Multiplying and Dividing Mixed Numbers: Simplifiying fractions before multiplying

To solve the problem $1\frac{3}{9} \times 2\frac{2}{4}$, we will follow these steps:

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

Let’s begin with each step in detail:

Step 1: Convert $1\frac{3}{9}$ and $2\frac{2}{4}$ to improper fractions.
- For $1\frac{3}{9}$: Convert the fraction $\frac{3}{9}$ to its simplest form, which is $\frac{1}{3}$. Then, the mixed number $1\frac{1}{3}$ becomes $1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}$.
- For $2\frac{2}{4}$: The fraction $\frac{2}{4}$ simplifies to $\frac{1}{2}$. Then, the mixed number $2\frac{1}{2}$ becomes $2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$.

Step 2: Multiply the improper fractions:
$\frac{4}{3} \times \frac{5}{2} = \frac{4 \times 5}{3 \times 2} = \frac{20}{6}$.

Simplify $\frac{20}{6}$:
Find the greatest common divisor (GCD) of 20 and 6, which is 2. Then $\frac{20}{6} = \frac{20 \div 2}{6 \div 2} = \frac{10}{3}$.

Step 3: Convert the improper fraction $\frac{10}{3}$ back to a mixed number:
Divide 10 by 3 to get 3 with a remainder of 1, thus $\frac{10}{3} = 3\frac{1}{3}$.

Therefore, the product is $3\frac{1}{3}$.

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 necessary.
• Step 4: 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 $2\frac{2}{6}$:

$2\frac{2}{6} = \frac{2 \times 6 + 2}{6} = \frac{12 + 2}{6} = \frac{14}{6}$

Simplifying $\frac{14}{6}$ by dividing the numerator and the denominator by 2, we get $\frac{14}{6} = \frac{7}{3}$.

For $1\frac{4}{10}$:

$1\frac{4}{10} = \frac{1 \times 10 + 4}{10} = \frac{10 + 4}{10} = \frac{14}{10}$

Simplifying $\frac{14}{10}$ by dividing the numerator and the denominator by 2, we get $\frac{14}{10} = \frac{7}{5}$.

Step 2: Multiply the improper fractions:

$\frac{7}{3} \times \frac{7}{5} = \frac{7 \times 7}{3 \times 5} = \frac{49}{15}$

Step 3: Simplify the resulting fraction, if necessary. In this case, $\frac{49}{15}$ is already in its simplest form.

Step 4: Convert the result back to a mixed number:

$\frac{49}{15}$ can be rewritten as $3\frac{4}{15}$, since 49 divided by 15 is 3 with a remainder of 4.

Therefore, the solution to the problem is $3\frac{4}{15}$.

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.
• Step 4: Convert the improper fraction back to a mixed number if necessary.

Let's begin:

Step 1: Convert to improper fractions
Convert $1\frac{6}{8}$ to an improper fraction:
$\frac{8 \times 1 + 6}{8} = \frac{14}{8}$.

Convert $2\frac{2}{6}$ to an improper fraction:
$\frac{6 \times 2 + 2}{6} = \frac{14}{6}$.

Step 2: Multiply the fractions
Multiply $\frac{14}{8}$ and $\frac{14}{6}$:
$\frac{14}{8} \times \frac{14}{6} = \frac{196}{48}$.

Step 3: Simplify the fraction
Find the greatest common divisor (GCD) of 196 and 48, which is 4. Simplify $\frac{196}{48}$:
$\frac{196 \div 4}{48 \div 4} = \frac{49}{12}$.

Step 4: Convert to a mixed number
$\frac{49}{12}$ as a mixed number is $4\frac{1}{12}$ since 49 divided by 12 is 4 with a remainder of 1.

Therefore, the solution to the problem is $4\frac{1}{12}$.

To solve this problem, we will convert the mixed numbers to improper fractions and multiply them.

