Multiplication and Division of Mixed Numbers

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

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Multiply the improper fractions.
• Step 3: Convert the result back to a mixed number.

Now, let's work through each step:

Step 1: Convert each mixed number to an improper fraction.
For $1\frac{1}{4}$:
- Whole number is 1, denominator is 4, and numerator is 1.
- Convert to improper fraction: $1\frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4}$.

For $1\frac{6}{8}$:
- Whole number is 1, denominator is 8, and numerator is 6.
- Convert to improper fraction: $1\frac{6}{8} = \frac{8 \times 1 + 6}{8} = \frac{14}{8}$.
- Simplify $\frac{14}{8}$ to $\frac{7}{4}$ by dividing both the numerator and the denominator by 2.

Step 2: Multiply the improper fractions:
$\frac{5}{4} \times \frac{7}{4} = \frac{5 \times 7}{4 \times 4} = \frac{35}{16}$.

Step 3: Convert the improper fraction back to a mixed number:
Divide 35 by 16. This gives 2 as the quotient with a remainder of 3.
Thus, $\frac{35}{16} = 2\frac{3}{16}$.

Therefore, the product of $1\frac{1}{4} \times 1\frac{6}{8}$ is $2\frac{3}{16}$.

To solve this problem, we'll convert the mixed numbers into improper fractions, multiply them, and simplify the result:

• Step 1: Convert mixed numbers to improper fractions.
  • $1\frac{4}{5}$ becomes $\frac{1 \times 5 + 4}{5} = \frac{9}{5}$.
  • $1\frac{1}{3}$ becomes $\frac{1 \times 3 + 1}{3} = \frac{4}{3}$.
• Step 2: Multiply the improper fractions.
  • $\frac{9}{5} \times \frac{4}{3} = \frac{9 \times 4}{5 \times 3} = \frac{36}{15}$.
• Step 3: Simplify the fraction $\frac{36}{15}$.
  • The greatest common divisor of 36 and 15 is 3.
  • $\frac{36 \div 3}{15 \div 3} = \frac{12}{5}$.
• Step 4: Convert the improper fraction $\frac{12}{5}$ back to a mixed number.
  • $12 \div 5$ is 2 with a remainder of 2.
  • The mixed number is $2\frac{2}{5}$.

Therefore, the product of $1\frac{4}{5} \times 1\frac{1}{3}$ is $2\frac{2}{5}$.

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

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Multiply the improper fractions.
• Step 3: Simplify the resulting fraction, if needed, and convert it back to a mixed number.

Now, let's work through each step:
Step 1: Convert the mixed numbers to improper fractions.
For $1\frac{4}{5}$:
$1\frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}$.
For $2\frac{1}{2}$:
$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$.

Step 2: Multiply the improper fractions:
$\frac{9}{5} \times \frac{5}{2} = \frac{9 \times 5}{5 \times 2} = \frac{45}{10}$.

Step 3: Simplify the fraction and convert it back to a mixed number:
$\frac{45}{10} = \frac{9}{2} = 4\frac{1}{2}$.

Therefore, the product of $1\frac{4}{5} \times 2\frac{1}{2}$ is $4\frac{1}{2}$, which corresponds to choice 2.

To solve the problem of multiplying the mixed numbers $2\frac{1}{4}$ and $1\frac{2}{3}$, we proceed as follows:

• Step 1: Convert Mixed Numbers to Improper Fractions

  • Convert $2\frac{1}{4}$ to an improper fraction: $2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$

  • Convert $1\frac{2}{3}$ to an improper fraction: $1\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}$

• Step 2: Multiply the Improper Fractions

• Now, multiply $\frac{9}{4}$ by $\frac{5}{3}$: $\frac{9}{4} \times \frac{5}{3} = \frac{9 \times 5}{4 \times 3} = \frac{45}{12}$

• Step 3: Simplify the Fraction

• Simplify $\frac{45}{12}$ by finding the greatest common divisor of 45 and 12, which is 3: $\frac{45 \div 3}{12 \div 3} = \frac{15}{4}$

• Step 4: Convert Back to a Mixed Number

• Convert $\frac{15}{4}$ into a mixed number: $15 \div 4 = 3 \quad \text{remainder} \quad 3$ So, $\frac{15}{4} = 3\frac{3}{4}$.

Based on the calculations, the product of $2\frac{1}{4}$ and $1\frac{2}{3}$ is $3\frac{3}{4}$.

Therefore, the solution to the problem is $3\frac{3}{4}$.

To solve the problem of multiplying the mixed numbers $2\frac{5}{6}$ and $1\frac{1}{4}$, we will follow these steps:

• Step 1: Convert mixed numbers to improper fractions.

For $2\frac{5}{6}$:
Multiply the whole number 2 by the denominator 6, resulting in 12. Add the numerator 5 to get 17.
Thus, $2\frac{5}{6} = \frac{17}{6}$.

For $1\frac{1}{4}$:
Multiply the whole number 1 by the denominator 4, resulting in 4. Add the numerator 1 to get 5.
Thus, $1\frac{1}{4} = \frac{5}{4}$.

• Step 2: Multiply the improper fractions.

Multiply $\frac{17}{6}$ by $\frac{5}{4}$:
The result is $\frac{17 \times 5}{6 \times 4} = \frac{85}{24}$.

• Step 3: Convert the result back to a mixed number.

To convert $\frac{85}{24}$ to a mixed number, divide 85 by 24:
85 divided by 24 is 3, with a remainder of 13.
Hence, $\frac{85}{24} = 3\frac{13}{24}$.

Therefore, the product of the mixed numbers $2\frac{5}{6}$ and $1\frac{1}{4}$ is $3\frac{13}{24}$.