Mixed Numbers

In this article, we will teach you the basics of everything you need to know about mixed numbers.
If you wish to delve deeper into a specific topic, you can access the corresponding extensive article.

Mixed Number and Fraction Greater Than 1

A fraction that is greater than 1 is a fraction whose numerator is larger than its denominator, this type of fractions can be converted into mixed numbers.

It is important that we remember similar topics:

How do you convert a mixed number to a fraction?

Multiply the whole number by the denominator.
To the obtained product, add the numerator. The final result will be the new numerator.
Nothing is changed in the denominator.

How do you convert an integer to a fraction?

The whole number is written in the numerator and the 1 in the denominator.

You can continue reading in these articles:

Practice Mixed Fractions

Examples with solutions for Mixed Fractions

Exercise #1

4:68= 4:\frac{6}{8}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll proceed as follows:

  • Step 1: Simplify the fraction 68\frac{6}{8}.
  • Step 2: Use the formula for dividing by a fraction by multiplying by its reciprocal.
  • Step 3: Simplify the resulting fraction or convert it to a mixed number.

Let's work through these steps:

Step 1: Simplify 68\frac{6}{8}.
68\frac{6}{8} simplifies to 34\frac{3}{4} by dividing the numerator and the denominator by 2 (the greatest common divisor).

Step 2: Find the reciprocal of 34\frac{3}{4} and multiply it by 4.
The reciprocal of 34\frac{3}{4} is 43\frac{4}{3}.
So, 4÷34=4×43=1634 \div \frac{3}{4} = 4 \times \frac{4}{3} = \frac{16}{3}.

Step 3: Simplify 163\frac{16}{3} to a mixed number.
163\frac{16}{3} can be expressed as 5135\frac{1}{3} since 16 divided by 3 is 5 with a remainder of 1.

Therefore, the solution to the problem is 5135\frac{1}{3}.

Answer

513 5\frac{1}{3}

Exercise #2

1:14= 1:\frac{1}{4}=

Video Solution

Step-by-Step Solution

To solve the division problem 1:14 1 : \frac{1}{4} , we will follow these steps:

  • Step 1: Express the division as a fraction operation: 1÷14 1 \div \frac{1}{4} .
  • Step 2: Use the invert-and-multiply rule. Find the reciprocal of 14\frac{1}{4}, which is 44.
  • Step 3: Multiply the whole number by the reciprocal: 1×4=4 1 \times 4 = 4 .

Thus, after performing these operations, we find that the result of the division 1:14 1 : \frac{1}{4} is 4 4 .

Answer

4 4

Exercise #3

7:78= 7:\frac{7}{8}=

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Rewrite the division as multiplication by the reciprocal of the fraction.
  • Step 2: Perform the multiplication calculation.

Now, let's work through each step:
Step 1: The given problem is 7:78 7:\frac{7}{8} , which means 7÷78 7 \div \frac{7}{8} .
Instead of dividing, multiply by the reciprocal:
7÷78=7×87 7 \div \frac{7}{8} = 7 \times \frac{8}{7} .

Step 2: Perform the multiplication:
7×87=7×87 7 \times \frac{8}{7} = \frac{7 \times 8}{7} .
The 77 in the numerator and denominator cancel each other out, resulting in:
567=8 \frac{56}{7} = 8 .

Therefore, the solution to the problem is 8 8 .

Answer

8 8

Exercise #4

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

Video Solution

Step-by-Step Solution

We need to find the value of 3:23 3:\frac{2}{3} , which means dividing 3 by 23\frac{2}{3}.

To solve this, follow these steps:

  • Step 1: Find the reciprocal of 23\frac{2}{3}. The reciprocal is obtained by swapping the numerator and the denominator, thus the reciprocal of 23\frac{2}{3} is 32\frac{3}{2}.
  • Step 2: Multiply 3 by the reciprocal 32\frac{3}{2}.
  • Step 3: Perform the multiplication: 3×323 \times \frac{3}{2}.

Let's execute these steps:

Step 2: Since multiplying a whole number by a fraction gives:

3×32=3×32=92 3 \times \frac{3}{2} = \frac{3 \times 3}{2} = \frac{9}{2}

Step 3: Convert the improper fraction 92\frac{9}{2} to a mixed number:

Divide 9 by 2 which gives 4 as the quotient and 1 as the remainder. Thus, the mixed number is 4124\frac{1}{2}.

Therefore, the solution to the ratio 3:233:\frac{2}{3} is 412\mathbf{4\frac{1}{2}}.

