Examples with solutions for Dividing Mixed Numbers and Fractions: Dividing a fraction by a whole

Exercise #1

13:3= \frac{1}{3}:3=

Video Solution

Step-by-Step Solution

To solve the problem 13:3 \frac{1}{3} : 3 , we will follow these clear steps:

  • Step 1: Understand that dividing by 3 is equivalent to multiplying by the reciprocal of 3, which is 13\frac{1}{3}.
  • Step 2: Convert the division problem 13:3\frac{1}{3} : 3 into a multiplication problem 13×13\frac{1}{3} \times \frac{1}{3}.
  • Step 3: Perform the multiplication of fractions:

Using the formula ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d}, we have:

13×13=1133=19\frac{1}{3} \times \frac{1}{3} = \frac{1 \cdot 1}{3 \cdot 3} = \frac{1}{9}.

Therefore, the solution to the problem is 19\frac{1}{9}.

Answer

19 \frac{1}{9}

Exercise #2

12:2= \frac{1}{2}:2=

Video Solution

Step-by-Step Solution

To solve 12:2 \frac{1}{2} : 2 , we need to rewrite the division as multiplication by the reciprocal of 2. The reciprocal of 2 is 12 \frac{1}{2} .

Thus, the expression becomes:

12×12=1×12×2\frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2}

Calculating the multiplication, we have:

14\frac{1}{4}

Therefore, the solution to the problem is 14 \frac{1}{4} , which corresponds to choice 3.

Answer

14 \frac{1}{4}

Exercise #3

12:3= \frac{1}{2}:3=

Video Solution

Step-by-Step Solution

To solve this problem of dividing a fraction by a whole number, we'll follow these steps:

  • Step 1: Change the whole number to a reciprocal fraction.
  • Step 2: Multiply the original fraction by the reciprocal.
  • Step 3: Simplify the resulting fraction, if necessary.

Now, let's apply these steps:
Step 1: The whole number 33 is converted to the reciprocal fraction 13\frac{1}{3}.
Step 2: Multiply the fraction 12\frac{1}{2} by 13\frac{1}{3}:

12×13=1×12×3=16\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}

Step 3: The resulting fraction 16\frac{1}{6} is already in its simplest form.

Therefore, when 12\frac{1}{2} is divided by 33, the resulting answer is 16\frac{1}{6}.

Answer

16 \frac{1}{6}

Exercise #4

12:4= \frac{1}{2}:4=

Video Solution

Step-by-Step Solution

To solve this problem, we need to compute 12÷4 \frac{1}{2} \div 4 . Here are the steps:

  • Step 1: Recognize that dividing by 4 is equivalent to multiplying by its reciprocal, 14 \frac{1}{4} .
  • Step 2: Rewrite the division as a multiplication: 12×14 \frac{1}{2} \times \frac{1}{4} .
  • Step 3: Perform the multiplication of fractions by multiplying their numerators and denominators. Thus, 1124=18 \frac{1 \cdot 1}{2 \cdot 4} = \frac{1}{8} .

Therefore, the solution to the problem is 18 \frac{1}{8} .

Answer

18 \frac{1}{8}

Exercise #5

23:5= \frac{2}{3}:5=

Video Solution

Step-by-Step Solution

To solve this problem of dividing a fraction by a whole number, we will follow these steps:

  • Step 1: Convert the division problem into a multiplication by the reciprocal.
  • Step 2: Multiply the fraction by the reciprocal of the whole number.
  • Step 3: Simplify the resulting fraction, if possible.

Let's work through these steps in detail:

Step 1: Convert the division into a multiplication by the reciprocal.
The given problem is 23:5 \frac{2}{3} : 5 . In arithmetic, division by a whole number can be converted into multiplication by its reciprocal. The reciprocal of the whole number 5 is 15 \frac{1}{5} . Therefore, the expression becomes:

23×15 \frac{2}{3} \times \frac{1}{5} .

Step 2: Multiply the fraction by the reciprocal.
We now multiply the numerators and the denominators:

23×15=2×13×5=215 \frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15} .

Step 3: Simplify the resulting fraction.
We check if the fraction 215 \frac{2}{15} can be simplified further. Since 2 and 15 have no common divisors besides 1, the fraction is already in its simplest form.

Therefore, the solution to the division problem 23:5 \frac{2}{3} : 5 is 215 \frac{2}{15} .

Upon examining the provided answer choices, we confirm that our solution, 215 \frac{2}{15} , matches choice number 4.

Answer

215 \frac{2}{15}

Exercise #6

45:2= \frac{4}{5}:2=

Video Solution

Step-by-Step Solution

To solve the problem of dividing the fraction 45 \frac{4}{5} by 2, we can utilize the method of multiplying by the reciprocal. Here’s how you can systematically approach it:

Given the division 45:2 \frac{4}{5} : 2 , we first express the division by finding the reciprocal.
Step 1: The reciprocal of 2 is 12 \frac{1}{2} .

