How to Divide Mixed Numbers

How to Divide Mixed Numbers

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A mixed number is a combination of two numbers: a whole number and a proper fraction (A proper fraction is a fraction which has a denominator which is greater than the numerator, i.e., 23, 47, 56 , etc.). Moreover, a mixed number can be converted into a fraction and it always lies between two whole numbers.

For ex: Let's take the mixed number 134. So, this mixed number comprises of two parts, a whole number which is 1 and a proper fraction 34. Now, if we convert this mixed number into an improper fraction which is 74 we find that it lies between the two whole numbers 1 and 2.
Some other examples of a mixed number are 212, 313, 415, etc.

Parts of a mixed number

A mixed number consists of three distinct parts: a whole number, a numerator and a denominator. Here, the numerator and the denominator are the parts of the proper fraction.

How to Convert Improper Fractions to Mixed Fractions

  1. First, we need to divide the numerator of the fraction by the denominator.
  2. Next, we need to write down the quotient as the whole number of the mixed fraction.
  3. Now, the remainder becomes the numerator and the divisor becomes the denominator of the improper part.

Ex: Let’s take the improper fraction 53
Now, when we divide 5 by 3, the quotient is 1. Also, the remainder is 2 and the divisor 3. So, the mixed number is 123.

Steps to Divide Mixed Numbers

To Divide two mixed numbers, follow these steps.

  1. Convert the mixed numbers into improper fractions, separately.
  2. Now Divide these improper fractions by changing the division sign into the multiplication sign. To do this, just flip the second fraction.
  3. Write the answer in the lowest terms.

Ex: Let’s divide 413÷215
So, the Division becomes (133÷115)=133×511=6533=13233

Free printable Worksheets

Related Topics

How to Add Mixed Numbers
How to Subtract Mixed Numbers
How to Divide Mixed Numbers
How to Convert Between Fractions, Decimals, and Mixed Numbers

Exercises for Dividing Mixed Numbers

1) 654 ÷ 223= 

2) 434 ÷ 147= 

3) 772 ÷ 434= 

4) 1043 ÷ 3510= 

5) 872 ÷ 764= 

6) 1072 ÷ 779= 

7) 796 ÷ 545= 

8) 553 ÷ 287= 

9) 10810 ÷ 179= 

10) 1083 ÷ 217= 

1) 654 ÷ 223= (6×4+5) × 34×(2×3+2)=8732= 22332
Solution:
Step 1:
Convert mixed numbers to fractions, 654=294   and  223=83
Step 2: Apply the fractions rule for multiplication, 294 ÷ 83= 294 × 38=  8732= 22332
2) 434 ÷ 147= (4×4+3) × 74×(1×7+4)=13344= 3144
Solution:
Step 1:
 Convert mixed numbers to fractions, 434=194   and  147=117
Step 2: Apply the fractions rule for multiplication, 194 ÷ 117= 194 × 711=  13344= 3144
3) 772 ÷ 434= (7×2+7) × 42×(4×4+3)=8438= 2838
Solution:
Step 1:
 Convert mixed numbers to fractions, 772=212   and  434=194
Step 2: Apply the fractions rule for multiplication, 212 ÷ 194= 212 × 419=  8438= 2838
4) 1043 ÷ 3510=  (10×2+3) × 102×(3×10+5)=6821= 3521
Solution:
Step 1:
 Convert mixed numbers to fractions, 1043=343   and  3510=3510
Step 2: Apply the fractions rule for multiplication, 343 ÷ 3510= 343 × 1035=  682= 3521
5) 872 ÷ 764= (8×2+7) × 42×(7×4+6)=9268= colorred1617
Solution:
Step 1:
 Convert mixed numbers to fractions, 872=232   and  764=344
Step 2: Apply the fractions rule for multiplication, 232 ÷ 344=  232 × 434=  9268= 1617
6) 1072 ÷ 779= (10×2+7) × 92×(7×9+7)=243140= 1103140
Solution:
Step 1:
 Convert mixed numbers to fractions, 1072=272   and  779=709
Step 2: Apply the fractions rule for multiplication, 232 ÷ 344= 272 × 970=  243140= 1103140
7) 796 ÷ 545= (7×6+9) × 56×(5×5+4)=255174= 12758
GCF(255,174) = 3
Solution:
Step 1:
 Convert mixed numbers to fractions, 796=516   and  545=295
Step 2: Apply the fractions rule for multiplication, 516 ÷ 295= 516 × 529=  255174= 12758
8) 553 ÷ 287= (5×3+5) × 73×(2×7+8)=14066= 2433
GCF(140,66) = 2
Solution:
Step 1:
 Convert mixed numbers to fractions, 553=203   and  287=227
Step 2: Apply the fractions rule for multiplication, 203 ÷ 227= 203 × 722=  14066= 2433
9) 10810 ÷ 179= (10×10+8) × 910×(1×9+7)=972160= 6340
GCF(972,160) = 6
Solution:
Step 1:
 Convert mixed numbers to fractions, 10810=10810   and  179=169
Step 2: Apply the fractions rule for multiplication, 10810 ÷ 169= 10810 × 916=  972160= 6340
10) 1083 ÷ 217= (10×3+8) × 73×(2×7+1)=26645= 54145
Solution:
Step 1:
 Convert mixed numbers to fractions, 1083=383   and  179=169
Step 2: Apply the fractions rule for multiplication 383 ÷ 169= 383 × 916=  26645= 54145

Dividing Mixed Numbers Quiz