Answer

412 4\frac{1}{2}

Exercise #5

3:57= 3:\frac{5}{7}=

Video Solution

Step-by-Step Solution

To divide the whole number 3 by the fraction 57\frac{5}{7}, we follow these steps:

  • Step 1: Identify the reciprocal of the fraction. The reciprocal of 57\frac{5}{7} is 75\frac{7}{5}.
  • Step 2: Multiply the whole number 3 by this reciprocal.
  • Step 3: Perform the multiplication to find the result.

Let's calculate this:
Step 1: The reciprocal of 57\frac{5}{7} is 75\frac{7}{5}.
Step 2: Multiply: 3×75=3×75=2153 \times \frac{7}{5} = \frac{3 \times 7}{5} = \frac{21}{5}.
Step 3: Convert the improper fraction 215\frac{21}{5} to a mixed number:

  • Divide 21 by 5. It goes 4 times with a remainder of 1.
  • The quotient is 4, and the remainder is 1. Therefore, 215=415\frac{21}{5} = 4\frac{1}{5}.

Thus, the solution to 3:573 : \frac{5}{7} is 4154\frac{1}{5}.

The correct choice among the given answers is: 4154\frac{1}{5}.

Answer

415 4\frac{1}{5}

Exercise #6

3:56= 3:\frac{5}{6}=

Video Solution

Step-by-Step Solution

To solve this problem, let's carry out the following steps:

  • Step 1: Recognize that the expression 3:56 3 : \frac{5}{6} represents division, so it becomes 3÷56 3 \div \frac{5}{6} .
  • Step 2: Use the rule that dividing by a fraction is the same as multiplying by its reciprocal. Thus, convert this to 3×65 3 \times \frac{6}{5} .
  • Step 3: Multiply 3 (which can be written as 31\frac{3}{1}) by 65\frac{6}{5}:
    31×65=3×61×5=185\frac{3}{1} \times \frac{6}{5} = \frac{3 \times 6}{1 \times 5} = \frac{18}{5}.
  • Step 4: Convert 185\frac{18}{5} to a mixed number. Divide 18 by 5:
    - 5 goes into 18 three times with a remainder of 3.
    - Therefore, 185=335\frac{18}{5} = 3\frac{3}{5}.

Thus, the solution to the problem is 335 3\frac{3}{5} .

Answer

335 3\frac{3}{5}

Exercise #7

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

Video Solution

Step-by-Step Solution

To solve the problem 4:47 4 : \frac{4}{7} , we'll apply the concept of dividing by a fraction:

Step 1: Convert the division to multiplication by the reciprocal of the fraction. The reciprocal of 47 \frac{4}{7} is 74 \frac{7}{4} .

Thus, the expression 4:47 4 : \frac{4}{7} is equivalent to 4×74 4 \times \frac{7}{4} .

Step 2: Perform the multiplication:

4×74=41×74 4 \times \frac{7}{4} = \frac{4}{1} \times \frac{7}{4}

Step 3: Multiply the numerators and the denominators:

4×71×4=284 \frac{4 \times 7}{1 \times 4} = \frac{28}{4}

Step 4: Simplify the fraction:

284=7 \frac{28}{4} = 7

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

Answer

7 7

Exercise #8

2:25= 2:\frac{2}{5}=

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Find the reciprocal of the fraction 25\frac{2}{5}.
  • Step 2: Multiply the whole number 2 by this reciprocal.
  • Step 3: Simplify the result, if necessary.

Now, let's work through each step:
Step 1: The reciprocal of the fraction 25\frac{2}{5} is 52\frac{5}{2}.
Step 2: Multiply the whole number 2 by 52\frac{5}{2}:

2×52=2×52=102 2 \times \frac{5}{2} = \frac{2 \times 5}{2} = \frac{10}{2}

Step 3: Simplify 102\frac{10}{2}:
Divide 10 by 2, which gives us 5.

Therefore, the solution to the problem is 5 5 .

Answer

5 5

Exercise #9

1:34= 1:\frac{3}{4}=

Video Solution

Step-by-Step Solution

To solve this problem, let's divide 11 by 34\frac{3}{4}. The solution involves converting the division into a multiplication:

  • Step 1: Recognize 1:34\,1:\frac{3}{4}\, as the division 134\frac{1}{\frac{3}{4}}.

  • Step 2: Convert division into multiplication: 134=1×43\frac{1}{\frac{3}{4}} = 1 \times \frac{4}{3}.

  • Step 3: Compute the multiplication: 1×43=431 \times \frac{4}{3} = \frac{4}{3}.

  • Step 4: Convert 43\frac{4}{3} into a mixed number: 1131\frac{1}{3}.

