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

## McGraw-Hill Math Grade 6 Answer Key Lesson 6.6 Adding Mixed Numbers with Unlike Denominators

**Exercises Add**

Question 1.

1\(\frac{2}{3}\) + 3\(\frac{1}{5}\)

Answer:

1\(\frac{2}{3}\) + 3\(\frac{1}{5}\) = 4\(\frac{13}{15}\)

Explanation:

1\(\frac{2}{3}\) + 3\(\frac{1}{5}\)

= {[(1Ã— 3) + 2] Ã· 3} + {[(3 Ã— 5) + 1] Ã· 5}

= [(3 + 2) Ã· 3] + [(15 + 1) Ã· 5]

= \(\frac{5}{3}\) + \(\frac{16}{5}\)

Question 2.

4\(\frac{1}{7}\) + 3\(\frac{3}{5}\)

Answer:

4\(\frac{1}{7}\) + 3\(\frac{3}{5}\) = 7\(\frac{26}{35}\)

Explanation:

4\(\frac{1}{7}\) + 3\(\frac{3}{5}\)

= {[(4 Ã— 7) + 1] Ã· 7} + {[(3 Ã— 5) + 3] Ã· 5}

= [(28 + 1) Ã· 7] + [(15 + 3) Ã· 5]

= (29 Ã· 7) + (18 Ã· 5)

=

Question 3.

5\(\frac{1}{9}\) + 2\(\frac{3}{7}\)

Answer:

5\(\frac{1}{9}\) + 2\(\frac{3}{7}\) = 7\(\frac{34}{63}\)

Explanation:

5\(\frac{1}{9}\) + 2\(\frac{3}{7}\)

= {[(5 Ã— 9) + 1] Ã· 9} + {[(2 Ã— 7) + 3] Ã· 7}

= [(45 + 1) Ã· 9] + [(14 + 3) Ã· 7]

= (46 Ã· 9) + (17 Ã· 7)

Question 4.

1\(\frac{2}{3}\) + 4\(\frac{1}{16}\)

Answer:

1\(\frac{2}{3}\) + 4\(\frac{1}{16}\) = 5\(\frac{35}{48}\)

Explanation:

1\(\frac{2}{3}\) + 4\(\frac{1}{16}\)

= {[(1 Ã— 3) + 2] Ã· 3} + {[(4 Ã— 16) + 1] Ã· 16}

= [(3 + 2) Ã· 3] + [(64 + 1) Ã· 16]

= (5 Ã· 3) + (65 Ã· 16)

Question 5.

10\(\frac{3}{7}\) + 2\(\frac{3}{11}\)

Answer:

10\(\frac{3}{7}\) + 2\(\frac{3}{11}\) = 12\(\frac{54}{77}\)

Explanation:

10\(\frac{3}{7}\) + 2\(\frac{3}{11}\)

= {[(10 Ã— 7) + 3] Ã· 7} + {[(2 Ã— 11) + 3] Ã· 11}

= [(70 + 3) Ã· 7] + [(22 + 3) Ã· 11]

= (73 Ã· 7) + (25 Ã· 11)

Question 6.

3\(\frac{1}{4}\) + 5\(\frac{2}{9}\)

Answer:

3\(\frac{1}{4}\) + 5\(\frac{2}{9}\) = 8\(\frac{17}{36}\)

Explanation:

3\(\frac{1}{4}\) + 5\(\frac{2}{9}\)

= {[(3 Ã— 4) + 1] Ã· 4} + {[(5 Ã— 9) + 2] Ã· 9}

= [(12 + 1) Ã· 4] + [(45 + 2) Ã· 9]

= (13 Ã· 4) + (47 Ã· 9)

Question 7.

11\(\frac{2}{7}\) + 12\(\frac{3}{8}\)

Answer:

11\(\frac{2}{7}\) + 12\(\frac{3}{8}\) = 23\(\frac{37}{56}\)

Explanation:

11\(\frac{2}{7}\) + 12\(\frac{3}{8}\)

= {[(11 Ã— 7) + 2] Ã· 7} + {[(12 Ã— 8) + 3] Ã· 8}

= [(77 + 2) Ã· 7] + [(96 + 3) Ã· 8]

= (79 Ã· 7) + (99 Ã· 8)

Question 8.

