Examples with solutions for Subtraction of Fractions: Complete the missing numbers

Exercise #1

Complete the missing fraction
34——=24 \frac{3}{4}-_{——}=\frac{2}{4}

What is the missing fraction?

Video Solution

Step-by-Step Solution

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 34(missing fraction)=24 \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: 3424=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: 32=1 3 - 2 = 1 .

Step 4: Write the result over the common denominator.
The missing fraction is 14 \frac{1}{4} .

Therefore, the solution to the problem is 14 \frac{1}{4} .

Answer

14 \frac{1}{4}

Exercise #2

Complete the missing fraction
25——=15 \frac{2}{5}-_{——}=\frac{1}{5}

What is the missing fraction?

Video Solution

Step-by-Step Solution

To solve the problem 25_=15 \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 25 \frac{2}{5} and the result (difference) is 15 \frac{1}{5} .

Step 2: Apply the formula from our analysis: MinuendDifference=Subtrahend \text{Minuend} - \text{Difference} = \text{Subtrahend} . That means 2515=_ \frac{2}{5} - \frac{1}{5} = \_ .

Step 3: Perform the subtraction by subtracting the numerators:

2515=215=15 \frac{2}{5} - \frac{1}{5} = \frac{2 - 1}{5} = \frac{1}{5} .

Therefore, the missing fraction is 15 \frac{1}{5} .

Answer

15 \frac{1}{5}

Exercise #3

Complete the missing fraction
79——=29 \frac{7}{9}-_{——}=\frac{2}{9}

What is the missing fraction?

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the given fractions and set up the equation based on subtraction.
  • Step 2: Execute the subtraction to find the missing fraction.

Let's work through these steps:

Step 1: Given the equation 79x=29 \frac{7}{9} - x = \frac{2}{9} , we want to find x x .
The equation given is 79x=29 \frac{7}{9} - x = \frac{2}{9} .

Step 2: To find x x , rearrange the equation to solve for x x :
x=7929 x = \frac{7}{9} - \frac{2}{9}

Step 3: Subtract 29 \frac{2}{9} from 79 \frac{7}{9} :
x=729=59 x = \frac{7 - 2}{9} = \frac{5}{9}

Therefore, the missing fraction is 59 \frac{5}{9} .

This matches with the correct answer choice provided in the options.

Answer

59 \frac{5}{9}

Exercise #4

Complete the missing fraction:
45——=35 \frac{4}{5}-_{——}=\frac{3}{5}

What is the missing fraction?

Video Solution

Step-by-Step Solution

To solve this problem, we need to determine the missing fraction in the equation 45_=35 \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 44 and 33. To find the missing fraction, calculate the difference between the numerators:

  • Step 1: Subtract the numerators: 43=14 - 3 = 1.
  • Step 2: The common denominator remains 55.
  • Step 3: Thus, the missing fraction is 15\frac{1}{5}.

Therefore, the missing fraction in the equation is 15\frac{1}{5}.

Comparing with the options provided, the correct choice is option 2: 15\frac{1}{5}.

Therefore, the solution to the problem is 15\frac{1}{5}.

Answer

15 \frac{1}{5}

Exercise #5

Complete the missing fraction
67——=27 \frac{6}{7}-_{——}=\frac{2}{7}

What is the missing fraction?

Video Solution

Step-by-Step Solution

To solve this problem, we'll complete the following steps:

  • Identify the given expressions
  • Adjust the equation to find the missing fraction
  • Calculate the correct value

Let's break this down:

We start with the problem statement:

67missing fraction=27\frac{6}{7} - \text{missing fraction} = \frac{2}{7}

To find the missing fraction, rearrange the equation:

Missing fraction=6727\text{Missing fraction} = \frac{6}{7} - \frac{2}{7}

Since the denominators are identical (both are 7), we subtract the numerators while keeping the denominator constant:

Missing fraction=627=47\text{Missing fraction} = \frac{6 - 2}{7} = \frac{4}{7}

Upon reevaluating our options, we find 47\frac{4}{7} matches option 4 in the answer choices.

The missing fraction that completes the equation is therefore 47\frac{4}{7}.

Answer

47 \frac{4}{7}

Exercise #6

Complete the missing fraction
38——=18 \frac{3}{8}-_{——}=\frac{1}{8}

What is the missing fraction?

Video Solution

Step-by-Step Solution

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

Start with the equation given in the problem:

38x=18 \frac{3}{8} - x = \frac{1}{8}

Step 1: Add xx to both sides to isolate it:

38=18+x \frac{3}{8} = \frac{1}{8} + x

Step 2: Subtract 18\frac{1}{8} from both sides to solve for xx:

3818=x \frac{3}{8} - \frac{1}{8} = x

Step 3: Simplify the left side of the equation:

  • Subtract the numerators: 31=23 - 1 = 2
  • Maintain the common denominator: 8

So we have:

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

Therefore, the missing fraction is 28\frac{2}{8}.

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

Choice 3: 28\frac{2}{8}

Therefore, the solution to the problem is 28\frac{2}{8}.

Answer

28 \frac{2}{8}

Exercise #7

Complete the missing fraction
95——=65 \frac{9}{5}-_{——}=\frac{6}{5}

What is the missing fraction?

Video Solution

Step-by-Step Solution

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

  • Step 1: Restate the equation in terms of subtraction.
  • Step 2: Perform the subtraction.
  • Step 3: Verify and simplify, if needed.

Now, let's work through each step:

Step 1: We are given the equation 95(missing fraction)=65 \frac{9}{5} - \text{(missing fraction)} = \frac{6}{5} .