Step 2: Now, multiply the fraction 45 \frac{4}{5} by 12 \frac{1}{2} :

45×12=4×15×2=410 \frac{4}{5} \times \frac{1}{2} = \frac{4 \times 1}{5 \times 2} = \frac{4}{10}

Step 3: Simplify the resulting fraction:

The numerator and the denominator have a common factor of 2. Dividing both by 2 gives:

4÷210÷2=25 \frac{4 \div 2}{10 \div 2} = \frac{2}{5}

Therefore, the solution to the problem 45:2 \frac{4}{5} : 2 is 25 \frac{2}{5} .

Answer

25 \frac{2}{5}

Exercise #7

34:4= \frac{3}{4}:4=

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Recognize that dividing by a number is equivalent to multiplying by its reciprocal.
  • Step 2: Apply this transformation to the problem, emphasizing the operation change.
  • Step 3: Perform the multiplication operation correctly.
  • Step 4: Simplify the resulting fraction to simplest terms.

Let's work through it:

Step 1: Start with the expression: 34÷4\frac{3}{4} \div 4.

Step 2: Convert the division by 4 into multiplication by its reciprocal, 14\frac{1}{4}. The expression becomes: 34×14\frac{3}{4} \times \frac{1}{4}.

Step 3: To multiply fractions, multiply the numerators together and the denominators together:
Numerator: 3×1=33 \times 1 = 3
Denominator: 4×4=164 \times 4 = 16

Therefore, the resulting fraction from the multiplication is 316\frac{3}{16}.

There is no need for additional simplification as 316\frac{3}{16} is already in simplest form.

Therefore, the solution to the problem is 316 \frac{3}{16} .

Answer

316 \frac{3}{16}

Exercise #8

27:3= \frac{2}{7}:3=

Video Solution

Step-by-Step Solution

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

  • Step 1: Rewrite the division as a multiplication by the reciprocal.
  • Step 2: Perform the multiplication of fractions.
  • Step 3: Simplify if necessary and find the solution among the given choices.

Now, let's work through each step:
Step 1: Rewrite the problem 27÷3 \frac{2}{7} \div 3 as a multiplication:
27×13 \frac{2}{7} \times \frac{1}{3}

Step 2: Multiply the numerators and the denominators:
2×17×3=221 \frac{2 \times 1}{7 \times 3} = \frac{2}{21}

Step 3: This fraction is already in its simplest form. Looking at the answer choices, we can conclude the correct answer is 221\frac{2}{21}.

Therefore, the correct solution to the problem is 221 \frac{2}{21} .

Answer

221 \frac{2}{21}

Exercise #9

47:5= \frac{4}{7}:5=

Video Solution

Step-by-Step Solution

To solve the problem of dividing 47\frac{4}{7} by 5, we will follow these steps:

  • Step 1: Understand that dividing by a number is the same as multiplying by its reciprocal.
  • Step 2: Convert the division problem into a multiplication problem using the reciprocal.
  • Step 3: Perform the multiplication of fractions.

Now, let's implement these steps:

Step 1: We have the fraction 47\frac{4}{7} and need to divide it by the whole number 5. In terms of fractions, 5 can be written as 51\frac{5}{1}.

Step 2: Change the division into multiplication. This requires us to multiply 47\frac{4}{7} by the reciprocal of 51\frac{5}{1}, which is 15\frac{1}{5}. Thus, the expression becomes:

47÷5=47×15\frac{4}{7} \div 5 = \frac{4}{7} \times \frac{1}{5}

Step 3: Multiply the fractions. To multiply fractions, multiply the numerators and multiply the denominators:

47×15=4×17×5=435\frac{4}{7} \times \frac{1}{5} = \frac{4 \times 1}{7 \times 5} = \frac{4}{35}

Therefore, the final result of dividing 47\frac{4}{7} by 5 is 435\frac{4}{35}.

Answer

435 \frac{4}{35}

Exercise #10

58:2= \frac{5}{8}:2=

Video Solution

Step-by-Step Solution

To solve the problem of dividing the fraction 58\frac{5}{8} by 2, we can follow these steps:

  • Step 1: Understand that dividing by a whole number is the same as multiplying by its reciprocal. That means 58÷2\frac{5}{8} \div 2 is equivalent to 58×12\frac{5}{8} \times \frac{1}{2}.
  • Step 2: Perform the multiplication of fractions. Multiply the numerators and the denominators:

58×12=5×18×2=516 \frac{5}{8} \times \frac{1}{2} = \frac{5 \times 1}{8 \times 2} = \frac{5}{16}

Therefore, the solution to the problem is 516\frac{5}{16}.

