Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 6.6 Adding Mixed Numbers with Unlike Denominators will engage students and is a great way of informal assessment.

Question 1.
1$$\frac{2}{3}$$ + 3$$\frac{1}{5}$$
1$$\frac{2}{3}$$ + 3$$\frac{1}{5}$$ = 4$$\frac{13}{15}$$

Explanation:
1$$\frac{2}{3}$$ + 3$$\frac{1}{5}$$
= {[(1× 3) + 2] ÷ 3} + {[(3 × 5) + 1] ÷ 5}
= [(3 + 2) ÷ 3] + [(15 + 1) ÷ 5]
= $$\frac{5}{3}$$ + $$\frac{16}{5}$$

Question 2.
4$$\frac{1}{7}$$ + 3$$\frac{3}{5}$$
4$$\frac{1}{7}$$ + 3$$\frac{3}{5}$$ = 7$$\frac{26}{35}$$

Explanation:
4$$\frac{1}{7}$$ + 3$$\frac{3}{5}$$
= {[(4 × 7) + 1] ÷ 7} + {[(3 × 5) + 3] ÷ 5}
= [(28 + 1) ÷ 7] + [(15 + 3) ÷ 5]
= (29 ÷ 7) + (18 ÷ 5)
=

Question 3.
5$$\frac{1}{9}$$ + 2$$\frac{3}{7}$$
5$$\frac{1}{9}$$ + 2$$\frac{3}{7}$$ = 7$$\frac{34}{63}$$

Explanation:
5$$\frac{1}{9}$$ + 2$$\frac{3}{7}$$
= {[(5 × 9) + 1] ÷ 9} + {[(2 × 7) + 3] ÷ 7}
= [(45 + 1) ÷ 9] + [(14 + 3) ÷ 7]
= (46 ÷ 9) + (17 ÷ 7)

Question 4.
1$$\frac{2}{3}$$ + 4$$\frac{1}{16}$$
1$$\frac{2}{3}$$ + 4$$\frac{1}{16}$$ = 5$$\frac{35}{48}$$

Explanation:
1$$\frac{2}{3}$$ + 4$$\frac{1}{16}$$
= {[(1 × 3) + 2] ÷ 3} + {[(4 × 16) + 1] ÷ 16}
= [(3 + 2) ÷ 3] + [(64 + 1) ÷ 16]
= (5 ÷ 3) + (65 ÷ 16)

Question 5.
10$$\frac{3}{7}$$ + 2$$\frac{3}{11}$$
10$$\frac{3}{7}$$ + 2$$\frac{3}{11}$$ = 12$$\frac{54}{77}$$

Explanation:
10$$\frac{3}{7}$$ + 2$$\frac{3}{11}$$
= {[(10 × 7) + 3] ÷ 7} + {[(2 × 11) + 3] ÷ 11}
= [(70 + 3) ÷ 7] + [(22 + 3) ÷ 11]
= (73 ÷ 7) + (25 ÷ 11)

Question 6.
3$$\frac{1}{4}$$ + 5$$\frac{2}{9}$$
3$$\frac{1}{4}$$ + 5$$\frac{2}{9}$$ = 8$$\frac{17}{36}$$

Explanation:
3$$\frac{1}{4}$$ + 5$$\frac{2}{9}$$
= {[(3 × 4) + 1] ÷ 4} + {[(5 × 9) + 2] ÷ 9}
= [(12 + 1) ÷ 4] + [(45 + 2) ÷ 9]
= (13 ÷ 4) + (47 ÷ 9)

Question 7.
11$$\frac{2}{7}$$ + 12$$\frac{3}{8}$$
11$$\frac{2}{7}$$ + 12$$\frac{3}{8}$$ = 23$$\frac{37}{56}$$

Explanation:
11$$\frac{2}{7}$$ + 12$$\frac{3}{8}$$
= {[(11 × 7) + 2] ÷ 7} + {[(12 × 8) + 3] ÷ 8}
= [(77 + 2) ÷ 7] + [(96 + 3) ÷ 8]
= (79 ÷ 7) + (99 ÷ 8)

Question 8.
12$$\frac{5}{6}$$ + 1$$\frac{1}{15}$$
12$$\frac{5}{6}$$ + 1$$\frac{1}{15}$$ = 13$$\frac{9}{10}$$

Explanation:
12$$\frac{5}{6}$$ + 1$$\frac{1}{15}$$
= {[(12 × 6) + 5] ÷ 6} + {[(1 × 15) + 1] ÷ 15}
= [(72 + 5) ÷ 6] + [(15 + 1) ÷ 15]
= (77 ÷ 6) + (16 ÷ 15)

Question 9.

