Multiplication of Fractions: Complete the missing numbers

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 the equation $\frac{1}{2} \times ? = \frac{1}{4}$, we need to find the number that makes this equation true.

Let's perform the operations step-by-step:

• Step 1: Start with the given equation: $\frac{1}{2} \times x = \frac{1}{4}$.
• Step 2: To isolate $x$, divide both sides by $\frac{1}{2}$. This gives us: $x = \frac{1}{4} \div \frac{1}{2}$.
• Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. Thus, we have: $x = \frac{1}{4} \times \frac{2}{1}$.
• Step 4: Multiply the fractions: $x = \frac{1 \times 2}{4 \times 1} = \frac{2}{4}$.
• Step 5: Simplify the fraction: $x = \frac{1}{2}$.

Therefore, the missing number is $\frac{1}{2}$. This matches choice 4 from the given options.

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

• Step 1: Identify the equation $\frac{2}{3} \times x = \frac{1}{3}$.
• Step 2: To isolate $x$, we'll divide both sides by $\frac{2}{3}$.
• Step 3: Perform the division by $\frac{2}{3}$ by multiplying by its reciprocal.

Let's work through each step:

Step 1: We start with the equation $\frac{2}{3} \times x = \frac{1}{3}$.

Step 2: To solve for $x$, divide both sides by $\frac{2}{3}$:

$x = \frac{1}{3} \div \frac{2}{3}$

Step 3: Dividing by a fraction is equivalent to multiplying by the reciprocal:

$x = \frac{1}{3} \times \frac{3}{2}$

Calculate the multiplication:

$x = \frac{1 \times 3}{3 \times 2} = \frac{3}{6}$

$x = \frac{1}{2}$

Therefore, the solution to the problem is $\frac{1}{2}$, which corresponds to choice .

To solve this problem, we’ll follow the division of fractions method:

• Step 1: Start with the given equation $\frac{2}{3} \times ? = \frac{1}{4}$.
• Step 2: To isolate the unknown, divide both sides of the equation by $\frac{2}{3}$. This can be done by multiplying $\frac{1}{4}$ by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$.
• Step 3: The calculation becomes: $\frac{1}{4} \times \frac{3}{2} = \frac{1 \times 3}{4 \times 2} = \frac{3}{8}$.

Therefore, the solution to the problem is $? = \frac{3}{8}$. Hence, the correct choice is option 2.

To solve the equation $\frac{2}{3} \times x = \frac{1}{6}$, we need to find the value of $x$ by isolating it.

• Step 1: Set the equation to solve for $x$:
  $\frac{2}{3} \times x = \frac{1}{6}$.
• Step 2: Isolate $x$ by dividing both sides by $\frac{2}{3}$:
  $x = \frac{1}{6} \div \frac{2}{3}$.
• Step 3: Performing the division by multiplying with the reciprocal:
  $x = \frac{1}{6} \times \frac{3}{2}$.
• Step 4: Simplify the expression:
  $\frac{1 \times 3}{6 \times 2} = \frac{3}{12} = \frac{1}{4}$.

Thus, the number that satisfies the equation is $\frac{1}{4}$.

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 this problem, we'll proceed with the following steps:

• Step 1: Set up the equation: $\frac{5}{7} \times x = \frac{1}{3}$.
• Step 2: Isolate $x$ by dividing both sides by $\frac{5}{7}$, which is equivalent to multiplying both sides by the reciprocal, $\frac{7}{5}$.
• Step 3: Simplify the resulting expression to find $x$.

Now, applying these steps:
Step 1: We have the equation $\frac{5}{7} \times x = \frac{1}{3}$.
Step 2: Multiply both sides by $\frac{7}{5}$ to isolate $x$:
$x = \frac{1}{3} \times \frac{7}{5}$.
Step 3: Simplify the calculation:
$x = \frac{1 \times 7}{3 \times 5} = \frac{7}{15}$.

Therefore, the solution to the problem is $x = \frac{7}{15}$.

To solve the problem $\frac{3}{4} \times ? = \frac{1}{5}$, we need to find the value of the question mark.

• Step 1: Set up the equation for the unknown variable.
  We know $\frac{3}{4} \times ? = \frac{1}{5}$. Thus, to isolate the question mark, we will divide both sides of the equation by $\frac{3}{4}$.
• Step 2: Perform the division.
  Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, $? = \frac{1}{5} \div \frac{3}{4} = \frac{1}{5} \times \frac{4}{3}$.
• Step 3: Simplify the multiplication.
  When multiplying fractions, multiply the numerators together and the denominators together:
  $? = \frac{1 \cdot 4}{5 \cdot 3} = \frac{4}{15}$.

This calculation shows that the missing number is $\frac{4}{15}$.

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

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 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 $\frac{5}{6}$.