Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 9.2 Proportions and Cross-Multiplying will engage students and is a great way of informal assessment.
McGraw-Hill Math Grade 6 Answer Key Lesson 9.2 Proportions and Cross-Multiplying
Exercises Solve for x.
Question 1.
\(\frac{4}{7}\) = \(\frac{x}{28}\)
Answer:
\(\frac{4}{7}\) = \(\frac{x}{28}\)
=> x = 16.
Explanation:
\(\frac{4}{7}\) = \(\frac{x}{28}\)
=> \(\frac{4}{7}\) × 28 = x
=> \(\frac{4}{1}\) × 4 = x
=> 16 = x.
Question 2.
\(\frac{3}{5}\) = \(\frac{12}{x}\)
Answer:
\(\frac{3}{5}\) = \(\frac{12}{x}\)
=> x = 20.
Explanation:
\(\frac{3}{5}\) = \(\frac{12}{x}\)
=> \(\frac{3}{5}\) × x = 12
=> x = 12 × \(\frac{5}{3}\)
=> x = 4 × \(\frac{5}{1}\)
=> x = 20.
Question 3.
\(\frac{12}{x}\) = \(\frac{36}{51}\)
Answer:
\(\frac{12}{x}\) = \(\frac{36}{51}\)
=> x = 17.
Explanation:
\(\frac{12}{x}\) = \(\frac{36}{51}\)
=> 12 = x × \(\frac{36}{51}\)
=> 12 × \(\frac{51}{36}\) = x
=> 1 × \(\frac{51}{3}\) = x
=> \(\frac{17}{1}\) = x
=> 17 = x.
Question 4.
\(\frac{2}{3}\) = \(\frac{x}{21}\)
Answer:
\(\frac{2}{3}\) = \(\frac{x}{21}\)
=> x = 14.
Explanation:
\(\frac{2}{3}\) = \(\frac{x}{21}\)
=> \(\frac{2}{3}\) × 21 = x
=> \(\frac{2}{1}\) × 7 = x
=> 14 = x.
Question 5.
\(\frac{x}{14}\) = \(\frac{2}{7}\)
Answer:
\(\frac{x}{14}\) = \(\frac{2}{7}\)
=> x = 4.
Explanation:
\(\frac{x}{14}\) = \(\frac{2}{7}\)
=> x = 14 × \(\frac{2}{7}\)
=> x = 2 × \(\frac{2}{1}\)
=> x = 4.
Question 6.
\(\frac{10}{55}\) = \(\frac{x}{11}\)
Answer:
\(\frac{10}{55}\) = \(\frac{x}{11}\)
=> x = 2.
Explanation:
\(\frac{10}{55}\) = \(\frac{x}{11}\)
=> \(\frac{10}{55}\) × 11 = x
=> \(\frac{10}{5}\) × 1 = x
=> \(\frac{2}{1}\) = x
=> 2 = x.
Question 7.
\(\frac{33}{44}\) = \(\frac{3}{x}\)
Answer:
\(\frac{33}{44}\) = \(\frac{3}{x}\)
=> x = 4.
Explanation:
\(\frac{33}{44}\) = \(\frac{3}{x}\)
=> \(\frac{33}{44}\) × x = 3
=> x = 3 × \(\frac{44}{33}\)
=> x = 1 × \(\frac{44}{11}\)
=> x = \(\frac{4}{1}\)
=> x = 4.
Question 8.
\(\frac{3}{51}\) = \(\frac{1}{x}\)
Answer:
\(\frac{3}{51}\) = \(\frac{1}{x}\)
=> x = 17.
Explanation:
\(\frac{3}{51}\) = \(\frac{1}{x}\)
=> \(\frac{3}{51}\) × x = 1
=> x = 1 × \(\frac{51}{3}\)
=> x = \(\frac{17}{1}\)
=> x = 17.
Question 9.
\(\frac{39}{63}\) = \(\frac{x}{126}\)
Answer:
\(\frac{39}{63}\) = \(\frac{x}{126}\)
=> x = 78.
Explanation:
\(\frac{39}{63}\) = \(\frac{x}{126}\)
=> \(\frac{39}{63}\) × 126 = x
=> \(\frac{13}{21}\) × 126 = x
=> \(\frac{13}{1}\) × 6 = x
=> 78 = x.
Question 10.
\(\frac{49}{14}\) = \(\frac{7}{x}\)
Answer:
\(\frac{49}{14}\) = \(\frac{7}{x}\)
=> x = 2.
