All Operations in Fractions: Complete the missing number

Let's solve the problem using the steps outlined in our analysis:

Start with the equation given in the problem:

$\frac{3}{8} - x = \frac{1}{8}$

Step 1: Add $x$ to both sides to isolate it:

$\frac{3}{8} = \frac{1}{8} + x$

Step 2: Subtract $\frac{1}{8}$ from both sides to solve for $x$:

$\frac{3}{8} - \frac{1}{8} = x$

Step 3: Simplify the left side of the equation:

• Subtract the numerators: $3 - 1 = 2$
• Maintain the common denominator: 8

So we have:

$\frac{2}{8} = x$

Therefore, the missing fraction is $\frac{2}{8}$.

Matching our solution to the answer choices, the correct choice is:

Choice 3: $\frac{2}{8}$

Therefore, the solution to the problem is $\frac{2}{8}$.

To find the missing fraction in the equation $\frac{2}{9} + ? = \frac{2}{3}$, we will perform the following steps:

• Step 1: Convert the fraction $\frac{2}{3}$ to have the same denominator as $\frac{2}{9}$.
• Step 2: Subtract $\frac{2}{9}$ from the new fraction.

Let's execute these steps:
Step 1: Convert $\frac{2}{3}$ into a fraction with a denominator of 9. To do this, multiply both the numerator and the denominator of $\frac{2}{3}$ by 3 to obtain an equivalent fraction:
$\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$

Step 2: Subtract $\frac{2}{9}$ from $\frac{6}{9}$:
$\frac{6}{9} - \frac{2}{9} = \frac{4}{9}$

Thus, the fraction that we need to add to $\frac{2}{9}$ to get $\frac{2}{3}$ is $\frac{4}{9}$.

The correct answer to the problem is $\frac{4}{9}$.

To solve the equation $\frac{5}{6} \times ? = \frac{1}{3}$, we need to find the missing number represented by "?".

We can solve this problem by using the following steps:

• Step 1: Identify the equation we are working with:
  We have the equation $\frac{5}{6} \times ? = \frac{1}{3}$.
• Step 2: Isolate the unknown variable, "?":
  To do this, divide both sides of the equation by $\frac{5}{6}$.
• Perform the division:
  $? = \frac{\frac{1}{3}}{\frac{5}{6}} = \frac{1}{3} \times \frac{6}{5}$
• Step 3: Simplify the expression:
  Now, multiply $\frac{1}{3}$ by the reciprocal of $\frac{5}{6}$:
  $? = \frac{1 \times 6}{3 \times 5} = \frac{6}{15}$
• Simplify the fraction $\frac{6}{15}$:
  The greatest common divisor of 6 and 15 is 3, so divide both the numerator and the denominator by 3:
  $? = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

Therefore, the solution to the problem is $\frac{2}{5}$.

To solve the problem, let's use the equation provided:

$\frac{2}{4} \times x = \frac{2}{7}$

Step 1: Isolate the missing fraction $x$ by dividing both sides by $\frac{2}{4}$.

$x = \frac{\frac{2}{7}}{\frac{2}{4}}$

Step 2: Simplify the division of the fractions. Recall that dividing by a fraction is the same as multiplying by its reciprocal.

$x = \frac{2}{7} \times \frac{4}{2}$

Step 3: Simplify the multiplication by canceling common factors. Here, $\frac{4}{2}$ simplifies to 2.

$x = \frac{2 \times 4}{7 \times 2} = \frac{4}{7}$

Therefore, the missing fraction $x$ is $\frac{4}{7}$.

Thus, the correct answer is:

$\frac{4}{7}$ (corresponds to choice 3)

To solve the problem $\frac{2}{5} - \_ = \frac{1}{5}$, we will use the concept of subtraction of fractions to find the missing fraction.

Let's follow these steps:

• Step 1: Identify the given fractions.
• Step 2: Use the subtraction identity to find the missing fraction.
• Step 3: Solve for the missing fraction.

