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

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 #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

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 #4

7×68= 7\times\frac{6}{8}=

Video Solution

Step-by-Step Solution

To solve the multiplication of an integer with a fraction, we need to follow these steps:

  • Step 1: Multiply the integer 7 by the numerator of the fraction, which is 6.
  • Step 2: Keep 8 as the denominator.
  • Step 3: Simplify the resulting fraction.
  • Step 4: Convert to a mixed number if needed.

Now, let's work through each step:

Step 1: Multiply 7 by 6, which gives us 42 42 as the numerator.

Step 2: The denominator remains 8, so we have the fraction 428\frac{42}{8}.

Step 3: Simplify 428\frac{42}{8} by finding the greatest common divisor (GCD) of 42 and 8. The GCD is 2.

We divide the numerator and the denominator by 2: 42÷28÷2=214\frac{42 \div 2}{8 \div 2} = \frac{21}{4}.

Step 4: Convert 214\frac{21}{4} into a mixed number:

Divide 21 by 4, which equals 5 with a remainder of 1. Thus, 214\frac{21}{4} is equivalent to the mixed number 5145\frac{1}{4}.

Therefore, the solution to the problem is 5145\frac{1}{4}.

Answer

514 5\frac{1}{4}

Exercise #5

8×59= 8\times\frac{5}{9}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying 88 by 59\frac{5}{9}, we can follow these steps:

  • Step 1: Convert the whole number 88 into a fraction by expressing it as 81\frac{8}{1}.
  • Step 2: Multiply the numerators together: 8×5=408 \times 5 = 40.
  • Step 3: Multiply the denominators together: 1×9=91 \times 9 = 9.
  • Step 4: Write the product as a fraction: 409\frac{40}{9}.
  • Step 5: Convert the improper fraction 409\frac{40}{9} into a mixed number:
    • Divide 40 by 9, which gives 4 (quotient) with a remainder of 4.
    • Write the mixed number as 4494\frac{4}{9}.

Therefore, the solution to the multiplication problem 8×598 \times \frac{5}{9} is 449 4\frac{4}{9} .

Answer

449 4\frac{4}{9}

Exercise #6

10×79= 10\times\frac{7}{9}=

Video Solution

Step-by-Step Solution

To solve the problem 10×79 10 \times \frac{7}{9} , we follow these steps:

  • Step 1: Multiply the whole number by the numerator. Calculate 10×7=70 10 \times 7 = 70 .
  • Step 2: Divide this product by the denominator. Calculate 709 \frac{70}{9} .
  • Step 3: If the result is an improper fraction, convert it to a mixed number. Divide 70 by 9, which goes 7 times with a remainder of 7. This can be expressed as the mixed number 779 7\frac{7}{9} .

Let's work through each step:
Step 1: Multiply 10 by 7 to get 70.
Step 2: Divide 70 by 9 to get 7 remainder 7.
Step 3: The proper whole number from the division is 7, with the remainder over the original fraction denominator giving us the final fraction 79 \frac{7}{9} .

Thus, the product 10×79 10 \times \frac{7}{9} is 779 7\frac{7}{9} .

Answer

779 7\frac{7}{9}

Exercise #7

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 #8

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 #9

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 #10

6×34= 6\times\frac{3}{4}=

Video Solution

Step-by-Step Solution

To solve the problem 6×346 \times \frac{3}{4}, we follow these steps:

  • Step 1: Express the integer 6 as a fraction: 61 \frac{6}{1} .
  • Step 2: Multiply the fractions: 61×34\frac{6}{1} \times \frac{3}{4} .
  • Step 3: Multiply the numerators: 6×3=186 \times 3 = 18.
  • Step 4: Multiply the denominators: 1×4=41 \times 4 = 4.
  • Step 5: Form the resulting fraction: 184\frac{18}{4}.
  • Step 6: Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 2: 184÷22=92\frac{18}{4} \div \frac{2}{2} = \frac{9}{2}.
  • Step 7: Convert 92\frac{9}{2} to a mixed number: Divide 9 by 2 to get 4 with a remainder of 1, thus 92=412\frac{9}{2} = 4\frac{1}{2}.

Therefore, the solution to the problem is 412 4\frac{1}{2} .

Answer

412 4\frac{1}{2}

Exercise #11

7×25= 7\times\frac{2}{5}=

Video Solution

Step-by-Step Solution

To solve the problem 7×25 7 \times \frac{2}{5} , we will follow a structured approach:

  • Step 1: Multiply the whole number by the numerator of the fraction.
  • Step 2: Retain the denominator of the fraction.
  • Step 3: Simplify the resulting fraction, if possible.

Let's work through each step:

Step 1: Multiply the whole number by the numerator.
We have 7×2=14 7 \times 2 = 14 .

Step 2: Keep the denominator the same.
The resulting fraction is 145\frac{14}{5}.

Step 3: Convert the improper fraction to a mixed number if possible.
Divide the numerator by the denominator: 14÷5=2 14 \div 5 = 2 with a remainder of 4 4 .
This results in the mixed number 245 2\frac{4}{5} .

Therefore, the solution to the problem 7×25 7 \times \frac{2}{5} is 245 2\frac{4}{5} , which corresponds to choice 3 in the provided options.

Answer

245 2\frac{4}{5}

Exercise #12

8×12= 8\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this mathematical problem, we need to multiply a whole number, 8, with the fraction, 12\frac{1}{2}.

Here are the steps:

  • Step 1: Identify the given values. The integer is 8 and the fraction is 12\frac{1}{2}.
  • Step 2: Apply the multiplication formula for an integer and a fraction: a×bc=a×bc a \times \frac{b}{c} = \frac{a \times b}{c} .
  • Step 3: Multiply the integer by the numerator of the fraction: 8×1=8 8 \times 1 = 8 .
  • Step 4: Divide the result by the denominator of the fraction: 82=4\frac{8}{2} = 4.
  • Step 5: Simplify the fraction if necessary. In this case, 82\frac{8}{2} simplifies directly to 4.

Therefore, the multiplication of 8 by 12\frac{1}{2} is 4 4 .

In the context of the multiple-choice options provided, the correct answer is choice (4): 4 4 .

Answer

4 4

Exercise #13

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 #14

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 #15

3×67= 3\times\frac{6}{7}=

Video Solution

Step-by-Step Solution

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

  • Convert the whole number into a fraction.
  • Multiply the fractions.
  • Simplify the result.

Now, let's work through each step:

Step 1: Convert the whole number 3 into a fraction:
3 becomes 31 \frac{3}{1} .

Step 2: Multiply the fraction 31 \frac{3}{1} by 67 \frac{6}{7} :
The numerators are 3×6=18 3 \times 6 = 18 .
The denominators are 1×7=7 1 \times 7 = 7 .
The result is 187 \frac{18}{7} .

Step 3: Convert 187 \frac{18}{7} to a mixed number:
Divide the numerator by the denominator: 18 divided by 7 is 2 with a remainder of 4.
Thus, 187=247 \frac{18}{7} = 2\frac{4}{7} .

Therefore, the solution to the problem is 247 2\frac{4}{7} .

Answer

247 2\frac{4}{7}