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

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 6.8 Estimating Sums and Differences of Fractions and Mixed NumbersÂ 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.
$$\frac{3}{4}$$ + $$\frac{5}{6}$$
$$\frac{3}{4}$$ + $$\frac{5}{6}$$ = 1 $$\frac{7}{12}$$

Explanation:
$$\frac{3}{4}$$ + $$\frac{5}{6}$$

Question 2.
$$\frac{4}{5}$$ + $$\frac{1}{7}$$
$$\frac{4}{5}$$ + $$\frac{1}{7}$$ = $$\frac{33}{35}$$

Explanation:
$$\frac{4}{5}$$ + $$\frac{1}{7}$$

Question 3.
$$\frac{1}{3}$$ + $$\frac{4}{7}$$
$$\frac{1}{3}$$ + $$\frac{4}{7}$$ = $$\frac{19}{21}$$

Explanation:
$$\frac{1}{3}$$ + $$\frac{4}{7}$$

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

Explanation:
$$\frac{5}{6}$$ + $$\frac{4}{8}$$

Question 5.
1$$\frac{1}{5}$$ + 2$$\frac{5}{6}$$
1$$\frac{1}{5}$$ + 2$$\frac{5}{6}$$ = 4$$\frac{1}{30}$$

Explanation:
1$$\frac{1}{5}$$ + 2$$\frac{5}{6}$$
= {[(1 Ã— 5) + 1] Ã· 5} + {[(2 Ã— 6) + 5] Ã· 6}
= [(5 + 1) Ã· 5] + [(12 + 5) Ã· 6]
= (6 Ã· 5) + (17 Ã· 6)

Question 6.
7$$\frac{4}{5}$$ + 4$$\frac{1}{3}$$
7$$\frac{4}{5}$$ + 4$$\frac{1}{3}$$ = 12$$\frac{2}{15$$

Explanation:
7$$\frac{4}{5}$$ + 4$$\frac{1}{3}$$
= {[(7 Ã— 5) + 4] Ã· 5} + {[(4 Ã— 3) + 1] Ã· 3}
= [(35 + 4) Ã· 5] + [(12 + 1) Ã· 3]
= (39 Ã· 5) + (13 Ã· 3)

Question 7.
5$$\frac{1}{5}$$ – 2$$\frac{3}{5}$$
5$$\frac{1}{5}$$ – 2$$\frac{3}{5}$$ = 2$$\frac{3}{5}$$

Explanation:
5$$\frac{1}{5}$$ – 2$$\frac{3}{5}$$
= {[(5 Ã— 5) + 1] Ã· 5} – {[(2 Ã— 5) + 3] Ã· 5}
= [(25 + 1) Ã· 5] – [(10 + 3) Ã· 5]
= (26 Ã· 5) – (13 Ã· 5)

Question 8.
7$$\frac{1}{2}$$ – $$\frac{3}{4}$$
7$$\frac{1}{2}$$ – $$\frac{3}{4}$$ = 6$$\frac{3}{4}$$

Explanation:
7$$\frac{1}{2}$$ – $$\frac{3}{4}$$
{[(7 Ã— 2) + 1] Ã· 2} – $$\frac{3}{4}$$
= [(14 + 1) Ã· 2] – $$\frac{3}{4}$$
= (15 Ã· 2) – (3 Ã· 4)

Question 9.
12$$\frac{1}{8}$$ – $$\frac{2}{3}$$
12$$\frac{1}{8}$$ – $$\frac{2}{3}$$ = 11$$\frac{11}{24}$$

Explanation:
12$$\frac{1}{8}$$ – $$\frac{2}{3}$$
= {[(12 Ã— 8) + 1] Ã· 8} – $$\frac{2}{3}$$
= [(96 + 1) Ã· 8] – $$\frac{2}{3}$$
= (97 Ã· 8) – (2 Ã· 3)

Question 10.
4$$\frac{4}{7}$$ + 4$$\frac{4}{7}$$
4$$\frac{4}{7}$$ + 4$$\frac{4}{7}$$ = 9$$\frac{1}{7}$$

Explanation:
4$$\frac{4}{7}$$ + 4$$\frac{4}{7}$$
{[(4 Ã— 7) + 4] Ã· 7} + {[(4 Ã— 7) + 4] Ã· 7}
= [(28 + 4) Ã· 7] + [(28 + 4) Ã· 7]
= (32 Ã· 7) + (32 Ã· 7)

Question 11.
13$$\frac{5}{8}$$ – 12$$\frac{1}{4}$$
13$$\frac{5}{8}$$ – 12$$\frac{1}{4}$$ = 1$$\frac{3}{8}$$

Explanation:
13$$\frac{5}{8}$$ – 12$$\frac{1}{4}$$
{[(13 Ã— 8) + 5] Ã· 8} – {[(12 Ã— 4) + 1] Ã· 4}
= [(104 + 5) Ã· 8] – [(48 + 1) Ã· 4]
= (109 Ã· 8) – (49 Ã· 4)

Question 12.
17$$\frac{1}{7}$$ – 13$$\frac{3}{4}$$
17$$\frac{1}{7}$$ – 13$$\frac{3}{4}$$ = 3$$\frac{11}{28}$$

Explanation:
17$$\frac{1}{7}$$ – 13$$\frac{3}{4}$$
{[(17 Ã— 7) + 1] Ã· 7} – {[(13 Ã— 4) + 3] Ã· 4}
= [(119 + 1) Ã· 7] – [(52 + 3) Ã· 4]
= (120 Ã· 7) – (55 Ã· 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?
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$$\frac{4}{9}$$Â  – 2(1$$\frac{7}{8}$$)
= {[(25 Ã— 9 ) + 4] Ã· 9} – 2{[(1 Ã— 8) + 7] Ã· 8}
= [(225 + 4) Ã· 9] – 2[(8 + 7) Ã· 8]
= (229 Ã· 9) – 2(15 Ã· 8)
= (229 Ã· 9) – (15 Ã· 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?
Number of cords of wood he has now = 4$$\frac{2}{15}$$
Number of cords of wood he already had = 1$$\frac{4}{5}$$
Number of cords of wood he again gathered today = 2$$\frac{1}{3}$$
= 1$$\frac{4}{5}$$ + 2$$\frac{1}{3}$$