Answer

516 \frac{5}{16}

Exercise #11

35:4= \frac{3}{5}:4=

Video Solution

Step-by-Step Solution

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

  • Step 1: Convert the whole number to a fraction and find its reciprocal.
  • Step 2: Multiply the given fraction by this reciprocal.
  • Step 3: Simplify the result, if possible.

Let's tackle each step:
Step 1: Convert 4 4 to a fraction, which is 41 \frac{4}{1} , and find the reciprocal giving 14 \frac{1}{4} .
Step 2: Multiply 35 \frac{3}{5} by 14 \frac{1}{4} to get 35×14=3×15×4=320 \frac{3}{5} \times \frac{1}{4} = \frac{3 \times 1}{5 \times 4} = \frac{3}{20} .
Step 3: The fraction 320 \frac{3}{20} is already in its simplest form.

Therefore, the solution to the problem is 320 \frac{3}{20} .

Answer

320 \frac{3}{20}

Exercise #12

67:2= \frac{6}{7}:2=

Video Solution

Step-by-Step Solution

To solve the problem 67÷2 \frac{6}{7} \div 2 , we need to remember how to divide a fraction by a whole number:

Step 1: Convert the division problem into a multiplication problem by multiplying by the reciprocal of the whole number. The reciprocal of 2 is 12 \frac{1}{2} .

Step 2: Therefore, we rewrite the problem as 67×12 \frac{6}{7} \times \frac{1}{2} .

Step 3: Multiply the numerators together and the denominators together:

6×17×2=614 \frac{6 \times 1}{7 \times 2} = \frac{6}{14}

Step 4: Simplify the fraction 614 \frac{6}{14} by finding the greatest common divisor of 6 and 14, which is 2. Divide both the numerator and the denominator by 2:

6÷214÷2=37 \frac{6 \div 2}{14 \div 2} = \frac{3}{7}

Therefore, the solution to the problem is 37 \frac{3}{7} .

Answer

37 \frac{3}{7}

Exercise #13

34:3= \frac{3}{4}:3=

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Identify the problem as dividing the fraction 34 \frac{3}{4} by the whole number 3.
  • Step 2: Understand that dividing by 3 is equivalent to multiplying by its reciprocal, which is 13 \frac{1}{3} .
  • Step 3: Multiply 34 \frac{3}{4} by 13 \frac{1}{3} .
  • Step 4: Simplify the result if possible.

Let's solve this step-by-step:
Step 1: The given expression is 34÷3 \frac{3}{4} \div 3 .
Step 2: Rewrite the division as a multiplication using the reciprocal: 34×13 \frac{3}{4} \times \frac{1}{3} .
Step 3: Perform the multiplication: 34×13=3×14×3=312 \frac{3}{4} \times \frac{1}{3} = \frac{3 \times 1}{4 \times 3} = \frac{3}{12} .
Step 4: Simplify 312 \frac{3}{12} by dividing the numerator and the denominator by their greatest common divisor, which is 3:
312=3÷312÷3=14\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}.

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

Answer

14 \frac{1}{4}

Exercise #14

910:2= \frac{9}{10}:2=

Video Solution

Step-by-Step Solution

To solve the problem of dividing 910 \frac{9}{10} by 2, follow these steps:

  • Step 1: Identify the reciprocal of the whole number 2. The reciprocal of 2 is 12 \frac{1}{2} .
  • Step 2: Convert the division problem into a multiplication problem using the reciprocal: 910÷2=910×12 \frac{9}{10} \div 2 = \frac{9}{10} \times \frac{1}{2} .
  • Step 3: Perform the multiplication: Multiply the numerators and the denominators.
  • Calculation: 9×110×2=920 \frac{9 \times 1}{10 \times 2} = \frac{9}{20} .
  • Step 4: Simplify the fraction if necessary. In this case, 920 \frac{9}{20} is already in its simplest form.

Therefore, the solution to the problem is 920 \frac{9}{20} .

Upon reviewing the provided choices, we identify that choice 4: 920 \frac{9}{20} is correct.

Answer

920 \frac{9}{20}

Exercise #15

49:6= \frac{4}{9}:6=

Video Solution

Step-by-Step Solution

To solve the problem 49:6 \frac{4}{9} : 6 , we follow these steps:

  • Convert the whole number 66 to its reciprocal, which is 16\frac{1}{6}.
  • Rewrite the division as multiplication: 49×16\frac{4}{9} \times \frac{1}{6}.
  • Multiply the numerators: 4×1=44 \times 1 = 4.
  • Multiply the denominators: 9×6=549 \times 6 = 54.
  • Write the result as a fraction: 454\frac{4}{54}.
  • Simplify the fraction by finding the greatest common divisor of 4 and 54, which is 2.
  • Divide both the numerator and the denominator by 2: 4÷254÷2=227\frac{4 \div 2}{54 \div 2} = \frac{2}{27}.

Therefore, the solution to the problem is 227 \frac{2}{27} .

Answer

227 \frac{2}{27}