• Step 1: Convert Mixed Numbers to Improper Fractions

For the first mixed number $2\frac{10}{20}$:
- Convert $2\frac{10}{20}$ to an improper fraction:
Initially, $10/20$ can be simplified to $1/2$ (since $\gcd(10, 20) = 10$). Therefore, the mixed number $2\frac{1}{2}$ is equal to:
$2 \times 2 + 1 = 4 + 1 = 5$
Thus, $2\frac{1}{2}$ becomes $\frac{5}{2}$.

For the second mixed number $1\frac{4}{16}$:
- Simplify $4/16$ to $1/4$ (since $\gcd(4, 16) = 4$). Hence, $1\frac{4}{16}$ simplifies to $1\frac{1}{4}$:
$1 \times 4 + 1 = 4 + 1 = 5$
Thus, $1\frac{1}{4}$ becomes $\frac{5}{4}$.

• Step 2: Multiply the Improper Fractions

Multiply the fractions $\frac{5}{2} \times \frac{5}{4}$:
$\frac{5 \times 5}{2 \times 4} = \frac{25}{8}$

• Step 3: Simplify and Convert to Mixed Number

Convert $\frac{25}{8}$ back to a mixed number by dividing:
- Divide 25 by 8, which goes 3 times (remainder 1).
Thus, $\frac{25}{8} = 3\frac{1}{8}$.

Therefore, the solution to the problem is $3\frac{1}{8}$.

To solve this problem, we'll convert the given mixed numbers to improper fractions, multiply them, and simplify the result. Let's proceed step by step:

• Step 1: Convert the mixed numbers to improper fractions.
  For $1\frac{4}{6}$: Multiply the whole number by the denominator and add the numerator: $1\frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{10}{6}$.
  For $1\frac{2}{8}$: Similarly, multiply the whole number by the denominator and add the numerator: $1\frac{2}{8} = \frac{1 \times 8 + 2}{8} = \frac{10}{8}$.
• Step 2: Multiply the improper fractions.
  $\frac{10}{6} \times \frac{10}{8} = \frac{10 \times 10}{6 \times 8} = \frac{100}{48}$.
• Step 3: Simplify the resulting fraction.
  Find the GCD of 100 and 48, which is 4. Divide both the numerator and the denominator by 4:
  $\frac{100}{48} = \frac{100 \div 4}{48 \div 4} = \frac{25}{12}$.
• Step 4: Convert the simplified improper fraction back to a mixed number.
  Divide 25 by 12: 25 divided by 12 is 2 with a remainder of 1. So, $\frac{25}{12} = 2\frac{1}{12}$.

Therefore, the solution to the problem is $2\frac{1}{12}$. This matches the correct answer choice 2.

To solve the given problem, we'll follow these steps:

• Convert the mixed numbers to improper fractions.
• Multiply the improper fractions.
• Simplify the result and convert back to a mixed number if necessary.

Let's work through these steps:

1. Convert each mixed number to an improper fraction:

• For $2\frac{4}{12}$, first simplify the fraction $\frac{4}{12}$ to $\frac{1}{3}$. So, $2\frac{1}{3}$ becomes:

$\frac{2 \times 3 + 1}{3} = \frac{7}{3}$.

• For $1\frac{2}{4}$, first simplify the fraction $\frac{2}{4}$ to $\frac{1}{2}$. So, $1\frac{1}{2}$ becomes:

$\frac{1 \times 2 + 1}{2} = \frac{3}{2}$.

2. Multiply the improper fractions:

The multiplication of $\frac{7}{3}$ and $\frac{3}{2}$ is:

$\frac{7}{3} \times \frac{3}{2} = \frac{21}{6}$.

3. Simplify the resulting fraction $\frac{21}{6}$:

$\frac{21}{6} = \frac{7}{2}$ after dividing the numerator and denominator by 3.

4. Convert the improper fraction back to a mixed number:

$\frac{7}{2} = 3\frac{1}{2}$.

