Engage NY Eureka Math Grade 6 Module 4 Lesson 25 Answer Key

Eureka Math Grade 6 Module 4 Lesson 25 Opening Exercise Answer Key

Opening Exercise:

Identify a value for the variable that would make each equation or inequality into a true number sentence. Is this the only possible answer? State when the equation or inequality is true using equality and inequality symbols.

a. 3 + g = 15
12 is the only value of g that will make the equation true. The equation is true when g = 12.

b. 30 > 2d
Answers will vary. There is more than one value of d that will make the inequality true. The inequality is true when d < 15.

c. $$\frac{15}{f}$$ < 5
Answers will vary. There is more than one value off that will make the inequality true. The inequality is true when f > 3.

d. 42 â‰¤ 50 – m
Answers will vary. There is more than one value of m that will make the inequality true. The inequality is true when m â‰¤ 8.

Example:

Each of the following numbers, if substituted for the variable, makes one of the equations below into a true number sentence. Match the number to that equation: 3, 6, 15, 16, 44.

a. n + 26 = 32
6

b. n – 12 = 32
44

c. 17n = 51
3

d. 42 = n
16

e. $$\frac{n}{3}$$ = 5
15

Eureka Math Grade 6 Module 4 Lesson 25 Problem Set Answer Key

Find the solution to each equation.

Question 1.
43 = y
y = 64

Question 2.
8a = 24
a = 3

Question 3.
32 = g – 4
g = 36

Question 4.
56 = j + 29
j = 27

Question 5.
$$\frac{48}{r}$$ = 12
r = 4

Question 6.
k = 15 – 9
k = 6

Question 7.
x . $$\frac{1}{5}$$ = 60
x = 300

Question 8.
m + 3 . 45 = 12 . 8
m = 9 . 35

Question 9.
a = 15
a = 1

Eureka Math Grade 6 Module 4 Lesson 25 Exit Ticket Answer Key

Find the solution to each equation.

Question 1.
7f = 49
f = 7

Question 2.
1 = $$\frac{r}{12}$$
r = 12

Question 3.
1.5 = d + 0.8
d = 0.7

Question 4.
92 = h
h = 81

Question 5.
q = 45 – 19
q = 26

Question 6.
40 = $$\frac{1}{2}$$p
p = 80

Eureka Math Grade 6 Module 4 Lesson 25 Division of Fractions Answer Key

Division of Fractions – Round 1:

Directions: Evaluate each expression and simplify:

Question 1.
9 ones Ã· 3ones
$$\frac{9}{3}$$ = 3

Question 2.
9 Ã· 3
$$\frac{9}{3}$$ = 3

Question 3.
9tens Ã· 3tens
$$\frac{9}{3}$$ = 3

Question 4.
90 Ã· 30
$$\frac{9}{3}$$ = 3

Question 5.
9 hundreds Ã· 3 hundreds
$$\frac{9}{3}$$ = 3

Question 6.
900 Ã· 300
$$\frac{9}{3}$$ = 3

Question 7.
9 halves Ã· 3 halves
$$\frac{9}{3}$$ = 3

Question 8.
$$\frac{9}{2}$$ Ã· $$\frac{9}{2}$$
$$\frac{9}{3}$$ = 3

Question 9.
9 fourths Ã· 9 fourths
$$\frac{9}{3}$$ = 3

Question 10.
$$\frac{9}{4}$$ $$\frac{3}{4}$$
$$\frac{9}{3}$$ = 3

Question 11.
$$\frac{9}{8}$$ Ã· $$\frac{3}{8}$$
$$\frac{9}{3}$$ =3

Question 12.
$$\frac{2}{3}$$ Ã· $$\frac{1}{3}$$
$$\frac{2}{1}$$ = 2

Question 13.
$$\frac{1}{3}$$ Ã· $$\frac{2}{3}$$
$$\frac{1}{2}$$

Question 14.
$$\frac{6}{7}$$ Ã· $$\frac{2}{7}$$
$$\frac{6}{2}$$ = 3

Question 15.
$$\frac{5}{7}$$ Ã· $$\frac{2}{7}$$
$$\frac{5}{2}$$ = 2$$\frac{1}{2}$$