Step 2: To find the missing fraction, rearrange this as subtraction: Missing fraction=9565 \text{Missing fraction} = \frac{9}{5} - \frac{6}{5} .

Step 3: Perform the subtraction:

Missing fraction=9565=965=35 \text{Missing fraction} = \frac{9}{5} - \frac{6}{5} = \frac{9 - 6}{5} = \frac{3}{5} .

Thus, the missing fraction is 35 \frac{3}{5} .

Therefore, the solution to the problem is 35 \frac{3}{5} .

Answer

35 \frac{3}{5}

Exercise #8

Complete the missing fraction
107——=57 \frac{10}{7}-_{——}=\frac{5}{7}

What is the missing fraction?

Video Solution

Step-by-Step Solution

To find the missing fraction in the equation 107missing fraction=57 \frac{10}{7} - \text{missing fraction} = \frac{5}{7} , follow these steps:

Step 1: Identify the given equation.
According to the problem, we have:

107missing fraction=57 \frac{10}{7} - \text{missing fraction} = \frac{5}{7}

Step 2: Rearrange the equation to solve for the missing fraction.
If we let the missing fraction be x x , our equation becomes:

107x=57 \frac{10}{7} - x = \frac{5}{7}

Step 3: Isolate x x by subtracting 57 \frac{5}{7} from both sides of the equation:

x=10757 x = \frac{10}{7} - \frac{5}{7}

Step 4: Simplify the subtraction.
Since the denominators are the same, we subtract the numerators directly:

x=1057 x = \frac{10 - 5}{7}

x=57 x = \frac{5}{7}

Therefore, the missing fraction in the equation is 57 \frac{5}{7} .

Answer

57 \frac{5}{7}

Exercise #9

Complete the missing fraction
56——=26 \frac{5}{6}-_{——}=\frac{2}{6}

What is the missing fraction?

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the fractions in the problem.
  • Step 2: Use the subtraction property of fractions with the same denominator.
  • Step 3: Solve for the missing fraction.

Now, let's work through each step:
Step 1: We are given 56missing fraction=26 \frac{5}{6} - \text{missing fraction} = \frac{2}{6} .
Step 2: Using the property of subtraction, we can set up the equation as follows:
Let the missing fraction be x6 \frac{x}{6} . Then:
56x6=26 \frac{5}{6} - \frac{x}{6} = \frac{2}{6}

Step 3: By manipulating the numerators, we have:
5x=2 5 - x = 2
Solving for x x , we get:
x=52=3 x = 5 - 2 = 3

Therefore, the missing fraction is 36 \frac{3}{6} .

Answer

36 \frac{3}{6}

Exercise #10

Complete the missing fraction
35——=25 \frac{3}{5}-_{——}=\frac{2}{5}

What is the missing fraction?

Video Solution

Step-by-Step Solution

To solve this problem, we will subtract the given result fraction from the initial fraction to find the missing fraction.

Step 1: Identify the given fractions.
We are given 35 \frac{3}{5} and need to identify the fraction that, when subtracted, results in 25 \frac{2}{5} .

Step 2: Perform the subtraction on the numerators.
The equation we form is:

35missing fraction=25 \frac{3}{5} - \text{missing fraction} = \frac{2}{5}

We rearrange this to solve for the missing fraction:
missing fraction=3525\text{missing fraction} = \frac{3}{5} - \frac{2}{5}

Step 3: Calculate the difference of the numerators since the denominators are the same:
325=15\frac{3 - 2}{5} = \frac{1}{5}

Thus, the missing fraction is 15 \frac{1}{5} .

Therefore, the solution to the problem is 15 \frac{1}{5} .

Answer

15 \frac{1}{5}

Exercise #11

Complete the missing fraction
23——=13 \frac{2}{3}-_{——}=\frac{1}{3}

What is the missing fraction?

Video Solution

Step-by-Step Solution

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

  • Identify the fractions involved: 23 \frac{2}{3} and 13 \frac{1}{3} .
  • Recognize that the denominators are the same, which simplifies subtraction.
  • Subtract the fraction 13 \frac{1}{3} from 23 \frac{2}{3} to determine the missing fraction.

Let’s calculate the missing fraction:

Given the equation:

23missing fraction=13 \frac{2}{3} - \text{missing fraction} = \frac{1}{3}

Rearrange to solve for the missing fraction:

missing fraction=2313\text{missing fraction} = \frac{2}{3} - \frac{1}{3}

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

2313=213=13\frac{2}{3} - \frac{1}{3} = \frac{2-1}{3} = \frac{1}{3}

The missing fraction is thus 13\frac{1}{3}.

Therefore, the solution to the problem is 13\frac{1}{3}.

Answer

13 \frac{1}{3}

Exercise #12

Complete the missing fraction
32——=12 \frac{3}{2}-_{——}=\frac{1}{2}

What is the missing fraction?

Video Solution

Step-by-Step Solution

To solve the problem, we start with the equation:

32x=12 \frac{3}{2} - x = \frac{1}{2}

We need to determine the value of x x . To do this, let's isolate x x on one side of the equation:

Step 1: Rearrange the equation to solve for x x :

x=3212 x = \frac{3}{2} - \frac{1}{2}

Step 2: Perform the subtraction. Since the denominators are the same, you can directly subtract the numerators:

x=312 x = \frac{3 - 1}{2}

Step 3: Simplify the expression:

x=22 x = \frac{2}{2}

x=1 x = 1

Thus, the missing fraction is 1 1 .

Answer

1 1