Thus, the solution to the problem is $\boxed{3\frac{1}{2}}$.

Let's solve the problem by following these steps:

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

Step 1:
Convert $1\frac{4}{12}$ to an improper fraction.

Calculate the improper fraction: $1\frac{4}{12} = \frac{1 \times 12 + 4}{12} = \frac{16}{12}$

Convert $1\frac{4}{14}$ to an improper fraction.

Calculate the improper fraction: $1\frac{4}{14} = \frac{1 \times 14 + 4}{14} = \frac{18}{14}$

Step 2:
Multiply the two improper fractions:

$\frac{16}{12} \times \frac{18}{14} = \frac{16 \times 18}{12 \times 14}$

Simplify the multiplication:

• Numerator: $16 \times 18 = 288$
• Denominator: $12 \times 14 = 168$

The resulting fraction is $\frac{288}{168}$.

Step 3:
Simplify $\frac{288}{168}$.

Find the greatest common divisor (GCD) of 288 and 168, which is 24.

• Divide numerator by GCD: $288 \div 24 = 12$
• Divide denominator by GCD: $168 \div 24 = 7$

The simplified fraction is $\frac{12}{7}$.

Convert $\frac{12}{7}$ back to a mixed number:

12 divided by 7 is 1 with a remainder of 5, so the mixed number is $1\frac{5}{7}$.

Thus, the solution to the problem is $\boxed{1\frac{5}{7}}$.

To solve this problem, we will follow these steps:

• Convert the mixed numbers to improper fractions.
• Simplify the fractions when possible.
• Multiply the improper fractions.
• Convert the resulting improper fraction back to a mixed number and simplify.

Here's the step-by-step solution:

Step 1: Convert $3 \frac{6}{9}$ and $3 \frac{4}{20}$ to improper fractions.

For $3 \frac{6}{9}$, which can be simplified to $3 \frac{2}{3}$: $3 + \frac{6}{9} = 3 + \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}$.

For $3 \frac{4}{20}$, which can be simplified to $3 \frac{1}{5}$: $3 + \frac{4}{20} = 3 + \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5}$.

Step 2: Simplify fractions if possible. The fractions $\frac{11}{3}$ and $\frac{16}{5}$ are already in simplest form.

Step 3: Multiply the fractions:

$\frac{11}{3} \times \frac{16}{5} = \frac{11 \times 16}{3 \times 5} = \frac{176}{15}$.

Step 4: Convert the resulting improper fraction to a mixed number.

Divide 176 by 15: $176 \div 15 = 11$ remainder $11$. Thus, $\frac{176}{15} = 11 \frac{11}{15}$.

Therefore, the solution to the problem is $11 \frac{11}{15}$, which matches choice 3.

Therefore, the final answer is $11 \frac{11}{15}$.

To solve the problem $1\frac{2}{8} \times 1\frac{7}{14}$, follow these steps:

• Step 1: Convert the Mixed Numbers to Improper Fractions
  For $1\frac{2}{8}$, the improper fraction is calculated as:
  $1\frac{2}{8} = 1 + \frac{2}{8} = \frac{8}{8} + \frac{2}{8} = \frac{10}{8}$
• For $1\frac{7}{14}$, simplify $\frac{7}{14} = \frac{1}{2}$, hence: $1\frac{7}{14} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}$
• Step 2: Multiply the Improper Fractions
  Multiply the fractions $\frac{10}{8}$ and $\frac{3}{2}$:
  $\frac{10}{8} \times \frac{3}{2} = \frac{10 \times 3}{8 \times 2} = \frac{30}{16}$
• Step 3: Simplify the Resulting Fraction
  Simplify $\frac{30}{16}$ by finding the greatest common divisor (GCD) of 30 and 16, which is 2:
  $\frac{30}{16} = \frac{30 \div 2}{16 \div 2} = \frac{15}{8}$
• Step 4: Convert Back to a Mixed Number
  Convert $\frac{15}{8}$ to a mixed number:
  $\frac{15}{8} = 1\frac{7}{8}$

Therefore, the solution to the problem is $1\frac{7}{8}$.

