Solve the following exercise:
Solve the following exercise:
\( \frac{6}{7}-\frac{1}{2}+\frac{3}{14}=\text{?} \)
Solve the following exercise:
\( \frac{2}{7}+\frac{1}{2}-\frac{7}{14}=\text{?} \)
Solve the following exercise:
\( \frac{2}{5}+\frac{1}{2}-\frac{1}{3}=\text{?} \)
Solve the following exercise:
\( \frac{9}{10}-\frac{4}{5}+\frac{1}{2}=\text{?} \)
Solve the following exercise:
\( \frac{4}{10}+\frac{1}{5}-\frac{1}{2}=\text{?} \)
Solve the following exercise:
To solve the expression , we will follow these steps:
Let's work through the steps:
Step 1: The denominators are 7, 2, and 14. The least common multiple (LCM) of these numbers is 14.
Step 2: Convert each fraction:
Step 3: Perform the operations:
Step 4: Simplify the fraction if possible. Here, simplifies to ; however, since the given choices list and it matches, there is no need for further simplification within the context of this question.
Therefore, the solution to the problem is .
Solve the following exercise:
To solve the expression , follow these steps:
Therefore, the solution to the problem is , which corresponds to choice .
Solve the following exercise:
To solve the problem , we will follow these steps:
Now, let's proceed with the solution:
Step 1: The denominators are 5, 2, and 3. The least common multiple of these numbers is 30. Thus, the LCD is 30.
Step 2: Convert each fraction to have the common denominator of 30:
- Convert to a fraction with denominator 30: .
- Convert to a fraction with denominator 30: .
- Convert to a fraction with denominator 30: .
Step 3: With all fractions having the same denominator, perform the operations:
.
Step 4: Since is in its simplest form, no further simplification is needed.
Therefore, the correct answer is .
Solve the following exercise:
To solve the expression , we first seek a common denominator for the fractions. The denominators are 10, 5, and 2.
The least common multiple of these numbers is 10, as it is the smallest number that all denominators divide perfectly.
Now, the expression becomes .
Perform the operations:
Thus, the value of the expression is .
The correct answer is .
Solve the following exercise:
To solve the expression , we will follow these steps:
Step 1: Find a Common Denominator
The denominators we have are 10, 5, and 2. The least common denominator (LCD) among these numbers is 10.
Step 2: Convert Fractions to Equivalent Fractions with the LCD
- is already using 10 as the denominator.
- .
- .
Step 3: Perform the Arithmetic Operations
Substitute the converted fractions into the original expression:
Combine the numerators over the common denominator:
Step 4: Simplify the Result
The fraction is already in its simplest form.
Therefore, the solution to the problem is .
Solve the following exercise:
\( \frac{3}{8}+\frac{1}{2}-\frac{1}{4}=\text{?} \)
Complete the following exercise:
\( \frac{1}{4}:\frac{1}{2}+\frac{1}{4}=\text{?} \)
Complete the following exercise:
\( \frac{1}{2}:\frac{1}{2}-\frac{1}{4}=\text{?} \)
Solve the following exercise:
\( \frac{3}{4}:\frac{5}{4}+\frac{1}{2}=\text{?} \)
\( \frac{3}{4}\times\frac{3}{4}-\frac{1}{4}= \)
Solve the following exercise:
To solve the problem, let's work through the following steps:
Step 1: Identify the least common denominator (LCD) for all fractions.
- The denominators are 8, 2, and 4. The LCM of these numbers is 8.
Step 2: Convert each fraction to have this common denominator of 8.
- is already with a denominator of 8.
- can be rewritten as because .
- can be rewritten as because .
Step 3: Perform the arithmetic operations.
- Add and , which gives .
- Subtract from , giving .
Step 4: Simplify the answer if necessary.
is already in its simplest form.
Therefore, the solution to the problem is .
Complete the following exercise:
To solve the problem , follow these steps:
Step 1: Perform the division .
Step 2: Now add the result from Step 1 to .
Therefore, the solution to the problem is .
Complete the following exercise:
To solve the problem, , follow these steps:
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 each step:
Step 1: We need to calculate . Using the division of fractions formula, this becomes:
.
Step 2: Simplify . Divide the numerator and the denominator by their greatest common divisor, which is 4:
.