Step 1: The initial fraction (minuend) is $\frac{2}{5}$ and the result (difference) is $\frac{1}{5}$.

Step 2: Apply the formula from our analysis: $\text{Minuend} - \text{Difference} = \text{Subtrahend}$. That means $\frac{2}{5} - \frac{1}{5} = \_$.

Step 3: Perform the subtraction by subtracting the numerators:

$\frac{2}{5} - \frac{1}{5} = \frac{2 - 1}{5} = \frac{1}{5}$.

Therefore, the missing fraction is $\frac{1}{5}$.

To solve this problem, let's follow these steps:

• Convert the fractions to have a common denominator.
• Subtract to find the missing value.
• Simplify the resulting fraction.

Step 1: Start with the equation $\frac{1}{10} + ? = \frac{3}{4}$.
Step 2: Rewrite it to find the missing term: $? = \frac{3}{4} - \frac{1}{10}$.

Step 3: To subtract, find a common denominator. The least common multiple of 4 and 10 is 20:

• Convert $\frac{3}{4}$ to have a denominator of 20: $\frac{3}{4} = \frac{15}{20}$.
• Convert $\frac{1}{10}$ to have a denominator of 20: $\frac{1}{10} = \frac{2}{20}$.

Step 4: Subtract $\frac{2}{20}$ from $\frac{15}{20}$:
$\frac{15}{20} - \frac{2}{20} = \frac{13}{20}$.

Step 5: Verify with the provided choices. The correct answer choice is the fraction $\frac{13}{20}$, which matches choice 4.

Therefore, the solution to the problem is $\frac{13}{20}$.

To solve this problem, we aim to find $x$ in the equation $x + \frac{3}{4} = \frac{4}{5}$.

Step 1: Isolate $x$ by subtracting $\frac{3}{4}$ from both sides.

$x = \frac{4}{5} - \frac{3}{4}$

Step 2: Find a common denominator for the fractions $\frac{4}{5}$ and $\frac{3}{4}$. The least common denominator of 5 and 4 is 20.

Convert $\frac{4}{5}$ to a fraction with a denominator of 20:

$\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}$

Convert $\frac{3}{4}$ to a fraction with a denominator of 20:

$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

Step 3: Subtract the two fractions:

$x = \frac{16}{20} - \frac{15}{20} = \frac{16 - 15}{20} = \frac{1}{20}$

Therefore, the missing fraction $x$ is $\frac{1}{20}$.

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

• Identify the fractions involved in the given equation.
• Subtract the result fraction from the starting fraction to find the missing fraction.

Now, let's work through each step:

Step 1: Identify the fractions.
The given equation is $\frac{3}{4} - \text{(missing fraction)} = \frac{2}{4}$.

Step 2: Subtract the result fraction from the starting fraction.
We rearrange the equation to find the missing fraction: $\frac{3}{4} - \frac{2}{4} = \text{missing fraction}$.

Step 3: Perform the subtraction.
Since the denominators are the same (4), we subtract the numerators: $3 - 2 = 1$.

Step 4: Write the result over the common denominator.
The missing fraction is $\frac{1}{4}$.

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

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

• Identify the fractions involved: $\frac{2}{3}$ and $\frac{1}{3}$.
• Recognize that the denominators are the same, which simplifies subtraction.
• Subtract the fraction $\frac{1}{3}$ from $\frac{2}{3}$ to determine the missing fraction.

Let’s calculate the missing fraction:

Given the equation:

$\frac{2}{3} - \text{missing fraction} = \frac{1}{3}$

Rearrange to solve for the missing fraction:

$\text{missing fraction} = \frac{2}{3} - \frac{1}{3}$

Because the fractions have a common denominator, subtract the numerators:

$\frac{2}{3} - \frac{1}{3} = \frac{2-1}{3} = \frac{1}{3}$

The missing fraction is thus $\frac{1}{3}$.

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

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

• Step 1: Identify the known values and the variable to solve for.
• Step 2: Rearrange the equation to isolate the unknown variable.
• Step 3: Perform the arithmetic calculation to find the solution.

