First step:
Let's reduce the fractions if possible.
Second step:
Let's convert the mixed numbers into fractions.
First step:
Let's reduce the fractions if possible.
Second step:
Let's convert the mixed numbers into fractions.
We will operate according to the method of numerator by numerator and denominator by denominator.
We will change the operation from division to multiplication and swap the locations between the numerator and the denominator in the second fraction -that is, the fraction that is after the sign.
Then we will solve by multiplying numerator by numerator and denominator by denominator.
\( 1\frac{1}{4}\times1\frac{6}{8}= \)
\( 2\frac{5}{6}\times1\frac{1}{4}= \)
\( 1\frac{4}{5}\times2\frac{1}{2}= \)
\( 2\frac{1}{4}\times1\frac{2}{3}= \)
\( 1\frac{4}{5}\times1\frac{1}{3}= \)
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Convert each mixed number to an improper fraction.
For :
- Whole number is 1, denominator is 4, and numerator is 1.
- Convert to improper fraction: .
For :
- Whole number is 1, denominator is 8, and numerator is 6.
- Convert to improper fraction: .
- Simplify to by dividing both the numerator and the denominator by 2.
Step 2: Multiply the improper fractions:
.
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, .
Therefore, the product of is .
To solve the problem of multiplying the mixed numbers and , we will follow these steps:
For :
Multiply the whole number 2 by the denominator 6, resulting in 12. Add the numerator 5 to get 17.
Thus, .
For :
Multiply the whole number 1 by the denominator 4, resulting in 4. Add the numerator 1 to get 5.
Thus, .
Multiply by :
The result is .
To convert to a mixed number, divide 85 by 24:
85 divided by 24 is 3, with a remainder of 13.
Hence, .
Therefore, the product of the mixed numbers and is .
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Convert the mixed numbers to improper fractions.
For :
.
For :
.
Step 2: Multiply the improper fractions:
.
Step 3: Simplify the fraction and convert it back to a mixed number:
.
Therefore, the product of is , which corresponds to choice 2.
To solve the problem of multiplying the mixed numbers and , we proceed as follows:
Step 1: Convert Mixed Numbers to Improper Fractions
Convert to an improper fraction:
Convert to an improper fraction:
Step 2: Multiply the Improper Fractions
Now, multiply by :
Step 3: Simplify the Fraction
Simplify by finding the greatest common divisor of 45 and 12, which is 3:
Step 4: Convert Back to a Mixed Number
Convert into a mixed number: So, .
Based on the calculations, the product of and is .
Therefore, the solution to the problem is .
To solve this problem, we'll convert the mixed numbers into improper fractions, multiply them, and simplify the result:
Therefore, the product of is .
\( 4\frac{2}{3}\times1\frac{1}{5} \)
\( 3\frac{2}{5}\times1\frac{1}{6}= \)
\( 1\frac{3}{9}\times2\frac{2}{4}= \)
\( 1\frac{4}{6}\times1\frac{2}{8}= \)
\( 2\frac{4}{12}\times1\frac{2}{4}= \)
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Convert mixed numbers to improper fractions:
For :
Multiply the whole number 4 by the denominator 3 and add the numerator 2:
.
Thus, .
For :
Multiply the whole number 1 by the denominator 5 and add the numerator 1:
.
Thus, .
Step 2: Multiply the improper fractions and :
.
Step 3: Simplify the resulting fraction 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:
.
Convert the improper fraction to a mixed number:
Divide 28 by 5: Quotient is 5, remainder is 3.
Thus, .
Therefore, the solution to the problem is .
To solve the problem of multiplying by , follow these steps:
Conclusion: .
The correct choice from the options provided is Choice 4: .
To solve the problem , we will follow these steps:
Let’s begin with each step in detail:
Step 1: Convert and to improper fractions.
- For : Convert the fraction to its simplest form, which is . Then, the mixed number becomes
.
- For : The fraction simplifies to . Then, the mixed number becomes
.
Step 2: Multiply the improper fractions:
.
Simplify :
Find the greatest common divisor (GCD) of 20 and 6, which is 2. Then .
Step 3: Convert the improper fraction back to a mixed number:
Divide 10 by 3 to get 3 with a remainder of 1, thus .
Therefore, the product is .
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:
Therefore, the solution to the problem is . This matches the correct answer choice 2.
To solve the given problem, we'll follow these steps:
Let's work through these steps:
1. Convert each mixed number to an improper fraction:
.
.
2. Multiply the improper fractions:
The multiplication of and is:
.
3. Simplify the resulting fraction :
after dividing the numerator and denominator by 3.
4. Convert the improper fraction back to a mixed number:
.
Thus, the solution to the problem is .
\( 2\frac{2}{6}\times1\frac{4}{10}= \)
\( 1\frac{6}{8}\times2\frac{2}{6}= \)
\( 1\frac{4}{12}\times1\frac{4}{14}= \)
\( 2\frac{10}{20}\times1\frac{4}{16}= \)\( \)
\( 3\frac{4}{5}\times2\frac{1}{2}= \)
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Convert each mixed number to an improper fraction.
For :
Simplifying by dividing the numerator and the denominator by 2, we get .
For :
Simplifying by dividing the numerator and the denominator by 2, we get .
Step 2: Multiply the improper fractions:
Step 3: Simplify the resulting fraction, if necessary. In this case, is already in its simplest form.
Step 4: Convert the result back to a mixed number:
can be rewritten as , since 49 divided by 15 is 3 with a remainder of 4.
Therefore, the solution to the problem is .
To solve this problem, we'll follow these steps:
Let's begin:
Step 1: Convert to improper fractions
Convert to an improper fraction:
.
Convert to an improper fraction:
.
Step 2: Multiply the fractions
Multiply and :
.
Step 3: Simplify the fraction
Find the greatest common divisor (GCD) of 196 and 48, which is 4. Simplify :
.
Step 4: Convert to a mixed number
as a mixed number is since 49 divided by 12 is 4 with a remainder of 1.
Therefore, the solution to the problem is .
Let's solve the problem by following these steps:
Step 1:
Convert to an improper fraction.
Calculate the improper fraction:
Convert to an improper fraction.
Calculate the improper fraction:
Step 2:
Multiply the two improper fractions:
Simplify the multiplication:
The resulting fraction is .
Step 3:
Simplify .
Find the greatest common divisor (GCD) of 288 and 168, which is 24.
The simplified fraction is .
Convert back to a mixed number:
12 divided by 7 is 1 with a remainder of 5, so the mixed number is .
Thus, the solution to the problem is .
To solve this problem, we will convert the mixed numbers to improper fractions and multiply them.
For the first mixed number :
- Convert to an improper fraction:
Initially, can be simplified to (since ). Therefore, the mixed number is equal to:
Thus, becomes .
For the second mixed number :
- Simplify to (since ). Hence, simplifies to :
Thus, becomes .
Multiply the fractions :
Convert back to a mixed number by dividing:
- Divide 25 by 8, which goes 3 times (remainder 1).
Thus, .
Therefore, the solution to the problem is .
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 and into improper fractions.
For : Multiply the whole number 3 by the denominator 5, and add the numerator 4:
.
The improper fraction is .
For : Multiply the whole number 2 by the denominator 2, and add the numerator 1:
.
The improper fraction is .
Step 2: Multiply the improper fractions.
.
Step 3: Simplify and convert to a mixed number.
Divide 95 by 10. The quotient is 9 with a remainder of 5, so:
.
Since simplifies to , we get:
as the final answer.
Therefore, the solution to the problem is .