13$$\frac{2}{7}$$ + 3$$\frac{2}{9}$$ = 16$$\frac{32}{63}$$

Explanation:
13$$\frac{2}{7}$$ + 3$$\frac{2}{9}$$
= {[(13 × 7) + 2] ÷ 7} + {[(3 × 9) + 2] ÷ 9}
= [(91 + 2) ÷ 7] + [(27 + 2) ÷ 9]
= (93 ÷ 7) + (29 ÷ 9)

Question 10.

21$$\frac{1}{9}$$ + 3$$\frac{5}{6}$$ = 15$$\frac{17}{18}$$

Explanation:
21$$\frac{1}{9}$$ + 3$$\frac{5}{6}$$
= {[(21 × 9) + 1] ÷ 9} + {[(3 × 6) + 5] ÷ 6}
= [(108 + 1) ÷ 9] + [(18 + 5) ÷ 6]
= (109 ÷ 9) + (23 ÷ 6)

Question 11.

2$$\frac{2}{3}$$ + 2$$\frac{2}{5}$$ = 5$$\frac{1}{15}[/latex Explanation: 2[latex]\frac{2}{3}$$ + 2$$\frac{2}{5}$$
= {[(2 × 3) + 2] ÷ 3} + {[(2 × 5) + 2] ÷ 5}
= [(6 + 2) ÷ 3] + [(10 + 2) ÷ 5]
= (8 ÷ 3) + (12 ÷ 5)

Question 12.

3$$\frac{1}{5}$$ + 4$$\frac{5}{6}$$ = 8$$\frac{1}{30}$$

Explanation:
3$$\frac{1}{5}$$ + 4$$\frac{5}{6}$$
= {[(3 × 5) + 1] ÷ 5} + {[(4 × 6) + 5] ÷ 6}
= [(15 + 1) ÷ 5] + [(24 + 5) ÷ 6]
= (16 ÷ 5) + (29 ÷ 6)

Question 13.

3$$\frac{5}{9}$$ + 2$$\frac{3}{4}$$ = 6$$\frac{11}{36}$$

Explanation:
3$$\frac{5}{9}$$ + 2$$\frac{3}{4}$$
= {[(3 × 9) + 5] ÷ 9} + {[(2 × 4) + 3] ÷ 4}
= [(27 + 5) ÷ 9] + [(8 + 3) ÷ 4]
= (32 ÷ 9) + (11 ÷ 4)

Question 14.

5$$\frac{1}{2}$$ + 4$$\frac{1}{9}$$ = 9$$\frac{11}{18}$$

Explanation:
5$$\frac{1}{2}$$ + 4$$\frac{1}{9}$$
= {[(5 × 2) + 1] ÷ 2} + {[(4 × 9) + 1] ÷ 9}
= [(10 + 1) ÷ 2] + [(36 + 1) ÷ 9]
= (11 ÷ 2) + (37 ÷ 9)

Question 15.

4$$\frac{7}{8}$$ + 2$$\frac{2}{9}$$ = 7$$\frac{7}{72}$$

Explanation:
4$$\frac{7}{8}$$ + 2$$\frac{2}{9}$$
= {[(4 × 8) + 7] ÷ 8} + {[(2 × 9) + 2] ÷ 9}
= [(32 + 7) ÷ 8] + [(18 + 2) ÷ 9]
= (39 ÷ 8) + (20 ÷ 9)

Question 16.

3$$\frac{1}{2}$$ + 2$$\frac{2}{7}$$ = 5$$\frac{11}{14}$$
3$$\frac{1}{2}$$ + 2$$\frac{2}{7}$$