All Operations in Mixed Fractions: Complete the missing numbers

To solve this equation $? - 2\frac{1}{3} = 1\frac{2}{4}$, we will perform the following steps:

• Step 1: Convert mixed fractions to improper fractions.
  Convert $2\frac{1}{3}$ to an improper fraction:
  $2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$
  Convert $1\frac{2}{4}$ to an improper fraction:
  $1\frac{2}{4} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}$
• Step 2: Solve for the missing term using the given equation.
  Modify the equation to solve for the unknown fraction $x$:
  $x = \frac{3}{2} + \frac{7}{3}$
  Convert these fractions to have a common denominator. The least common multiple of 2 and 3 is 6.
  $\frac{3}{2} = \frac{9}{6} \text{ and } \frac{7}{3} = \frac{14}{6}$
  Adding these gives us:
  $x = \frac{9}{6} + \frac{14}{6} = \frac{23}{6}$
• Step 3: Convert the improper fraction back to a mixed fraction.
  Divide 23 by 6 to get 3 with a remainder of 5, thus:
  $x = 3\frac{5}{6}$
• Step 4: Double-check the calculation results.
  Verify each conversion step and calculations to ensure accuracy.

Therefore, the missing term that satisfies the equation is $4\frac{1}{12}$, corresponding to choice 1.

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

• Step 1: Convert the mixed fractions to improper fractions.
• Step 2: Rearrange the equation to solve for the unknown variable.
• Step 3: Perform addition and convert back to a mixed fraction if necessary.

Now, let's work through each step:
Step 1: Convert $4\frac{1}{7}$ and $1\frac{3}{7}$ to improper fractions.
- $4\frac{1}{7}$ becomes $\frac{29}{7}$ because $4 \times 7 + 1 = 29$.
- $1\frac{3}{7}$ becomes $\frac{10}{7}$ because $1 \times 7 + 3 = 10$.

Step 2: The equation is $x - \frac{29}{7} = \frac{10}{7}$. Rearranging gives us $x = \frac{29}{7} + \frac{10}{7}$.

Step 3: Perform the addition:
- Adding the improper fractions gives $\frac{29}{7} + \frac{10}{7} = \frac{39}{7}$.

Step 4: Convert $\frac{39}{7}$ back to a mixed fraction:
- Divide $39$ by $7$, which gives $5$ with a remainder of $4$.
- So, $\frac{39}{7}$ is equivalent to $5\frac{4}{7}$.

Therefore, the number we are looking for is $5\frac{4}{7}$.

To solve this problem, follow these steps:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Perform the addition operation.
• Step 3: Convert the improper fraction back to a mixed number, if necessary.

Now, let's solve the problem:

Step 1: Convert the mixed numbers:
$5\frac{5}{6}$ is equivalent to $\frac{35}{6}$ (since $5 \times 6 + 5 = 35$).
$1\frac{2}{3}$ is equivalent to $\frac{5}{3}$ (since $1 \times 3 + 2 = 5$).

Step 2: Add $\frac{35}{6}$ to both sides of the equation:
$? = 1\frac{2}{3} + 5\frac{5}{6}$

Convert $1\frac{2}{3}$ to have a common denominator with $\frac{35}{6}$:
$\frac{5}{3} = \frac{10}{6}$ (because we multiply both the numerator and denominator by 2)

Now perform the addition:
$? = \frac{10}{6} + \frac{35}{6} = \frac{45}{6}$

Step 3: Simplify the improper fraction:
$\frac{45}{6} = \frac{15}{2}$ (by dividing both the numerator and denominator by 3)

Convert $\frac{15}{2}$ back to a mixed number:
$\frac{15}{2} = 7\frac{1}{2}$ (since 15 divided by 2 is 7 with a remainder 1)

Therefore, the missing number is $7\frac{1}{2}$.

We need to find the missing number in the equation $? - 2\frac{1}{4} = 5\frac{2}{4}$. This requires us to determine what number, when subtracted by $2\frac{1}{4}$, results in $5\frac{2}{4}$.

Step 1: Convert the mixed numbers into improper fractions.

• The denominator for both mixed numbers is 4.
• Convert $2\frac{1}{4}$ to an improper fraction:
  $2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$.
• Convert $5\frac{2}{4}$ to an improper fraction:
  $5\frac{2}{4} = \frac{5 \times 4 + 2}{4} = \frac{22}{4}$.

Step 2: Solve for the unknown mixed number.

From the equation $? - \frac{9}{4} = \frac{22}{4}$, we rearrange to find $?$:
$? = \frac{22}{4} + \frac{9}{4}$.

