﻿ Addition of Mixed Numbers Worksheet | Problems & Solutions • Page 1
1.
$4\frac{3}{7}$ + $2\frac{5}{7}$ a. $6\frac{1}{7}$ b. $1\frac{1}{7}$ c. $\frac{18}{7}$ d. $7\frac{1}{7}$

Solution:

43 / 7 + 25 / 7

= 4 + 2 + 3 / 7 + 5 / 7

= 6 + 8 / 7

= 6 + 11 / 7
[8 / 7 = 7 / 7 + 1 / 7 = 1 + 1 / 7 = 11 / 7.]

= 6 + 1 + 1 / 7

= 71 / 7

2.
$3\frac{4}{7}$ + $2\frac{5}{7}$ a. $5\frac{1}{7}$ b. $\frac{58}{7}$ c. $6\frac{2}{7}$ d. $5\frac{4}{7}$

Solution:

34 / 7 + 25 / 7

= 3 + 2 + 4 / 7 + 5 / 7

= 5 + 4 + 57

= 5 + 9 / 7

= 5 + 12 / 7
[9 / 7 = 7 / 7 + 2 / 7 = 1 + 2 / 7 = 12 / 7.]

= 5 + 1 + 2 / 7

= 62 / 7

3.
$4\frac{4}{5}$ + $2\frac{3}{5}$ a. $7\frac{3}{5}$ b. $\frac{58}{7}$ c. $7\frac{2}{5}$ d. $6\frac{3}{5}$

Solution:

44 / 5 + 23 / 5

= 4 + 2 + 4 / 5 + 3 / 5

= 6 + 4 + 35

= 6 + 7 / 5

= 6 + 12 / 5
[7 / 5 = 5 / 5 + 2 / 5 = 1 + 2 / 5 = 12 / 5.]

= 6 + 1 + 2 / 5

= 72 / 5

4.
Find the sum of $7\frac{2}{5}$ and $5\frac{2}{7}$. a. $12\frac{23}{35}$ b. $12\frac{26}{35}$ c. $12\frac{5}{7}$ d. $12\frac{24}{35}$

5.
Find the sum of $13\frac{3}{10}$ and $10\frac{3}{13}$. a. $23\frac{71}{130}$ b. $23\frac{7}{13}$ c. $23\frac{69}{130}$ d. $23\frac{34}{65}$

6.
Find the sum of $6\frac{4}{5}$ and 4. a. $10\frac{4}{5}$ b. $\frac{4}{5}$ c. $11\frac{4}{5}$ d. $9\frac{4}{5}$

Solution:

645 + 4
[Original fractions.]

= 1045

So, the sum of 64 / 5 and 4 is 104 / 5.

7.
Find the value of $2\frac{1}{3}$ + $\frac{6}{7}$. a. $3\frac{1}{7}$ b. $3\frac{4}{21}$ c. $3\frac{2}{7}$ d. $3\frac{5}{21}$

Solution:

21 / 3 + 6 / 7
[Original fractions.]

= 21×7 / 3×7 + 6×3 / 7×3
[Multiply both the numerator and the denominator of 1 / 3 with 7 and 6 / 7 with 3 to make like fractions.]

= 27 / 21 + 18 / 21
[Simplify.]

= 225 / 21

= 2 + 21+4 / 21

= 2 + 21 / 21+ 4 / 21 = 2 + 1 + 4 / 21

= 34 / 21

The sum of the fractions is 34 / 21.

8.
Find the sum of $13\frac{3}{10}$ and $10\frac{3}{13}$. a. $23\frac{34}{65}$ b. $23\frac{71}{130}$ c. $23\frac{69}{130}$ d. $23\frac{7}{13}$

Solution:

133 / 10 + 103 / 13
[Original fractions.]

= 133×13 / 10×13 + 103×10 / 13×10
[Multiply both the numerator and the denominator of 3 / 10 with 13 and 3 / 13 with 10 to make both the fractions equal.]

= 1339 / 130 + 1030 / 130

= 2369 / 130

9.
Victor, Charles and Mike ate $2\frac{4}{7}$, $3\frac{3}{7}$ and 1 pizzas. How many pizzas did they all eat together? a. 7 b. 6 c. 8 d. 9

Solution:

= 247 + 337 + 1
The number of pizzas they together ate = sum of the pizzas each one ate
[Substitute.]

= 677

= 6 + 1
[Write the fraction 7 / 7as whole number 1 and add it to the whole number.]

= 7

So, they ate 7 pizzas.

10.
Find the sum of $2\frac{3}{10}$, $3\frac{3}{10}$, and $4\frac{3}{10}$. a. $10\frac{1}{10}$ b. $9\frac{9}{10}$ c. $9\frac{4}{5}$ d. 10

Solution:

23 / 10 + 33 / 10 + 43 / 10
[Original fractions.]

= 99 / 10