Now, let's work through each step:

Step 1: We have the equation $\frac{1}{4} \times ? = \frac{1}{5}$. Our task is to find the value of the question mark (?).

Step 2: To isolate the question mark, we divide both sides of the equation by $\frac{1}{4}$. This is equivalent to multiplying both sides by the reciprocal of $\frac{1}{4}$, which is $4$. Thus, we have:

$? = \frac{1}{5} \times 4$

Step 3: Perform the multiplication:

$? = \frac{1 \times 4}{5 \times 1} = \frac{4}{5}$

Therefore, the number that satisfies the equation is $\frac{4}{5}$.

The correct answer is choice 1: $\frac{4}{5}$.

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

• Step 1: Rearrange the equation $\frac{1}{6} + x = \frac{1}{2}$ to solve for $x$.
• Step 2: Subtract $\frac{1}{6}$ from both sides of the equation, so $x = \frac{1}{2} - \frac{1}{6}$.
• Step 3: Using a common denominator for subtraction.

Now, let's work through each step:
Step 1: Rearrange the equation: $x = \frac{1}{2} - \frac{1}{6}$.
Step 2: To subtract fractions, we need a common denominator. The least common denominator of 2 and 6 is 6.
Step 3: Rewrite each fraction with the common denominator:
$\frac{1}{2} = \frac{3}{6}$ And $\frac{1}{6}$ is already with the denominator 6.
Step 4: Subtract the fractions: $x = \frac{3}{6} - \frac{1}{6} = \frac{2}{6}$.
Step 5: Simplify $\frac{2}{6}$ to $\frac{1}{3}$.

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

To solve this problem, we need to determine the missing fraction in the equation $\frac{4}{5} - \_ = \frac{3}{5}$.

Since both fractions have the same denominator, we can focus solely on subtracting the numerators, as the denominators remain unchanged.

The numerators are $4$ and $3$. To find the missing fraction, calculate the difference between the numerators:

• Step 1: Subtract the numerators: $4 - 3 = 1$.
• Step 2: The common denominator remains $5$.
• Step 3: Thus, the missing fraction is $\frac{1}{5}$.

Therefore, the missing fraction in the equation is $\frac{1}{5}$.

Comparing with the options provided, the correct choice is option 2: $\frac{1}{5}$.

Therefore, the solution to the problem is $\frac{1}{5}$.

To solve this problem, we need to find the missing fraction $x$ such that $\frac{3}{5} \times x = \frac{2}{4}$. We'll follow these steps:

• Step 1: Simplify the fraction $\frac{2}{4}$ to $\frac{1}{2}$.
• Step 2: Set up the equation to solve for $x$. This gives us $\frac{3}{5} \times x = \frac{1}{2}$.
• Step 3: Isolate $x$ by dividing both sides by $\frac{3}{5}$, leading to $x = \frac{\frac{1}{2}}{\frac{3}{5}}$.
• Step 4: Simplify the complex fraction by multiplying by the reciprocal: $x = \frac{1}{2} \times \frac{5}{3}$.
• Step 5: Calculate the multiplication: $x = \frac{1 \times 5}{2 \times 3} = \frac{5}{6}$.

Therefore, the solution to the problem is $\frac{5}{6}$.

To solve this problem, we will focus on simplifying the fraction on the left side and comparing it to the fraction on the right side:

• Step 1: Simplify the fraction $\frac{7}{14}$. Since both 7 and 14 have a common factor of 7, we can divide both the numerator and denominator by 7 to get $\frac{1}{2}$.
• Step 2: We now have the equation $\frac{1}{2} + ? = \frac{1}{2}$.
• Step 3: To determine what needs to be added to $\frac{1}{2}$ to result in $\frac{1}{2}$, we can see that nothing needs to be added. Therefore, the unknown term $?$ should be 0.

This makes sense because adding zero to any number does not change its value.

Therefore, the solution to the problem is $0$.