Question 16.
$$\frac{3}{7}$$ Ã· $$\frac{4}{7}$$
$$\frac{3}{4}$$

Question 17.
$$\frac{6}{10}$$ Ã· $$\frac{2}{10}$$
$$\frac{6}{2}$$ = 3

Question 18.
$$\frac{6}{10}$$ Ã· $$\frac{4}{10}$$
$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$

Question 19.
$$\frac{6}{10}$$ Ã· $$\frac{8}{10}$$
$$\frac{6}{8}$$ = $$\frac{3}{4}$$

Question 20.
$$\frac{7}{12}$$ $$\frac{2}{12}$$
$$\frac{7}{2}$$ = 3$$\frac{1}{2}$$

Question 21.
$$\frac{6}{12}$$ Ã· $$\frac{9}{12}$$
$$\frac{6}{9}$$ = $$\frac{2}{3}$$

Question 22.
$$\frac{4}{12}$$ Ã· $$\frac{11}{12}$$
$$\frac{4}{11}$$

Question 23.
$$\frac{6}{10}$$ $$\frac{4}{10}$$
$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$

Question 24.
$$\frac{9}{3}$$ Ã· $$\frac{9}{3}$$ = $$\frac{9}{3}$$ Ã· $$\overline{10}$$
$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$

Question 25.
$$\frac{10}{12}$$ $$\frac{5}{12}$$
$$\frac{10}{5}$$ = 2

Question 26.
$$\frac{6}{4}$$ Ã· $$\frac{6}{4}$$ = $$\frac{6}{4}$$ Ã· $$\overline{10}$$
$$\frac{10}{5}$$ = 2

Question 27.
$$\frac{10}{12}$$ Ã· $$\frac{3}{12}$$
$$\frac{10}{3}$$ = 3$$\frac{1}{3}$$

Question 28.
$$\frac{10}{12}$$ Ã· $$\frac{1}{4}$$ = $$\frac{10}{12}$$ Ã· $$\overline{10}$$
$$\frac{10}{3}$$ = 3$$\frac{1}{3}$$

Question 29.
$$\frac{5}{6}$$ Ã· $$\frac{3}{12}$$ = $$\overline{10}$$ Ã· $$\frac{3}{12}$$
$$\frac{10}{3}$$ = 3$$\frac{1}{3}$$

Question 30.
$$\frac{5}{10}$$ $$\frac{2}{10}$$
$$\frac{5}{2}$$ = 2$$\frac{1}{2}$$

Question 31.
$$\frac{5}{10}$$ Ã· $$\frac{1}{5}$$ = $$\frac{5}{10}$$ Ã· $$\overline{10}$$
$$\frac{5}{2}$$ = 2$$\frac{1}{2}$$

Question 32.
$$\frac{1}{2}$$ Ã· $$\frac{2}{10}$$ = $$\overline{10}$$ Ã· $$\frac{2}{10}$$
$$\frac{5}{2}$$ = 2$$\frac{1}{2}$$

Question 33.
$$\frac{1}{2}$$ Ã· $$\frac{2}{4}$$
$$\frac{1}{2}$$ = 1

Question 34.
$$\frac{3}{4}$$ Ã· $$\frac{2}{8}$$
3

Question 35.
$$\frac{1}{2}$$ Ã· $$\frac{3}{8}$$
$$\frac{4}{3}$$ = 1$$\frac{1}{3}$$

Question 36.
$$\frac{1}{2}$$ Ã· $$\frac{1}{5}$$ = $$\overline{10}$$ Ã· $$\overline{10}$$
$$\frac{5}{2}$$ = 2$$\frac{1}{2}$$