Explanation:
\(\frac{49}{14}\) = \(\frac{7}{x}\)
=> \(\frac{49}{14}\) × x = 7
=> x = 7 × \(\frac{14}{49}\)
=> x = 1 × \(\frac{14}{7}\)
=> x = \(\frac{2}{1}\)
=> x = 2.
Question 11.
\(\frac{5}{11}\) = \(\frac{x}{121}\)
Answer:
\(\frac{5}{11}\) = \(\frac{x}{121}\)
=> x = 55.
Explanation:
\(\frac{5}{11}\) = \(\frac{x}{121}\)
=> \(\frac{5}{11}\) × 121 = x
=> \(\frac{5}{1}\) × 11 = x
=> 55 = x.
Question 12.
\(\frac{4}{13}\) = \(\frac{x}{52}\)
Answer:
\(\frac{4}{13}\) = \(\frac{x}{52}\)
=> x = 16.
Explanation:
\(\frac{4}{13}\) = \(\frac{x}{52}\)
=> \(\frac{4}{13}\) × 52 = x
=> \(\frac{4}{1}\) × 4 = x
=> 16 = x.
Question 13.
\(\frac{7}{8}\) = \(\frac{91}{x}\)
Answer:
\(\frac{7}{8}\) = \(\frac{91}{x}\)
=> x = 104.
Explanation:
\(\frac{7}{8}\) = \(\frac{91}{x}\)
=> \(\frac{7}{8}\) × x = 91
=> x = 91 × \(\frac{8}{7}\)
=> x = 13 × \(\frac{8}{1}\)
=> x = 104.
Question 14.
\(\frac{10}{31}\) = \(\frac{110}{x}\)
Answer:
\(\frac{10}{31}\) = \(\frac{110}{x}\)
=> x = 341.
Explanation:
\(\frac{10}{31}\) = \(\frac{110}{x}\)
=> \(\frac{10}{31}\) × x = 110
=> x = 110 × \(\frac{31}{10}\)
=> x = 11 × \(\frac{31}{1}\)
=> x = 341.
Question 15.
\(\frac{19}{57}\) = \(\frac{4}{x}\)
Answer:
\(\frac{19}{57}\) = \(\frac{4}{x}\)
=> x = 12.
Explanation:
\(\frac{19}{57}\) = \(\frac{4}{x}\)
=> \(\frac{19}{57}\) × x = 4.
=> x = 4 × \(\frac{57}{19}\)
=> x = 4 × \(\frac{3}{1}\)
=> x = 12.
Question 16.
\(\frac{13}{117}\) = \(\frac{x}{27}\)
Answer:
\(\frac{13}{117}\) = \(\frac{x}{27}\)
=> x = 3.
Explanation:
\(\frac{13}{117}\) = \(\frac{x}{27}\)
=> \(\frac{13}{117}\) × 27 = x
=> \(\frac{13}{39}\) × 9 = x
=> \(\frac{1}{3}\) × 9 = x
=> \(\frac{1}{1}\) × 3 = x
=> 3 = x.
Question 17.
\(\frac{4}{7}\) = \(\frac{x}{35}\)
Answer:
\(\frac{4}{7}\) = \(\frac{x}{35}\)
=> x = 20.
Explanation:
\(\frac{4}{7}\) = \(\frac{x}{35}\)
=> \(\frac{4}{7}\) × 35 = x
=> \(\frac{4}{1}\) × 5 = x
=> 20 = x.
Question 18.
\(\frac{22}{x}\) = \(\frac{5}{110}\)
Answer:
\(\frac{22}{x}\) = \(\frac{5}{110}\)
=> x = 484.
Explanation:
\(\frac{22}{x}\) = \(\frac{5}{110}\)
=> 22 = x × \(\frac{5}{110}\)
=> 22 × \(\frac{110}{5}\) = x
=> 22 × \(\frac{22}{1}\) = x
=> 484 = x.
Question 19.
\(\frac{x}{130}\) = \(\frac{7}{91}\)
Answer:
\(\frac{x}{130}\) = \(\frac{7}{91}\)
=> x = 10.
Explanation:
\(\frac{x}{130}\) = \(\frac{7}{91}\)
=> x = 130 × \(\frac{7}{91}\)
=> x = 10 × \(\frac{7}{7}\)
=> x = 10 × \(\frac{1}{1}\)
=> x = 10.
