#### Solved Examples and Worksheet for Adding Mixed Numbers-Unlike Denominators

Q1Find the sum of 713 and 349.
A. 1069
B. 1079
C. 979
D. 1059

Step: 1
713+ 349
[Original equation.]
Step: 2
= 739 + 349
[Rewrite the fractions of the mixed numbers using the LCD, 9.]
Step: 3
= 1079
Q2Find: 3123 + 6334

A. 414
B. 95512
C. 3
D. 523

Step: 1
3123 + 6334
[Original expression.]
Step: 2
= (31 + 63) + (23 + 34)
[Separate whole numbers from fractions.]
Step: 3
= (31 + 63) + (812 + 912)
[Use the LCD, 12 to rewrite the fractions with same denominator.]
Step: 4
= 94 + 1712
[Add the whole numbers and the fractions.]
Step: 5
= 94 + 1512
[Convert improper fraction into mixed number.]
Step: 6
= 95512
Q3Find the sum of 514 and 415.

A. 9920
B. 925
C. 912
D. 91120

Step: 1
514 + 415
[Original fractions.]
Step: 2
= 51×54×5 + 41×45×4
[Multiply both the numerator and the denominator of 14 with 5 and 15 with 4 to make both the fractions equal.]
Step: 3
= 5520 + 4420
Step: 4
= 9920
Q4What is the value of 7136 + 216?

A. 9736
B. 71216
C. 9136
D. 716

Step: 1
7136+ 216
[Original fractions.]
Step: 2
= 7136 + 21×66×6
[Multiply both the numerator and the denominator of 16 with 6 to make both the fractions equal.]
Step: 3
= 7136 + 2636
Step: 4
= 9736
Step: 5
So, the value of 7136 + 216 is 9736.
Q5What is the sum of 345 and 613?

A. 10215
B. 1015
C. 10415
D. 10115

Step: 1
345 + 613
[Original fractions.]
Step: 2
= 34 × 35 × 3 + 61 × 53 × 5
[Multiply both the numerator and the denominator of 45 with 3 and 13 with 5 to make both the denominators of the fractions equal.]
Step: 3
= 31215 + 6515
Step: 4
= 91715
Step: 5
= 9 + 1215
[1715 = 1515 + 215 = 1215.]
Step: 6
= 10215
Step: 7
So, 345 + 613 is 10215.
Q6Which of the following is the sum of 212, 334, and 434?

A. 9113
B. 1114
C. 13
D. 11

Step: 1
212 + 334 + 434
[Original mixed numbers.]
Step: 2
= 224 + 334 + 434
[Rewrite the fractional part in the mixed number 212 with a denominator of 4.]
Step: 3
= 984
Step: 4
= 9 + 2
[Write the fraction 84 as 2.]
Step: 5
= 11
Q7Find the sum of the mixed numbers 513 and 316.

A. 836
B. 236
C. 356
D. 336

Step: 1
513 + 316
[Original mixed numbers.]
Step: 2
= 52 × 12 × 3 + 316
[Rewrite the fractional part in the mixed number 513 with a denominator of 6.]
Step: 3
= 526 + 316
[Simplify.]
Step: 4
= 836
Q8Find the sum of the mixed numbers 212 and 414.

A. 634
B. 134
C. 454

Step: 1
212 + 414
[Original mixed numbers.]
Step: 2
= 22 × 12 × 2 + 414
[Rewrite the fractional part in the mixed number 212 with a denominator of 4.]
Step: 3
= 224 + 414
[Simplify.]
Step: 4
= 634
Q9Find the sum of the mixed numbers 412 and 623.

A. 1016
B. 1216
C. 1156
D. 1116

Step: 1
412 + 623
[Original mixed numbers.]
Step: 2
= (4 × 2) + 12 + (6 × 3) + 23
[Change to improper fractions.]
Step: 3
= 92 + 203
[Simplify.]
Step: 4
= 9 × 36 + 20 × 26
[Multiply the numerator and the denominator of 92 by 3 and 203 by 2 to make the denominators of both the fractions equal.]
Step: 5
= 276 + 406
[Simplify.]
Step: 6
= 676
[Simplify.]
Step: 7
= 1116
Q10Find the sum of 314 and 115.
A. 4920
B. 51120
C. 5920
D. 3920

Step: 1
314 + 115 = (3 × 4) + 14 + (1 × 5) + 15
[Change the mixed numbers to improper fractions.]
Step: 2
= 12 + 14 + 5 + 15
Step: 3
= 134 + 65
Step: 4
= 13 × 54 × 5 + 6 × 45 × 4
[Multiply both the numerator and denominator of 134 with 5 and 65 with 4 to make both the fractions have same denominator.]
Step: 5
= 6520 + 2420
[Multiply.]
Step: 6
= 65 + 2420
[Add the fractions as the denominators are same.]
Step: 7
= 8920