Mixed Fractions - Examples, Exercises and Solutions

To solve the problem of multiplying $8$ by $\frac{5}{9}$, we can follow these steps:

• Step 1: Convert the whole number $8$ into a fraction by expressing it as $\frac{8}{1}$.
• Step 2: Multiply the numerators together: $8 \times 5 = 40$.
• Step 3: Multiply the denominators together: $1 \times 9 = 9$.
• Step 4: Write the product as a fraction: $\frac{40}{9}$.
• Step 5: Convert the improper fraction $\frac{40}{9}$ into a mixed number:
• Divide 40 by 9, which gives 4 (quotient) with a remainder of 4.
• Write the mixed number as $4\frac{4}{9}$.

Therefore, the solution to the multiplication problem $8 \times \frac{5}{9}$ is $4\frac{4}{9}$.

To solve this problem, we'll pursue a step-by-step method:

• Step 1: Simplify the fraction $\frac{8}{12}$. The greatest common divisor of 8 and 12 is 4, so dividing both the numerator and denominator by 4 gives $\frac{2}{3}$.
• Step 2: Multiply the integer 3 by the simplified fraction $\frac{2}{3}$.

Let's proceed with these steps:
Step 1: Simplify $\frac{8}{12}$:
$\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$.

Step 2: Multiply the integer by the fraction:
$3 \times \frac{2}{3} = \frac{3 \times 2}{3} = \frac{6}{3} = 2$.

Thus, the result of the multiplication is $\boxed{2}$.

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 multiplication of an integer with a fraction, we need to follow these steps:

• Step 1: Multiply the integer 7 by the numerator of the fraction, which is 6.
• Step 2: Keep 8 as the denominator.
• Step 3: Simplify the resulting fraction.
• Step 4: Convert to a mixed number if needed.

Now, let's work through each step:

Step 1: Multiply 7 by 6, which gives us $42$ as the numerator.

Step 2: The denominator remains 8, so we have the fraction $\frac{42}{8}$.

Step 3: Simplify $\frac{42}{8}$ by finding the greatest common divisor (GCD) of 42 and 8. The GCD is 2.

We divide the numerator and the denominator by 2: $\frac{42 \div 2}{8 \div 2} = \frac{21}{4}$.

Step 4: Convert $\frac{21}{4}$ into a mixed number:

Divide 21 by 4, which equals 5 with a remainder of 1. Thus, $\frac{21}{4}$ is equivalent to the mixed number $5\frac{1}{4}$.

Therefore, the solution to the problem is $5\frac{1}{4}$.

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 $2\frac{5}{8}$.