Question 37.
$$\frac{2}{4}$$ Ã· $$\frac{1}{3}$$
$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$

Question 38.
$$\frac{1}{4}$$ Ã· $$\frac{4}{6}$$
$$\frac{3}{8}$$

Question 39.
$$\frac{3}{4}$$ Ã· $$\frac{2}{6}$$
$$\frac{9}{4}$$ = 2$$\frac{1}{2}$$

Question 40.
$$\frac{5}{6}$$ Ã· $$\frac{1}{4}$$
$$\frac{10}{3}$$ = 3$$\frac{1}{3}$$

Question 41.
$$\frac{2}{9}$$ Ã· $$\frac{5}{6}$$
$$\frac{4}{15}$$

Question 42.
$$\frac{5}{9}$$ Ã· $$\frac{1}{6}$$
$$\frac{15}{3}$$ = 5

Question 43.
$$\frac{1}{2}$$ Ã· $$\frac{1}{7}$$
$$\frac{7}{2}$$ = 3$$\frac{1}{2}$$

Question 44.
$$\frac{5}{7}$$ Ã· $$\frac{1}{2}$$
$$\frac{10}{7}$$ = 1$$\frac{3}{7}$$

Division of Fractions – Round 2:

Directions: Evaluate each expression:

Question 1.
12ones Ã· 2ones
$$\frac{12}{2}$$ = 6

Question 2.
12 Ã· 2
$$\frac{12}{2}$$ = 6

Question 3.
12tens Ã· 2tens
$$\frac{12}{2}$$ = 6

Question 4.
120 Ã· 20
$$\frac{12}{2}$$ = 6

Question 5.
12 hundreds Ã· 2 hundreds
$$\frac{12}{2}$$ = 6

Question 6.
1,200 Ã· 200
$$\frac{12}{2}$$ = 6

Question 7.
12 halves Ã· 2 halves
$$\frac{12}{2}$$ = 6

Question 8.
$$\frac{12}{2}$$ Ã· $$\frac{2}{2}$$
$$\frac{12}{2}$$ = 6

Question 9.
12 fourths Ã· 3 fourths
$$\frac{12}{3}$$ = 4

Question 10.
$$\frac{12}{4}$$ Ã· $$\frac{12}{2}$$
$$\frac{12}{3}$$ = 4

Question 11.
$$\frac{12}{8}$$ Ã· $$\frac{3}{8}$$
$$\frac{12}{2}$$ = 4

Question 12.
$$\frac{2}{4}$$ Ã· $$\frac{1}{4}$$
$$\frac{2}{1}$$ = 2

Question 13.
$$\frac{1}{4}$$ Ã· $$\frac{2}{4}$$
$$\frac{1}{2}$$

Question 14.
$$\frac{4}{5}$$ Ã· $$\frac{2}{5}$$
$$\frac{4}{2}$$ = 2

Question 15.
$$\frac{2}{5}$$ Ã· $$\frac{4}{5}$$
$$\frac{2}{4}$$ = $$\frac{1}{2}$$

Question 16.
$$\frac{3}{5}$$ Ã· $$\frac{4}{5}$$
$$\frac{3}{4}$$

Question 17.
$$\frac{6}{8}$$ Ã· $$\frac{2}{8}$$
$$\frac{6}{2}$$ = 3

Question 18.
$$\frac{6}{8}$$ Ã· $$\frac{4}{8}$$
$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$

Question 19.
$$\frac{6}{8}$$ Ã· $$\frac{5}{8}$$
$$\frac{6}{5}$$ = 1$$\frac{1}{5}$$

Question 20.
$$\frac{6}{10}$$ Ã· $$\frac{2}{10}$$
$$\frac{6}{2}$$ = 3

Question 21.
$$\frac{7}{10}$$ Ã· $$\frac{8}{10}$$
$$\frac{7}{8}$$

Question 22.
$$\frac{4}{10}$$ Ã· $$\frac{7}{10}$$
$$\frac{4}{7}$$

Question 23.
$$\frac{6}{12}$$ Ã· $$\frac{4}{12}$$
$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$

