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.

\(\frac{4}{9}\) = \(\frac{36}{81}\) ______

Answer:

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.

\(\frac{5}{7}\) = \(\frac{35}{42}\) ______

Answer:

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.

\(\frac{4}{3}\) = \(\frac{12}{9}\) ______

Answer:

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.

\(\frac{9}{8}\) = \(\frac{16}{18}\) _____

Answer:

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.

\(\frac{5}{12}\) = \(\frac{125}{300}\) _____

Answer:

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.

\(\frac{6}{5}\) = \(\frac{36}{32}\) _____

Answer:

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.

\(\frac{7}{11}\) = \(\frac{84}{132}\) _____

Answer:

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.

\(\frac{5}{8}\) = \(\frac{25}{40}\) _____

Answer:

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.

\(\frac{10}{6}\) = \(\frac{n}{36}\) _____

Answer:

n = 60,

Explanation:

\(\frac{10}{6}\) = \(\frac{n}{36}\),

= \(\frac{10X36}{nX6}\),

= \(\frac{360}{6n}\),

n = \(\frac{360}{6}\),

n = 60.

Question 10.

\(\frac{4}{x}\) = \(\frac{16}{24}\) _____

Answer:

x = 6,

Explanation:

\(\frac{4}{x}\) = \(\frac{16}{24}\),

= \(\frac{4X24}{xX16}\),

= \(\frac{96}{16x}\),

x = \(\frac{96}{16}\),

x = 6.

Question 11.

\(\frac{13}{26}\) = \(\frac{y}{78}\) _____

Answer:

y = 39,

Explanation:

\(\frac{13}{26}\) = \(\frac{y}{78}\),

= \(\frac{13X78}{yX26}\),

= \(\frac{1014}{26y}\),

y = \(\frac{1014}{26}\),

y = 39.

Question 12.

\(\frac{11}{m}\) = \(\frac{132}{60}\) _____

Answer:

m = 5,

Explanation:

\(\frac{11}{m}\) = \(\frac{132}{60}\),

= \(\frac{11X60}{mX132}\),

= \(\frac{660}{132m}\),

m = \(\frac{660}{132}\),

m = 5.

Question 13.

\(\frac{18}{28}\) = \(\frac{n}{42}\) _____

Answer:

n = 27,

Explanation:

\(\frac{18}{28}\) = \(\frac{n}{42}\),

= \(\frac{18X42}{nX28}\),

= \(\frac{756}{28n}\),

n = \(\frac{756}{28}\),

n = 27.

Question 14.

\(\frac{x}{19}\) = \(\frac{15}{57}\) _____

Answer:

x = 5,

Explanation:

\(\frac{x}{19}\) = \(\frac{15}{57}\),

= \(\frac{xX57}{19X15}\),

= \(\frac{57x}{285}\),

x = \(\frac{285}{57}\),

x = 5.

Question 15.

\(\frac{x}{52}\) = \(\frac{58}{104}\) _____

Answer:

x = 29,

Explanation:

\(\frac{x}{52}\) = \(\frac{58}{104}\),

= \(\frac{xX104}{52X58}\),

= \(\frac{104x}{3016}\),

x = \(\frac{3016}{104}\),

x = 29.

Question 16.

\(\frac{18}{15}\) = \(\frac{n}{10}\) _____

Answer:

n = 12,

Explanation:

\(\frac{18}{15}\) = \(\frac{n}{10}\),

= \(\frac{18X10}{nX15}\),

= \(\frac{180}{15n}\),

n = \(\frac{180}{15}\),

n = 12.