To solve the problem of multiplying these mixed fractions, we will proceed through the following steps:

• Step 1: Convert each mixed number into an improper fraction.
  $3\frac{4}{6}$ must first be simplified to $3\frac{2}{3}$.
  To convert $3\frac{2}{3}$ to an improper fraction: $3 \times 3 + 2 = 11$, so we have $\frac{11}{3}$.
  For $2\frac{2}{4}$, simplify $\frac{2}{4}$ to $\frac{1}{2}$ making the fraction $2\frac{1}{2}$.
  Convert $2\frac{1}{2}$ to an improper fraction: $2 \times 2 + 1 = 5$, so we have $\frac{5}{2}$.
• Step 2: Multiply the two improper fractions:
  The calculation is $\frac{11}{3} \times \frac{5}{2} = \frac{11 \times 5}{3 \times 2} = \frac{55}{6}$.
• Step 3: Simplify $\frac{55}{6}$ by converting it back to a mixed number.
  Divide 55 by 6 which gives 9 as the quotient and 1 as the remainder. Therefore, $\frac{55}{6} = 9\frac{1}{6}$.

Therefore, the result of the multiplication is $9\frac{1}{6}$.

To solve this problem, follow these steps:

• Step 1: Convert mixed numbers to improper fractions.
• Step 2: Simplify the fractions if feasible.
• Step 3: Multiply the improper fractions.
• Step 4: Convert the result back to a mixed number.

Let's work through the steps:

Step 1: Convert the mixed numbers to improper fractions.

$3\frac{5}{15} = 3 + \frac{5}{15} = \frac{45}{15} + \frac{5}{15} = \frac{50}{15}$, simplifying yields $\frac{10}{3}$.

$2\frac{2}{10} = 2 + \frac{2}{10} = \frac{20}{10} + \frac{2}{10} = \frac{22}{10}$, simplifying yields $\frac{11}{5}$.

Step 2: Multiply the fractions.

$\frac{10}{3} \times \frac{11}{5} = \frac{110}{15}$.

Step 3: Simplify the result of the multiplication.

$\frac{110}{15}$ can be simplified by dividing the numerator and the denominator by 5, yielding $\frac{22}{3}$.

Step 4: Convert the resulting improper fraction back to a mixed number.

Dividing, $22 \div 3 = 7$ with a remainder of 1, so $\frac{22}{3} = 7\frac{1}{3}$.

Therefore, the solution to the problem is $7\frac{1}{3}$.

To solve this problem, we'll convert the mixed numbers into improper fractions and perform the multiplication.

• Convert $4\frac{10}{12}$ into an improper fraction:
  Multiply the whole number 4 by the denominator 12, then add the numerator 10: $4 \times 12 + 10 = 58$.
  The improper fraction is $\frac{58}{12}$.
• Convert $2\frac{2}{10}$ into an improper fraction:
  Multiply the whole number 2 by the denominator 10, then add the numerator 2: $2 \times 10 + 2 = 22$.
  The improper fraction is $\frac{22}{10}$.
• Multiply the two improper fractions:
  $\frac{58}{12} \times \frac{22}{10} = \frac{58 \times 22}{12 \times 10} = \frac{1276}{120}$.
• Simplify the result:
  First, find the greatest common divisor (GCD) of 1276 and 120, which is 4.
  Divide both numerator and denominator by 4 to simplify:
  $\frac{1276 \div 4}{120 \div 4} = \frac{319}{30}$.
• Convert $\frac{319}{30}$ into a mixed number:
  Divide 319 by 30: the quotient is 10 and the remainder is 19.
  Thus, $\frac{319}{30} = 10\frac{19}{30}$.

Therefore, the solution to the problem is $10\frac{19}{30}$, which corresponds to choice 3.