Step 3: Add to the result :
The common denominator for addition is 10. Therefore:
and .
Add these two fractions:
.
Therefore, the solution to the problem is .
To solve this mathematical problem, follow these steps:
Let's execute each step in detail:
Step 1: Calculate the product of and .
To multiply two fractions, multiply their numerators and their denominators separately:
Step 2: Subtract from .
Before we subtract from , we need a common denominator. The common denominator for these fractions is 16:
Now subtract from :
Therefore, the solution to the given problem is .
\( \frac{1}{2}\times\frac{1}{2}+\frac{3}{4}= \)
\( \frac{3}{5}\times\frac{2}{3}+\frac{2}{5}= \)
\( \frac{2}{3}\times\frac{1}{3}+\frac{2}{9}= \)
\( \frac{3}{4}\times\frac{1}{2}+\frac{5}{8}= \)
\( \frac{4}{4}\times\frac{1}{2}+\frac{3}{8}= \)
To solve , follow these steps:
Therefore, the correct solution to the expression is .
To solve the problem , we proceed with the following steps:
The multiplication yields:
Both 6 and 15 share a common factor of 3:
Since the fractions and have the same denominator, add the numerators while keeping the denominator:
Therefore, the solution to the problem is .
To solve this problem, let's follow these steps:
Now, let's work through the calculations:
Step 1: Multiply by .
The formula for multiplying fractions is:
.
Substitute the values:
.
Step 2: Add to the product.
We found in Step 1 that .
Now add .
Therefore, the solution to the expression is .
To solve the problem , we'll follow these steps:
Now, let's work through the steps:
Step 1: Compute the product of the first two fractions:
Step 2: Add the resulting fraction to by finding a common denominator:
The fractions and already have the same denominator, so we can simply add them:
Therefore, the solution to the problem is .
To solve the expression , follow these steps:
Thus, the final result is .
\( \frac{2}{3}\times\frac{2}{3}+\frac{4}{9}= \)
\( \frac{1}{4}\times\frac{1}{2}+\frac{3}{8}= \)
\( \frac{1}{4}\times\frac{4}{5}+\frac{11}{20}= \)
\( \frac{4}{5}\times\frac{1}{2}+\frac{3}{10}= \)
Solve the following exercise:
\( \frac{1}{10}+\frac{3}{5}-\frac{1}{2}=\text{?} \)
To solve the given problem, we will follow these steps:
Let's go through each step:
Step 1: Multiply the fractions .
Step 2: The result from step 1 is , which cannot be further simplified.
Step 3: Add the result from Step 2 to given in the problem:
We have two fractions and , and since they already have a common denominator, we add them directly:
.
Step 4: The fraction is already in its simplest form.
Therefore, the solution to the problem is .
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Multiply the fractions:
Step 2: We find that the result is already simplified.
Step 3: Add to :
The fractions have the same denominator, allowing for direct addition.
Therefore, the solution to the problem is .
To solve this problem, we'll approach it in the following steps:
Step 1: Perform the Multiplication
The expression begins with multiplying two fractions: . Using the formula for multiplying fractions, we get:
Simplifying by dividing both numerator and denominator by 4 gives:
Step 2: Add the Result to the Second Fraction
Now, we need to add to . To do this, we first find a common denominator.
The least common denominator between 5 and 20 is 20. Convert to twentieths:
Now add to :
Step 3: Simplify the Final Result
Simplify by dividing the numerator and the denominator by 5:
Therefore, the solution to the problem is . This matches choice 1, which is .
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Multiply by . According to the multiplication rule for fractions, we have:
Step 2: We need to add to . Since these fractions have the same denominator, we can add them directly:
Step 3: The sum is already in simplest form.
Therefore, the solution to the problem is , which matches choice .
Solve the following exercise:
To solve the exercise , we must follow these steps:
Step 1: Find the Least Common Denominator (LCD).
The denominators we have are 10, 5, and 2. The LCD for these numbers is 10.
Step 2: Convert each fraction to have the common denominator of 10.
- is already with the denominator 10.
- Convert :
- Convert :
Step 3: Perform the addition and subtraction.
Now operate:
Step 4: Simplify the result.
The fraction simplifies to because both the numerator and denominator are divisible by 2.
Therefore, the solution to the problem is .