Multiplying and Dividing Mixed Numbers: By multiplication only

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 $3\frac{13}{24}$.

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 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 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 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 the problem of multiplying $3 \frac{2}{5}$ by $1 \frac{1}{6}$, follow these steps:

• Step 1: Convert Mixed Numbers to Improper Fractions.
  - For $3 \frac{2}{5}$, convert by multiplying 3 (the whole number) by 5 (the denominator) and adding 2 (the numerator):
  $(3 \times 5) + 2 = 15 + 2 = 17$. Thus, $3 \frac{2}{5} = \frac{17}{5}$.
  - For $1 \frac{1}{6}$, convert by multiplying 1 (the whole number) by 6 (the denominator) and adding 1 (the numerator):
  $(1 \times 6) + 1 = 6 + 1 = 7$. Thus, $1 \frac{1}{6} = \frac{7}{6}$.
• Step 2: Multiply the Improper Fractions.
  Multiply $\frac{17}{5}$ by $\frac{7}{6}$:
  $\frac{17}{5} \times \frac{7}{6} = \frac{17 \times 7}{5 \times 6} = \frac{119}{30}$.
• Step 3: Convert the Result to a Mixed Number.
  Divide 119 by 30. The quotient is 3 with a remainder of 29, so the mixed number is $3 \frac{29}{30}$.

Conclusion: $3 \frac{2}{5} \times 1 \frac{1}{6} = 3 \frac{29}{30}$.

The correct choice from the options provided is Choice 4: $3 \frac{29}{30}$.

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

• Step 1: Convert $4\frac{2}{3}$ and $1\frac{1}{5}$ to improper fractions.
• Step 2: Multiply these improper fractions.
• Step 3: Simplify the result, if necessary, and convert it back to a mixed number.

Now, let's work through each step:
Step 1: Convert mixed numbers to improper fractions:
For $4\frac{2}{3}$:
Multiply the whole number 4 by the denominator 3 and add the numerator 2:
$4 \times 3 + 2 = 12 + 2 = 14$.
Thus, $4\frac{2}{3} = \frac{14}{3}$.
For $1\frac{1}{5}$:
Multiply the whole number 1 by the denominator 5 and add the numerator 1:
$1 \times 5 + 1 = 5 + 1 = 6$.
Thus, $1\frac{1}{5} = \frac{6}{5}$.

Step 2: Multiply the improper fractions $\frac{14}{3}$ and $\frac{6}{5}$:
$\frac{14}{3} \times \frac{6}{5} = \frac{14 \times 6}{3 \times 5} = \frac{84}{15}$.

Step 3: Simplify the resulting fraction $\frac{84}{15}$ and convert it to a mixed number if necessary:
Find the greatest common divisor (GCD) of 84 and 15, which is 3.
Divide both numerator and denominator by their GCD:
$\frac{84 \div 3}{15 \div 3} = \frac{28}{5}$.

Convert the improper fraction $\frac{28}{5}$ to a mixed number:
Divide 28 by 5: Quotient is 5, remainder is 3.
Thus, $\frac{28}{5} = 5\frac{3}{5}$.

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

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

• Convert each mixed number to an improper fraction.
• Multiply the two improper fractions.
• Convert the result back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed numbers to improper fractions.
For $4\frac{4}{7}$:
Multiply the whole number by the denominator: $4 \times 7 = 28$.
Add the numerator to this product: $28 + 4 = 32$.
Thus, $4\frac{4}{7} = \frac{32}{7}$.

For $2\frac{1}{2}$:
Multiply the whole number by the denominator: $2 \times 2 = 4$.
Add the numerator: $4 + 1 = 5$.
Thus, $2\frac{1}{2} = \frac{5}{2}$.

Step 2: Multiply the two improper fractions:
$\frac{32}{7} \times \frac{5}{2} = \frac{32 \times 5}{7 \times 2} = \frac{160}{14}$.

Step 3: Simplify $\frac{160}{14}$ and convert to a mixed number:
First, simplify the fraction by finding the greatest common divisor of 160 and 14, which is 2.
$\frac{160}{14} = \frac{160 \div 2}{14 \div 2} = \frac{80}{7}$.

Convert $\frac{80}{7}$ to a mixed number:
Divide 80 by 7, which gives a quotient of 11 and a remainder of 3.
Thus, $\frac{80}{7} = 11\frac{3}{7}$.

Therefore, the solution to the problem is $11\frac{3}{7}$.

To solve the problem $5 \frac{1}{7} \times 1 \frac{3}{4}$, we will first convert both mixed numbers into improper fractions and then multiply them.

