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:
\(\frac{x}{52}\) = \(\frac{58}{104}\) = \(\frac{x X 104}{52 X 58}\) = \(\frac{104x}{3016}\),
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.