to a mixed number:

Divide 9 by 2 which gives 4 as the quotient and 1 as the remainder. Thus, the mixed number is $4\frac{1}{2}$.

Therefore, the solution to the ratio $3:\frac{2}{3}$ is $\mathbf{4\frac{1}{2}}$.

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 this problem, let's carry out the following steps:

• Step 1: Recognize that the expression $3 : \frac{5}{6}$ represents division, so it becomes $3 \div \frac{5}{6}$.
• Step 2: Use the rule that dividing by a fraction is the same as multiplying by its reciprocal. Thus, convert this to $3 \times \frac{6}{5}$.
• Step 3: Multiply 3 (which can be written as $\frac{3}{1}$) by $\frac{6}{5}$:
  $\frac{3}{1} \times \frac{6}{5} = \frac{3 \times 6}{1 \times 5} = \frac{18}{5}$.
• Step 4: Convert $\frac{18}{5}$ to a mixed number. Divide 18 by 5:
  - 5 goes into 18 three times with a remainder of 3.
  - Therefore, $\frac{18}{5} = 3\frac{3}{5}$.

Thus, the solution to the problem is $3\frac{3}{5}$.

To divide the whole number 3 by the fraction $\frac{5}{7}$, we follow these steps:

• Step 1: Identify the reciprocal of the fraction. The reciprocal of $\frac{5}{7}$ is $\frac{7}{5}$.
• Step 2: Multiply the whole number 3 by this reciprocal.
• Step 3: Perform the multiplication to find the result.

Let's calculate this:
Step 1: The reciprocal of $\frac{5}{7}$ is $\frac{7}{5}$.
Step 2: Multiply: $3 \times \frac{7}{5} = \frac{3 \times 7}{5} = \frac{21}{5}$.
Step 3: Convert the improper fraction $\frac{21}{5}$ to a mixed number:

• Divide 21 by 5. It goes 4 times with a remainder of 1.
• The quotient is 4, and the remainder is 1. Therefore, $\frac{21}{5} = 4\frac{1}{5}$.

Thus, the solution to $3 : \frac{5}{7}$ is $4\frac{1}{5}$.

The correct choice among the given answers is: $4\frac{1}{5}$.

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 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 $2\frac{4}{7}$.