# McGraw Hill Math Grade 8 Lesson 6.2 Answer Key Proportions and Cross-Multiplying

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.2 Proportions and Cross-Multiplying to secure good marks & knowledge in the exams.

## McGraw-Hill Math Grade 8 Answer Key Lesson 6.2 Proportions and Cross-Multiplying

Exercises Solve
Indicate (True or False) whether the ratios are equal.

Question 1.
$$\frac{4}{9}$$ = $$\frac{36}{81}$$ ______
True,

Explanation:
$$\frac{4}{9}$$ = $$\frac{36}{81}$$,
When we multiply numerator and denominator with 9, we get equal ratios.
$$\frac{4×9}{9×9}$$ = $$\frac{36}{81}$$.

Question 2.
$$\frac{5}{7}$$ = $$\frac{35}{42}$$ ______
False,

Explanation:
$$\frac{5}{7}$$ = $$\frac{35}{42}$$,
When we multiply numerator and denominator with 7, we get $$\frac{35}{49}$$ ratios.
$$\frac{35}{49}$$  is not equal to  $$\frac{35}{42}$$.
hence, $$\frac{5}{7}$$ = $$\frac{35}{42}$$ is false.

Question 3.
$$\frac{4}{3}$$ = $$\frac{12}{9}$$ ______
True,

Explanation:
$$\frac{4}{3}$$ = $$\frac{3}{9}$$,
When we multiply numerator and denominator with 3, we get equal ratios.
$$\frac{4×3}{3×3}$$ = $$\frac{12}{9}$$.

Question 4.
$$\frac{9}{8}$$ = $$\frac{16}{18}$$ _____
False,

Explanation:
$$\frac{9}{8}$$ = $$\frac{16}{18}$$,
When we multiply numerator and denominator with 2, we get $$\frac{18}{16}$$ ratios.
$$\frac{18}{16}$$ is not equal to $$\frac{16}{18}$$.
hence, $$\frac{9}{8}$$ = $$\frac{16}{18}$$ is false.

Question 5.
$$\frac{5}{12}$$ = $$\frac{125}{300}$$ _____
True,

Explanation:
$$\frac{5}{12}$$ = $$\frac{125}{300}$$,
When we multiply numerator and denominator with 25, we get equal ratios.
$$\frac{5×25}{12×25}$$ = $$\frac{125}{300}$$.

Question 6.
$$\frac{6}{5}$$ = $$\frac{36}{32}$$ _____
False,

Explanation:
$$\frac{6}{5}$$ = $$\frac{36}{32}$$,
When we multiply numerator and denominator with 6, we get $$\frac{36}{30}$$ ratios.
$$\frac{36}{30}$$ is not equal to $$\frac{36}{32}$$.
hence, $$\frac{6}{5}$$ = $$\frac{36}{32}$$ is false.

Question 7.
$$\frac{7}{11}$$ = $$\frac{84}{132}$$ _____
True,

Explanation:
$$\frac{7}{11}$$ = $$\frac{84}{132}$$,
When we multiply numerator and denominator with 12, we get equal ratios.
$$\frac{7×12}{11×12}$$ = $$\frac{84}{132}$$.

Question 8.
$$\frac{5}{8}$$ = $$\frac{25}{40}$$ _____
True,

Explanation:
$$\frac{5}{8}$$ = $$\frac{25}{40}$$,
When we multiply numerator and denominator with 5, we get equal ratios.
$$\frac{5×5}{8×5}$$ = $$\frac{25}{40}$$.

Solve for the unknown variable.

Question 9.
$$\frac{10}{6}$$ = $$\frac{n}{36}$$ _____
n = 60,

Explanation:
$$\frac{10}{6}$$ = $$\frac{n}{36}$$,

= $$\frac{10X36}{nX6}$$,

= $$\frac{360}{6n}$$,

n = $$\frac{360}{6}$$,
n = 60.

Question 10.
$$\frac{4}{x}$$ = $$\frac{16}{24}$$ _____
x = 6,

Explanation:
$$\frac{4}{x}$$ = $$\frac{16}{24}$$,

= $$\frac{4X24}{xX16}$$,

= $$\frac{96}{16x}$$,

x = $$\frac{96}{16}$$,
x = 6.

Question 11.
$$\frac{13}{26}$$ = $$\frac{y}{78}$$ _____
y = 39,

Explanation:
$$\frac{13}{26}$$ = $$\frac{y}{78}$$,

= $$\frac{13X78}{yX26}$$,

= $$\frac{1014}{26y}$$,

y = $$\frac{1014}{26}$$,
y = 39.

Question 12.
$$\frac{11}{m}$$ = $$\frac{132}{60}$$ _____
m = 5,

Explanation:
$$\frac{11}{m}$$ = $$\frac{132}{60}$$,

= $$\frac{11X60}{mX132}$$,

= $$\frac{660}{132m}$$,

m = $$\frac{660}{132}$$,
m = 5.

Question 13.
$$\frac{18}{28}$$ = $$\frac{n}{42}$$ _____
n = 27,

Explanation:
$$\frac{18}{28}$$ = $$\frac{n}{42}$$,

= $$\frac{18X42}{nX28}$$,

= $$\frac{756}{28n}$$,

n = $$\frac{756}{28}$$,
n = 27.

Question 14.
$$\frac{x}{19}$$ = $$\frac{15}{57}$$ _____
x = 5,

Explanation:
$$\frac{x}{19}$$ = $$\frac{15}{57}$$,

= $$\frac{xX57}{19X15}$$,

= $$\frac{57x}{285}$$,

x = $$\frac{285}{57}$$,
x = 5.

Question 15.
$$\frac{x}{52}$$ = $$\frac{58}{104}$$ _____
x = 29,

Explanation:
$$\frac{x}{52}$$ = $$\frac{58}{104}$$,

= $$\frac{xX104}{52X58}$$,

= $$\frac{104x}{3016}$$,

x = $$\frac{3016}{104}$$,
x = 29.

Question 16.
$$\frac{18}{15}$$ = $$\frac{n}{10}$$ _____
$$\frac{18}{15}$$ = $$\frac{n}{10}$$,
= $$\frac{18X10}{nX15}$$,
= $$\frac{180}{15n}$$,
n = $$\frac{180}{15}$$,