12\(\frac{5}{6}\) + 1\(\frac{1}{15}\)

Answer:

12\(\frac{5}{6}\) + 1\(\frac{1}{15}\) = 13\(\frac{9}{10}\)

Explanation:

12\(\frac{5}{6}\) + 1\(\frac{1}{15}\)

= {[(12 Ã— 6) + 5] Ã· 6} + {[(1 Ã— 15) + 1] Ã· 15}

= [(72 + 5) Ã· 6] + [(15 + 1) Ã· 15]

= (77 Ã· 6) + (16 Ã· 15)

Question 9.

Answer:

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

Explanation:

13\(\frac{2}{7}\) + 3\(\frac{2}{9}\)

= {[(13 Ã— 7) + 2] Ã· 7} + {[(3 Ã— 9) + 2] Ã· 9}

= [(91 + 2) Ã· 7] + [(27 + 2) Ã· 9]

= (93 Ã· 7) + (29 Ã· 9)

Question 10.

Answer:

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

Explanation:

21\(\frac{1}{9}\) + 3\(\frac{5}{6}\)

= {[(21 Ã— 9) + 1] Ã· 9} + {[(3 Ã— 6) + 5] Ã· 6}

= [(108 + 1) Ã· 9] + [(18 + 5) Ã· 6]

= (109 Ã· 9) + (23 Ã· 6)

Question 11.

Answer:

2\(\frac{2}{3}\) + 2\(\frac{2}{5}\) = 5\(\frac{1}{15}[/latex

Explanation:

2[latex]\frac{2}{3}\) + 2\(\frac{2}{5}\)

= {[(2 Ã— 3) + 2] Ã· 3} + {[(2 Ã— 5) + 2] Ã· 5}

= [(6 + 2) Ã· 3] + [(10 + 2) Ã· 5]

= (8 Ã· 3) + (12 Ã· 5)

Question 12.

Answer:

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

Explanation:

3\(\frac{1}{5}\) + 4\(\frac{5}{6}\)

= {[(3 Ã— 5) + 1] Ã· 5} + {[(4 Ã— 6) + 5] Ã· 6}

= [(15 + 1) Ã· 5] + [(24 + 5) Ã· 6]

= (16 Ã· 5) + (29 Ã· 6)

Question 13.

Answer:

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

Explanation:

3\(\frac{5}{9}\) + 2\(\frac{3}{4}\)

= {[(3 Ã— 9) + 5] Ã· 9} + {[(2 Ã— 4) + 3] Ã· 4}

= [(27 + 5) Ã· 9] + [(8 + 3) Ã· 4]

= (32 Ã· 9) + (11 Ã· 4)

Question 14.

Answer:

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

Explanation:

5\(\frac{1}{2}\) + 4\(\frac{1}{9}\)

= {[(5 Ã— 2) + 1] Ã· 2} + {[(4 Ã— 9) + 1] Ã· 9}

= [(10 + 1) Ã· 2] + [(36 + 1) Ã· 9]

= (11 Ã· 2) + (37 Ã· 9)

Question 15.

Answer:

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

Explanation:

4\(\frac{7}{8}\) + 2\(\frac{2}{9}\)

= {[(4 Ã— 8) + 7] Ã· 8} + {[(2 Ã— 9) + 2] Ã· 9}

= [(32 + 7) Ã· 8] + [(18 + 2) Ã· 9]

= (39 Ã· 8) + (20 Ã· 9)

Question 16.

Answer:

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

Explanation:

3\(\frac{1}{2}\) + 2\(\frac{2}{7}\)

= {[(3 Ã— 2) + 1] Ã· 2} + {[(2 Ã— 7) + 2] Ã· 7}

= [(6 + 1) Ã· 2] + [(14 + 2) Ã· 7]

= (7 Ã· 2) + (16 Ã· 7)