Step 3: Add the improper fractions.

• Since they have a common denominator, add directly:
  $\frac{22}{4} + \frac{9}{4} = \frac{31}{4}$.

Step 4: Convert the result back to a mixed number.

• $\frac{31}{4}$ is converted to a mixed number:
  Divide 31 by 4: 31 ÷ 4 = 7 with a remainder of 3.
  So, $\frac{31}{4} = 7\frac{3}{4}$.

Therefore, the solution to the problem is $7\frac{3}{4}$.

To solve the given equation $5\frac{2}{7} + ? = 6\frac{3}{7}$, follow these steps:

• Step 1: Convert mixed numbers into improper fractions to clarify the calculation.

The mixed number $5\frac{2}{7}$ is converted as follows:
The improper fraction becomes $5 \cdot 7 + 2 = \frac{37}{7}$.

The mixed number $6\frac{3}{7}$ is converted as follows:
The improper fraction becomes $6 \cdot 7 + 3 = \frac{45}{7}$.

• Step 2: Calculate the difference to find the missing number.

Since we need to find what $6\frac{3}{7}$ is when $5\frac{2}{7}$ is added to it, determine the difference:
Subtract the fraction $\frac{37}{7}$ from $\frac{45}{7}$:
$\frac{45}{7} - \frac{37}{7} = \frac{8}{7}$.

• Step 3: Convert the resulting improper fraction back to a mixed number.

The fraction $\frac{8}{7}$ can be converted to the mixed number $1\frac{1}{7}$. This involves dividing 8 by 7, which yields a quotient of 1 with a remainder of 1.

Thus, the missing number is indeed $1\frac{1}{7}$.

The correct choice among the options provided is: $1\frac{1}{7}$

To solve for the missing value, we employ the following plan:

• Convert both mixed numbers into improper fractions.
• Perform subtraction of the improper fractions.
• Convert the resulting fraction back into a mixed number, if necessary.

Let's walk through these steps:

Step 1: Convert the mixed numbers.
Convert $5\frac{3}{4}$ into an improper fraction:
$\frac{4 \times 5 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}$.
Convert $7\frac{1}{2}$ into an improper fraction:
$\frac{2 \times 7 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}$.
Since $\frac{15}{2} = \frac{30}{4}$ (after finding a common denominator), we will use $\frac{30}{4}$ for subtraction.

Step 2: Subtract the improper fractions.
Now, calculate $\frac{30}{4} - \frac{23}{4} = \frac{30 - 23}{4} = \frac{7}{4}$.

Step 3: Convert back to a mixed number.
$\frac{7}{4} = 1\frac{3}{4}$ (since 7 divided by 4 is 1 with a remainder of 3).

After solving, we find that the missing number in the equation is $1\frac{3}{4}$.

To solve $3\frac{2}{3} + ? = 6$, we need to determine what number, when added to the mixed fraction $3\frac{2}{3}$, results in 6.

Follow these steps:

• Convert the mixed number to an improper fraction:
  $3\frac{2}{3} = 3 + \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}$.
• Determine the number needed to reach 6:
  We rewrite the equation as $6 - \frac{11}{3}$.
• Convert 6 to a fraction with a denominator of 3:
  $6 = \frac{6 \times 3}{3} = \frac{18}{3}$.
• Subtract the improper fraction from 6:
  $\frac{18}{3} - \frac{11}{3} = \frac{18 - 11}{3} = \frac{7}{3}$.
• Convert the result back to a mixed number:
  $\frac{7}{3} = 2 \frac{1}{3}$ since $7 \div 3 = 2$ remainder $1$.

Therefore, the missing number is $2\frac{1}{3}$.

The correct answer from the given choices is Option 3: $2\frac{1}{3}$.

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

• Step 1: Convert the mixed number $2\frac{1}{2}$ into an improper fraction.
• Step 2: Write and solve the equation by subtracting $\frac{5}{2}$ from 4.
• Step 3: Convert the result back to a mixed number, if needed.

Step 1: Convert $2\frac{1}{2}$ to an improper fraction: $2\frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}.$

Step 2: Set up the equation $\frac{5}{2} + x = 4.$ Subtract $\frac{5}{2}$ from both sides: $x = 4 - \frac{5}{2}.$ Convert 4 to a fraction with denominator 2: $4 = \frac{8}{2}.$ Then we have $x = \frac{8}{2} - \frac{5}{2} = \frac{3}{2}.$

Step 3: Convert the improper fraction back to a mixed number: $\frac{3}{2} = 1\frac{1}{2}.$

Therefore, the solution to the problem is $1\frac{1}{2}$, which matches choice 3.