Practice questions available in **McGraw Hill Math Grade 6 Answer Key PDF Lesson 6.8 Estimating Sums and Differences of Fractions and Mixed Numbers** will engage students and is a great way of informal assessment.

## McGraw-Hill Math Grade 6 Answer Key Lesson 6.8 Estimating Sums and Differences of Fractions and Mixed Numbers

**Exercises Estimate**

Question 1.

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

Answer:

\(\frac{3}{4}\) + \(\frac{5}{6}\) = 1 \(\frac{7}{12}\)

Explanation:

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

Question 2.

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

Answer:

\(\frac{4}{5}\) + \(\frac{1}{7}\) = \(\frac{33}{35}\)

Explanation:

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

Question 3.

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

Answer:

\(\frac{1}{3}\) + \(\frac{4}{7}\) = \(\frac{19}{21}\)

Explanation:

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

Question 4.

\(\frac{5}{6}\) + \(\frac{4}{8}\)

Answer:

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

Explanation:

\(\frac{5}{6}\) + \(\frac{4}{8}\)

Question 5.

1\(\frac{1}{5}\) + 2\(\frac{5}{6}\)

Answer:

1\(\frac{1}{5}\) + 2\(\frac{5}{6}\) = 4\(\frac{1}{30}\)

Explanation:

1\(\frac{1}{5}\) + 2\(\frac{5}{6}\)

= {[(1 × 5) + 1] ÷ 5} + {[(2 × 6) + 5] ÷ 6}

= [(5 + 1) ÷ 5] + [(12 + 5) ÷ 6]

= (6 ÷ 5) + (17 ÷ 6)

Question 6.

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

Answer:

7\(\frac{4}{5}\) + 4\(\frac{1}{3}\) = 12\(\frac{2}{15\)

Explanation:

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

= {[(7 × 5) + 4] ÷ 5} + {[(4 × 3) + 1] ÷ 3}

= [(35 + 4) ÷ 5] + [(12 + 1) ÷ 3]

= (39 ÷ 5) + (13 ÷ 3)

Question 7.

5\(\frac{1}{5}\) – 2\(\frac{3}{5}\)

Answer:

5\(\frac{1}{5}\) – 2\(\frac{3}{5}\) = 2\(\frac{3}{5}\)

Explanation:

5\(\frac{1}{5}\) – 2\(\frac{3}{5}\)

= {[(5 × 5) + 1] ÷ 5} – {[(2 × 5) + 3] ÷ 5}

= [(25 + 1) ÷ 5] – [(10 + 3) ÷ 5]

= (26 ÷ 5) – (13 ÷ 5)

Question 8.

7\(\frac{1}{2}\) – \(\frac{3}{4}\)

Answer:

7\(\frac{1}{2}\) – \(\frac{3}{4}\) = 6\(\frac{3}{4}\)

Explanation:

7\(\frac{1}{2}\) – \(\frac{3}{4}\)

{[(7 × 2) + 1] ÷ 2} – \(\frac{3}{4}\)

= [(14 + 1) ÷ 2] – \(\frac{3}{4}\)

= (15 ÷ 2) – (3 ÷ 4)

Question 9.

12\(\frac{1}{8}\) – \(\frac{2}{3}\)

Answer:

12\(\frac{1}{8}\) – \(\frac{2}{3}\) = 11\(\frac{11}{24}\)

Explanation:

12\(\frac{1}{8}\) – \(\frac{2}{3}\)

= {[(12 × 8) + 1] ÷ 8} – \(\frac{2}{3}\)

= [(96 + 1) ÷ 8] – \(\frac{2}{3}\)

= (97 ÷ 8) – (2 ÷ 3)

Question 10.

4\(\frac{4}{7}\) + 4\(\frac{4}{7}\)

Answer:

4\(\frac{4}{7}\) + 4\(\frac{4}{7}\) = 9\(\frac{1}{7}\)

Explanation:

4\(\frac{4}{7}\) + 4\(\frac{4}{7}\)

{[(4 × 7) + 4] ÷ 7} + {[(4 × 7) + 4] ÷ 7}

= [(28 + 4) ÷ 7] + [(28 + 4) ÷ 7]

= (32 ÷ 7) + (32 ÷ 7)

Question 11.

13\(\frac{5}{8}\) – 12\(\frac{1}{4}\)

Answer:

13\(\frac{5}{8}\) – 12\(\frac{1}{4}\) = 1\(\frac{3}{8}\)

Explanation:

13\(\frac{5}{8}\) – 12\(\frac{1}{4}\)

{[(13 × 8) + 5] ÷ 8} – {[(12 × 4) + 1] ÷ 4}

= [(104 + 5) ÷ 8] – [(48 + 1) ÷ 4]

= (109 ÷ 8) – (49 ÷ 4)

Question 12.

17\(\frac{1}{7}\) – 13\(\frac{3}{4}\)

Answer:

17\(\frac{1}{7}\) – 13\(\frac{3}{4}\) = 3\(\frac{11}{28}\)

Explanation:

17\(\frac{1}{7}\) – 13\(\frac{3}{4}\)

{[(17 × 7) + 1] ÷ 7} – {[(13 × 4) + 3] ÷ 4}

= [(119 + 1) ÷ 7] – [(52 + 3) ÷ 4]

= (120 ÷ 7) – (55 ÷ 4)

Question 13.

Leslie had 25\(\frac{4}{9}\) ounces of cat food left in a bag. If she feeds each of her two cats 1\(\frac{7}{8}\) ounces of food, about how much cat food will she have left?

Answer:

Number of ounces of cat food left with her = 21\(\frac{25}{36}\)

Explanation:

Number of ounces of cat food Leslie had left in a bag = 25\(\frac{4}{9}\)

Number of ounces of cat food she feeds each of her two cats = 1\(\frac{7}{8}\)

Number of ounces of cat food left with her = Number of ounces of cat food Leslie had left in a bag – Number of ounces of cat food she feeds each of her two cats

= 25\(\frac{4}{9}\) – 2(1\(\frac{7}{8}\))

= {[(25 × 9 ) + 4] ÷ 9} – 2{[(1 × 8) + 7] ÷ 8}

= [(225 + 4) ÷ 9] – 2[(8 + 7) ÷ 8]

= (229 ÷ 9) – 2(15 ÷ 8)

= (229 ÷ 9) – (15 ÷ 4)

Question 14.

James was gathering wood for the fireplace. He already had 1\(\frac{4}{5}\) cords of wood and he gathered another 2\(\frac{1}{3}\) cords today. About how many cords of wood does James have now?

Answer:

Number of cords of wood he has now = 4\(\frac{2}{15}\)

Explanation:

Number of cords of wood he already had = 1\(\frac{4}{5}\)

Number of cords of wood he again gathered today = 2\(\frac{1}{3}\)

Number of cords of wood he has now = Number of cords of wood he already had + Number of cords of wood he again gathered today

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

= {[(1 × 5) + 4] ÷ 5} + {[(2 × 3) + 1] ÷ 3}

= [(5 + 4) ÷ 5] + [(6 + 1) ÷ 3]

= (9 ÷ 5) + (7 ÷ 3)