Question 24.
$$\frac{6}{12}$$ Ã· $$\frac{2}{6}$$ = $$\frac{6}{12}$$ Ã· $$\overline{12}$$
$$\frac{6}{4}$$ = 1$$\frac{1}{2}$$

Question 25.
$$\frac{8}{14}$$ Ã· $$\frac{7}{14}$$
$$\frac{8}{7}$$ = 1$$\frac{1}{7}$$

Question 26.
$$\frac{8}{14}$$ Ã· $$\frac{1}{2}$$ = $$\frac{8}{14}$$ Ã· $$\overline{14}$$
$$\frac{8}{7}$$ = 1$$\frac{1}{7}$$

Question 27.
$$\frac{11}{14}$$ = $$\frac{2}{14}$$
$$\frac{11}{2}$$ = 5$$\frac{1}{2}$$

Question 28.
$$\frac{11}{14}$$ Ã· $$\frac{1}{7}$$ = $$\frac{11}{14}$$ Ã· $$\overline{14}$$
$$\frac{11}{2}$$ = 5$$\frac{1}{2}$$

Question 29.
$$\frac{1}{7}$$ Ã· $$\frac{6}{14}$$ = $$\overline{14}$$ Ã· $$\frac{6}{14}$$
$$\frac{2}{6}$$ = $$\frac{1}{3}$$

Question 30.
$$\frac{7}{18}$$ Ã· $$\frac{3}{18}$$
$$\frac{7}{3}$$ = 2$$\frac{1}{3}$$

Question 31.
$$\frac{7}{18}$$ Ã· $$\frac{1}{6}$$ = $$\frac{7}{18}$$ Ã· $$\overline{18}$$
$$\frac{7}{3}$$ = 2$$\frac{1}{3}$$

Question 32.
$$\frac{1}{3}$$ Ã· $$\frac{12}{18}$$ = $$\overline{18}$$ Ã· $$\frac{12}{18}$$
$$\frac{6}{12}$$ = $$\frac{1}{2}$$

Question 33.
$$\frac{1}{6}$$ Ã· $$\frac{4}{18}$$
$$\frac{3}{4}$$

Question 34.
$$\frac{4}{12}$$ Ã· $$\frac{8}{6}$$
$$\frac{4}{16}$$ = $$\frac{1}{4}$$

Question 35.
$$\frac{1}{3}$$ Ã· $$\frac{3}{15}$$
$$\frac{5}{3}$$ = 1$$\frac{2}{3}$$

Question 36.
$$\frac{2}{6}$$ Ã· $$\frac{1}{9}$$ = $$\overline{18}$$ Ã· $$\overline{18}$$
$$\frac{6}{2}$$ = 3

Question 37.
$$\frac{1}{6}$$ Ã· $$\frac{4}{9}$$
$$\frac{3}{8}$$

Question 38.
$$\frac{2}{3}$$ Ã· $$\frac{3}{4}$$
$$\frac{8}{9}$$

Question 39.
$$\frac{1}{3}$$ Ã· $$\frac{3}{5}$$
$$\frac{5}{9}$$

Question 40.
$$\frac{1}{7}$$ Ã· $$\frac{1}{2}$$
$$\frac{2}{7}$$

Question 41.
$$\frac{5}{6}$$ Ã· $$\frac{2}{9}$$
$$\frac{15}{4}$$ = 3$$\frac{3}{4}$$

Question 42.
$$\frac{5}{9}$$ Ã· $$\frac{2}{6}$$
$$\frac{10}{6}$$ = 1$$\frac{2}{3}$$
$$\frac{5}{6}$$ Ã· $$\frac{4}{9}$$
$$\frac{15}{8}$$ = 1$$\frac{7}{8}$$
$$\frac{1}{2}$$ Ã· $$\frac{4}{5}$$
$$\frac{5}{8}$$