Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
To solve the problem , we follow these steps:
First, we need to find a common denominator for the fractions and . The denominators are 3 and 5, and their least common multiple (LCM) is 15.
We will convert each fraction to an equivalent fraction with the denominator 15:
Now that both fractions have the same denominator, we can subtract the numerators:
Therefore, the solution to the problem is .
Solve the following exercise:
To solve this problem, we'll follow these steps:
Now, let's work through these steps:
Step 1: The denominators are and . The common denominator is the product .
Step 2: Convert each fraction:
Step 3: Subtract the fractions with a common denominator:
Finally, simplify . The greatest common divisor of 2 and 12 is 2, so:
Therefore, the solution to the problem is .
Solve the following exercise:
To solve the subtraction of fractions , we will follow these steps:
Now, let's work through each step in detail:
Step 1: The LCM of 5 and 2 is 10, since 10 is the smallest number that both 5 and 2 divide into evenly.
Step 2: Convert each fraction to have a denominator of 10.
For :
Multiply numerator and denominator by 2 to get .
For :
Multiply numerator and denominator by 5 to get .
Step 3: Subtract the fractions:
.
Step 4: There is no further simplification needed for as it is already in its simplest form.
Therefore, the solution to the problem is .
The correct answer, choice (4), is .
Solve the following exercise:
To solve the problem of subtracting from , we need a common denominator.
First, find the least common denominator (LCD) of 5 and 4, which is 20. This is done by multiplying the denominators: .
Next, convert each fraction to an equivalent fraction with the denominator of 20:
Now perform the subtraction with these equivalent fractions:
The resulting fraction, , is already in its simplest form.
Therefore, the solution to the subtraction is .
Checking against the multiple-choice answers, the correct choice is the first one: .
Solve the following exercise:
To solve the subtraction of fractions , follow these steps:
Thus, the solution to the problem is .
Solve the following exercise:
Solve the following exercise:
To solve , follow these steps:
Step 1: Find the least common multiple (LCM) of the denominators 2 and 9.
The multiples of 2 are
The multiples of 9 are
The smallest common multiple is 18. Thus, the LCM of 2 and 9 is 18.
Step 2: Convert each fraction to an equivalent fraction with the common denominator 18.
For , the equivalent fraction with 18 as the denominator is calculated by finding the factor needed:
.
For , the equivalent fraction with 18 as the denominator is:
.
Step 3: Perform the subtraction of these equivalent fractions.
.
Therefore, the solution to the problem is .
To solve the problem of adding and , we'll proceed step-by-step:
Now, let's perform these steps in detail:
Step 1: Determine the common denominator.
The denominators are 9 and 2. The least common denominator (LCD) can be found by multiplying these because they have no common factors other than 1:
.
Step 2: Convert each fraction to have the common denominator of 18.
Step 3: Add the numerators of the converted fractions:
Step 4: Simplification (if needed):
The fraction is already in its simplest form.
Therefore, the sum of and is .
To solve , follow these steps:
Therefore, the solution to the problem is .
To solve this problem, we'll begin by finding a common denominator for the fractions and .
Step 1: Identify the denominators, which are 3 and 4. Multiply these to get a common denominator: .
Step 2: Convert each fraction to an equivalent fraction with the common denominator of 12.
Step 3: Add the resulting fractions: .
Thus, the sum of and is .
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: The denominators are 7 and 8. Their product is . So, the common denominator is 56.
Step 2: Convert to have a denominator of 56 by multiplying numerator and denominator by 8: .
Convert to have a denominator of 56 by multiplying numerator and denominator by 7: .
Step 3: Add these equivalent fractions: .
Step 4: The fraction is already in its simplest form.
Therefore, the solution to the problem is .
To solve the problem of adding and , we need to find a common denominator. We do this by multiplying the denominators: . This is the smallest common multiple of the two denominators and ensures that each fraction can be represented with a common base, allowing addition.
Let's convert each fraction to an equivalent fraction with the common denominator of 30:
Convert : Multiply both the numerator and the denominator by 6 to get .
Convert : Multiply both the numerator and the denominator by 5 to get .
Now, we add these equivalent fractions:
.
The resulting fraction, , is already in its simplest form because 17 is a prime number and does not share any common factors with 30 other than 1.
Thus, the sum of and is .
Upon reviewing the given choices, the correct and matching choice is:
Choice 2:
To solve the problem of adding and , we perform the following steps:
Therefore, the sum of and is .
To solve this problem, we will add the fractions and by finding a common denominator.
After calculating, we find that the sum of the fractions is .
Therefore, the correct answer to the problem is .
To solve the problem of adding , we need to find a common denominator.
Thus, the sum of and is .
Therefore, the correct solution to the problem is .
To solve the problem, let's follow a structured approach:
The resulting fraction after adding and is .
Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
Solve the following exercise:
To solve this problem, let's follow these steps:
Step 1: Simplify . It simplifies to .
Step 2: The denominators are now 3 and 2. Find the least common multiple of 3 and 2, which is 6.
Step 3: Convert each fraction to have the common denominator of 6:
Step 4: Add the fractions:
Step 5: The fraction is already in its simplest form.
Therefore, the solution to the problem is .
Solve the following exercise:
To solve the problem of adding the fractions and , we follow these steps:
Therefore, when you add and , the solution is .
Solve the following exercise:
To solve the addition of fractions , follow these steps:
Thus, the sum of and is .
Solve the following exercise:
To solve this problem, we will add the fractions and by finding a common denominator.
Thus, the sum of the fractions and is .
Solve the following exercise:
To solve the problem of adding and , we need to first convert these fractions to have a common denominator.
Step 1: Find the least common denominator (LCD).
- The denominators of the fractions are and .
- The common denominator can be found by multiplying and , which gives us .
Step 2: Convert each fraction to an equivalent fraction with the common denominator of .
- For , multiply both the numerator and the denominator by :
.
- For , multiply both the numerator and the denominator by :
.
Step 3: Add the resulting fractions.
- .
Therefore, the solution to the problem is , which simplifies our answer.