#### Solved Examples and Worksheet for Dividing Rational Numbers

Q1Find the quotient:
67 ÷ 34

A. 1828
B. 78
C. 87
D. 228

Step: 1
67 ÷ 34
[Original expression.]
Step: 2
= 67 × 43
[Multiply 67 by 43, the reciprocal of 34.]
Step: 3
= 27 × 41
[Cancel 6 with 3.]
Step: 4
= 2 × 47 × 1
[Multiply the numerators and the denominators separately.]
Step: 5
= 87
[Simplify.]
Q2Find the quotient:
3 ÷ 23

A. 412
B. 29
C. 323
D. 2

Step: 1
3 ÷ 23
[Original expression.]
Step: 2
= 31 ÷ 23
[Write the whole number 3 as a fraction with denominator of 1.]
Step: 3
= 31 × 32
[Multiply 31 by the reciprocal of 23.]
Step: 4
= 3 × 31 × 2
[Multiply the numerators and the denominators.]
Step: 5
= 92 = 412
[Convert improper fraction into mixed number.]
Q3Find the quotient:
2016 ÷ 215

A. 916
B. 221130
C. 655
D. 20815

Step: 1
2016 ÷ 215
[Divide 2016 by 215.]
Step: 2
= 1216 ÷ 115
[Rewrite the mixed numbers as improper fractions.]
Step: 3
= 1216 × 511
[Multiply 1216 by the reciprocal of 115.]
Step: 4
= 116 × 51
[Cancel 121 with 11.]
Step: 5
= 11 × 56 × 1
[Multiply the numerators and the denominators.]
Step: 6
= 556 = 916
[Rewrite the improper fraction as mixed fraction.]
Q4Find the quotient obtained when 3 is divided by 713.
A. 322
B. 922
C. 111
D. 411

Step: 1
3 ÷ 713
[Original expression.]
Step: 2
= 31 ÷ 713
[Rewrite the whole number 3, as a fraction with denominator 1.]
Step: 3
= 31 ÷ 223
[Rewrite the mixed number as improper fraction.]
Step: 4
= 31 × 322
[Multiply 31 by the reciprocal of 223.]
Step: 5
= 3 × 31 × 22
[Multiply the numerators and the denominators.]
Step: 6
= 922

Q5Jeff has a rope that measures 513 in. He wants to cut it into pieces each measuring 113 in. long. How many pieces would he get?

A. 3
B. 4
C. 5
D. 6

Step: 1
513 ÷ 113
[Original expression.]
Step: 2
= 163 ÷ 43
[Rewrite the mixed numbers as improper fractions.]
Step: 3
= 163 × 34
[Multiply 163 by the reciprocal of 43.]
Step: 4
= 41 × 11
[Cancel 3 with 3 and 16 with 4.]
Step: 5
= 4
[Simplify.]
Step: 6
Jeff gets 4 pieces.
Q6How many 110 oz are there in 12 lb?

A. 90
B. 70
C. 80
D. 100

Step: 1
12 lb = 162 oz = 8 oz
[Since 1 lb = 16 oz.]
Step: 2
8 ÷ 110
[Divide 8 by 110.]
Step: 3
= 81 ÷ 110
[Rewrite the whole number 8 as a fraction, with the denominator 1.]
Step: 4
= 81 × 101
[Multiply 81 with the reciprocal of 110.]
Step: 5
= 8 × 101 × 1
[Multiply the numerators and denominators.]
Step: 6
= 80
[Simplify.]
Step: 7
There are 80, 110 oz in 12 lb.
Q7Simplify: 12 ÷ 413

A. 9
B. 21013
C. 3641
D. 52

Step: 1
12 ÷ ( 413)
[Original expression.]
Step: 2
= 121 ÷ 133
[Rewrite the number 12 as a fraction and the mixed number 413 as an improper fraction.]
Step: 3
121 × 313
[ab ÷ cd = ab × dc.]
Step: 4
= (12)(3)(1)(13)
[ab × cd = acbd.]
Step: 5
= 3613
[Simplify the numerator and denominator.]
Step: 6
= 21013
[Rewrite the fraction as a mixed fraction.]
Step: 7
The simplified value of 12 ÷ 413 is 21013 .
Q8Simplify: 617 ÷ 919
A. 352663
B. 67
C. 549637
D. 387574

Step: 1
617 ÷ 919
[Original expression.]
Step: 2
= 437 ÷ 829
[Rewrite the mixed fractions as improper fractions.]
Step: 3
= 437 × 982
[ab ÷ cd = ab × dc.]
Step: 4
= (43)(9)(7)(82)
[ab × cd = acbd.]
Step: 5
= 387574
[Simplify the numerator and denominator.]
Step: 6
The simplified value of 617 ÷ 919 is 387574 .
Q9Simplify:
712 ÷ 113

A. 744
B. 447
C. 144
D. 17

Step: 1
712 ÷ 113
[Original expression.]
Step: 2
= 712 × 311
[Multiply by the reciprocal of 113 which is 311.]
Step: 3
= 7 × 312 × 11
Step: 4
= 7 × 14 × 11
[Cancel 12 with 3. ]
Step: 5
= 744
[Simplify.]
Q10Simplify:
47 ÷ 37

A. 43
B. 13
C. 14
D. 34

Step: 1
47 ÷ 37
[Original expression.]
Step: 2
= 47 × 73
[Multiply by the reciprocal of 37.]
Step: 3
= 4 × 77 × 3
[Multiply the numerators and the denominators.]
Step: 4
= 43
[Simplify.]
Q11Simplify the expression.
411 ÷ 211

A. 12
B. 12
C. 2
D. 3

Step: 1
411 ÷ 211
[Original expression.]
Step: 2
= 411 × 112
[Multiply by the reciprocal of 211.]
Step: 3
= 4 × 1111 × 2
[Multiply the numerators and the denominators.]
Step: 4
= 2
[Simplify.]
Q12Simplify the expression.
149 ÷ 73

A. 1
B. 12
C. 34
D. 23

Step: 1
149 ÷ 73
[Original expression.]
Step: 2
= 149 × 37
[Multiply by the reciprocal of 73.]
Step: 3
= 14 × 39 × 7
[Multiply the numerators and the denominators.]
Step: 4
= 23
[Simplify.]
Q13Find the number that makes the number sentence true.
335 ÷ 7 = ?

A. 1835
B. 1265
C. 37
D. 3518

Q14Divide: (- 240) ÷ 40

A. - 6
B. - 60
C. 6
D. 160

Step: 1
(- 240) ÷ 40
[Given expression.]
Step: 2
= - 6
[The quotient of a negative integer and a positive integer is negative.]
Correct Answer is :   - 6
Q15Divide: (- 560) ÷ 35

A. 16
B. 116
C. - 6
D. - 16

Step: 1
(- 560) ÷ 35
[Given expression.]
Step: 2
= - 16
[The quotient of a negative integer and a positive integer is negative.]
Correct Answer is :   - 16