• Convert each mixed number to an improper fraction:
  For $5 \frac{1}{7}$: Multiply the whole number 5 by the denominator 7 and add the numerator 1: $5 \times 7 + 1 = 36$. Therefore, $5 \frac{1}{7}$ becomes $\frac{36}{7}$.
  For $1 \frac{3}{4}$: Multiply the whole number 1 by the denominator 4 and add the numerator 3: $1 \times 4 + 3 = 7$. Therefore, $1 \frac{3}{4}$ becomes $\frac{7}{4}$.
• Multiply the improper fractions:
  Multiply the numerators: $36 \times 7 = 252$.
  Multiply the denominators: $7 \times 4 = 28$.
  Thus, $\frac{36}{7} \times \frac{7}{4} = \frac{252}{28}$.
• Simplify the resulting fraction, $\frac{252}{28}$:
  Divide both the numerator and denominator by their greatest common divisor, which is 28:
  $252 \div 28 = 9$ and $28 \div 28 = 1$.
  So, $\frac{252}{28} = 9$.

Therefore, the solution to the problem is $9$.

To solve the problem, we'll use the following steps:

• Step 1: Convert both mixed numbers into improper fractions.

• Step 2: Multiply the improper fractions.

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

Now, let’s work through each step:

Step 1: Convert $3\frac{4}{5}$ and $2\frac{1}{2}$ into improper fractions.
For $3\frac{4}{5}$: Multiply the whole number 3 by the denominator 5, and add the numerator 4:
$3 \times 5 + 4 = 15 + 4 = 19$.
The improper fraction is $\frac{19}{5}$.
For $2\frac{1}{2}$: Multiply the whole number 2 by the denominator 2, and add the numerator 1:
$2 \times 2 + 1 = 4 + 1 = 5$.
The improper fraction is $\frac{5}{2}$.

Step 2: Multiply the improper fractions.
$\frac{19}{5} \times \frac{5}{2} = \frac{19 \times 5}{5 \times 2} = \frac{95}{10}$.

Step 3: Simplify $\frac{95}{10}$ and convert to a mixed number.
Divide 95 by 10. The quotient is 9 with a remainder of 5, so:
$\frac{95}{10} = 9\frac{5}{10}$.
Since $\frac{5}{10}$ simplifies to $\frac{1}{2}$, we get:
$9\frac{1}{2}$ as the final answer.

Therefore, the solution to the problem is $9\frac{1}{2}$.

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

• Convert each mixed number into an improper fraction.
• Multiply the two improper fractions.
• Simplify the resulting fraction if necessary.
• Convert the final product back to a mixed number if desired.

Now, let's work through each step:

Step 1: Convert the mixed numbers into improper fractions.
For $2\frac{2}{7}$: $2\frac{2}{7} = \frac{2 \times 7 + 2}{7} = \frac{14 + 2}{7} = \frac{16}{7}$ For $1\frac{3}{4}$: $1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}$

Step 2: Multiply the improper fractions.
$\frac{16}{7} \times \frac{7}{4} = \frac{16 \times 7}{7 \times 4} = \frac{112}{28}$

Step 3: Simplify the resulting fraction.
Since $112 \div 28 = 4$, $\frac{112}{28} = 4$

The final result is a whole number, so there is no need for conversion back to a mixed number.

Therefore, the solution to the problem is $4$.

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

• Step 1: Convert both mixed numbers to improper fractions.
• Step 2: Multiply the improper fractions.
• Step 3: Simplify the result and convert back to a mixed number.

Now let's go through each step in detail:

Step 1: Convert to Improper Fractions
For the number $1\frac{4}{5}$:
- Multiply the whole number by the denominator: $1 \times 5 = 5$.
- Add the numerator: $5 + 4 = 9$.
- The improper fraction is $\frac{9}{5}$.

For the number $1\frac{1}{2}$:
- Multiply the whole number by the denominator: $1 \times 2 = 2$.
- Add the numerator: $2 + 1 = 3$.
- The improper fraction is $\frac{3}{2}$.

Step 2: Multiply the Improper Fractions
Multiply $\frac{9}{5}$ by $\frac{3}{2}$:
$\frac{9}{5} \times \frac{3}{2} = \frac{9 \times 3}{5 \times 2} = \frac{27}{10}$.

Step 3: Simplify and Convert Back to Mixed Number
- The fraction $\frac{27}{10}$ is already in simplest form.
- Convert it to a mixed number: Divide 27 by 10, which is 2 with a remainder of 7.
- Therefore, $\frac{27}{10} = 2\frac{7}{10}$.

Thus, the product of $1\frac{4}{5}$ and $1\frac{1}{2}$ is $2\frac{7}{10}$.