Question 20.
\(\frac{18}{6}\) = \(\frac{81}{x}\)
Answer:
\(\frac{18}{6}\) = \(\frac{81}{x}\)
=> x = 27.
Explanation:
\(\frac{18}{6}\) = \(\frac{81}{x}\)
=> \(\frac{18}{6}\) × x = 81.
=> x = 81 × \(\frac{6}{18}\)
=> x = 9 × \(\frac{6}{2}\)
=> x = 9 × \(\frac{3}{1}\)
=>x = 27.
Question 21.
\(\frac{10}{121}\) = \(\frac{220}{x}\)
Answer:
\(\frac{10}{121}\) = \(\frac{220}{x}\)
=> x = 2,662.
Explanation:
\(\frac{10}{121}\) = \(\frac{220}{x}\)
=> \(\frac{10}{121}\) × x = 220
=> x = 220 × \(\frac{121}{10}\)
=> x = 22 × \(\frac{121}{1}\)
=> x = 2,662.
Question 22.
\(\frac{23}{x}\) = \(\frac{92}{16}\)
Answer:
\(\frac{23}{x}\) = \(\frac{92}{16}\)
=> x = 4.
Explanation:
\(\frac{23}{x}\) = \(\frac{92}{16}\)
=> 23 = x × \(\frac{92}{16}\)
=> 23 × \(\frac{16}{92}\) = x
=> 1 × \(\frac{16}{4}\) = x
=> 1 × \(\frac{4}{1}\) = x
=> 4 = x.
Question 23.
\(\frac{23}{4}\) = \(\frac{92}{x}\)
Answer:
\(\frac{23}{4}\) = \(\frac{92}{x}\)
=> x = 16.
Explanation:
\(\frac{23}{4}\) = \(\frac{92}{x}\)
=> \(\frac{23}{4}\) × x = 92
=> x = 92 × \(\frac{4}{23}\)
=> x = 4 × \(\frac{4}{1}\)
=> x = 16.
Question 24.
\(\frac{x}{17}\) = \(\frac{48}{68}\)
Answer:
\(\frac{x}{17}\) = \(\frac{48}{68}\)
=> x = 12.
Explanation:
\(\frac{x}{17}\) = \(\frac{48}{68}\)
=> x = 17 × \(\frac{48}{68}\)
=> x = 1 × \(\frac{48}{4}\)
=> x = 1 × \(\frac{12}{1}\)
=> x = 12.
Question 25.
\(\frac{12}{x}\) = \(\frac{2}{7}\)
Answer:
\(\frac{12}{x}\) = \(\frac{2}{7}\)
=> x = 42.
Explanation:
\(\frac{12}{x}\) = \(\frac{2}{7}\)
=> 12 = x × \(\frac{2}{7}\)
=> 12 × \(\frac{7}{2}\) = x
=> 6 × \(\frac{7}{1}\) = x
=> 42 = x.
Question 26.
\(\frac{7}{x}\) = \(\frac{70}{120}\)
Answer:
\(\frac{7}{x}\) = \(\frac{70}{120}\)
=> x = 12.
Explanation:
\(\frac{7}{x}\) = \(\frac{70}{120}\)
=> 7 = x × \(\frac{70}{120}\)
=> 7 × \(\frac{120}{70}\) = x
=> 1 × \(\frac{120}{10}\) = x
=> \(\frac{12}{1}\) = x
=> 12 = x.
Question 27.
\(\frac{3}{4}\) = \(\frac{123}{x}\)
Answer:
\(\frac{3}{4}\) = \(\frac{123}{x}\)
=> x = 164.
Explanation:
\(\frac{3}{4}\) = \(\frac{123}{x}\)
=> \(\frac{3}{4}\) x = 123
=> x = 123 × \(\frac{4}{3}\)
=> x = 41 × \(\frac{4}{1}\)
=> x = 164.
Question 28.
\(\frac{x}{55}\) = \(\frac{28}{220}\)
Answer:
\(\frac{x}{55}\) = \(\frac{28}{220}\)
=> x = 7.
Explanation:
\(\frac{x}{55}\) = \(\frac{28}{220}\)
=> x = 55 × \(\frac{28}{220}\)
=> x = 11 × \(\frac{28}{44}\)
=> x = 1 × \(\frac{28}{4}\)
=> x = 1 × \(\frac{7}{1}\)
=> x = 7.