Therefore, the solution to the division 1:341 : \frac{3}{4} is 113 1\frac{1}{3}

The correct answer is (113)(1 \frac{1}{3}).

Answer

113 1\frac{1}{3}

Exercise #10

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

Video Solution

Step-by-Step Solution

To solve the expression 2:232:\frac{2}{3}, follow these steps:

  • Step 1: Rewrite the expression as a division problem:
    This means 2÷232 \div \frac{2}{3}.
  • Step 2: Convert the division to a multiplication by using the reciprocal:
    The reciprocal of 23\frac{2}{3} is 32\frac{3}{2}.
  • Step 3: Multiply by the reciprocal:
    2×32=2321=62=32 \times \frac{3}{2} = \frac{2 \cdot 3}{2 \cdot 1} = \frac{6}{2} = 3.

Therefore, the solution to the problem is 3 3 .

Answer

3 3

Exercise #11

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

Video Solution

Step-by-Step Solution

To solve the problem 4:35 4:\frac{3}{5} , follow these steps:

  • Step 1: Convert the division into a multiplication by using the reciprocal of 35\frac{3}{5}. The reciprocal is 53\frac{5}{3}.
  • Step 2: Multiply the whole number 4 by 53\frac{5}{3}:
    4×53=4×53=203 4 \times \frac{5}{3} = \frac{4 \times 5}{3} = \frac{20}{3}
  • Step 3: Simplify 203\frac{20}{3} to a mixed number:
    Perform the division 20÷320 \div 3, which gives 6 as a whole number and leaves a remainder of 2.
  • Thus, 203\frac{20}{3} as a mixed number is 623 6\frac{2}{3} .

Therefore, the solution to the problem is 623 6\frac{2}{3} .

Answer

623 6\frac{2}{3}

Exercise #12

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

Video Solution

Step-by-Step Solution

To solve the problem 3:34 3:\frac{3}{4} , we must perform division of the whole number 3 by the fraction 34\frac{3}{4}. Here are the steps:

  • Step 1: Recall the rule for dividing by a fraction. Dividing by 34\frac{3}{4} is the same as multiplying by its reciprocal, 43\frac{4}{3}.
  • Step 2: Rewrite the expression as a multiplication problem: 3×433 \times \frac{4}{3}.
  • Step 3: Perform the multiplication: 3×43=3×43=1233 \times \frac{4}{3} = \frac{3 \times 4}{3} = \frac{12}{3}.
  • Step 4: Simplify the fraction: 123=4\frac{12}{3} = 4.

The solution to the division 3:34 3:\frac{3}{4} is 4 4 .

Answer

4 4

Exercise #13

5:25= 5:\frac{2}{5}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll perform the division 5÷25 5 \div \frac{2}{5} by converting it into multiplication:

  • Step 1: Recognize that dividing by a fraction is the same as multiplying by its reciprocal.
  • Step 2: Convert the division into multiplication: 5÷25=5×52 5 \div \frac{2}{5} = 5 \times \frac{5}{2} .
  • Step 3: Multiply the whole number by the reciprocal of the fraction: 5×52=252 5 \times \frac{5}{2} = \frac{25}{2} .
  • Step 4: Convert the improper fraction to a mixed number: 252=1212 \frac{25}{2} = 12 \frac{1}{2} .

Through these steps, we find that the solution to the division problem is 1212 12 \frac{1}{2} .

Answer

1212 12\frac{1}{2}

Exercise #14

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

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the reciprocal of the divisor.
  • Step 2: Multiply the dividend by the reciprocal.

Now, let's work through each step:
Step 1: The divisor is 12 \frac{1}{2} . The reciprocal of 12 \frac{1}{2} is 2.

Step 2: Multiply the dividend, which is 3, by the reciprocal of the divisor:
3×2=6 3 \times 2 = 6

Therefore, the solution to the problem is 6 6 .

Answer

6 6

Exercise #15

1:23= 1:\frac{2}{3}=

Video Solution

Step-by-Step Solution

We need to evaluate the expression 1÷23 1 \div \frac{2}{3} .

To do this, we use the principle that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, the expression becomes:

1×32 1 \times \frac{3}{2} .

Next, we multiply the whole number by the reciprocal:

1×32=32 1 \times \frac{3}{2} = \frac{3}{2} .

To express 32\frac{3}{2} as a mixed number, we write it as:

112 1\frac{1}{2} .

Thus, the solution to the problem is 112 1\frac{1}{2} , which matches choice 3 from the options provided.

Answer

112 1\frac{1}{2}