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\( \Large \frac{5}{6} \div \frac{6}{7} \times ?-\frac{8}{9} \div 1\frac{3}{5}+\frac{3}{4} \times 3\frac{1}{3} = 2\frac{7}{9} \)

A) \( \Large \frac{7}{7} \)
B) \( \Large \frac{6}{7} \)
C) \( \Large \frac{8}{7} \)
D) None of these

Correct Answer:


B) \( \Large \frac{6}{7} \)

Description for Correct answer:
\( \Large \frac{5}{6} \div \frac{6}{7} \times ?-\frac{8}{9}\div 1\frac{3}{5}+\frac{3}{4}\times 3\frac{1}{3}=2\frac{7}{9} \)

= \( \Large \frac{5}{6} \div \frac{6}{7} \times x-\frac{8}{9} \div \frac{8}{5}+\frac{3}{4} \times \frac{10}{3}=\frac{25}{9} \)

= \( \Large \frac{5}{6} \div \frac{6}{7} \times x-\frac{8}{9} \times \frac{5}{8}+\frac{5}{2}=\frac{25}{9} \)

= \( \Large \frac{5}{6} \times \frac{7}{6}x-\frac{8}{9} \times \frac{5}{8}+\frac{5}{2}=\frac{25}{9} \)

= \( \Large \frac{35}{36}x-\frac{5}{9}+\frac{5}{2}=\frac{25}{9} \)

= \( \Large \frac{35x-20+90}{36}=\frac{25}{9} \)

\( \Large \frac{35x-20+90}{36}=\frac{25}{9} \)

\( \Large 35x+70 = 100 \)

\( \Large 35x = 100-70 = 30 \)

\( \Large x = \frac{30}{35}=\frac{6}{7} \)

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification

Comments

Similar Questions

1). \( \Large 5\frac{1}{2}+4\frac{1}{6}-x+2\frac{2}{3}=4\frac{1}{2} \)

A). \( \Large 2\frac{5}{6} \)

B). \( \Large 4\frac{5}{6} \)

C). \( \Large 7\frac{5}{6} \)

D). \( \Large 6\frac{5}{6} \)

2). How many \( \Large \frac{1}{8} \)'s are there in \( \Large 37\frac{1}{2} \)

A). 300

B). 400

C). 500

D). Cannot be determined

3). Simplify: \( \Large \frac{1.5+1\frac{2}{3} \div \frac{5}{3}}{\frac{4}{3} \times 1\frac{4}{5} \div \frac{2}{5}} \)

A). \( \Large \frac{2}{5} \)

B). \( \Large \frac{5}{12} \)

C). \( \Large \frac{5}{6} \)

D). \( \Large \frac{2}{3} \)

4). Simplify: \( \Large \frac{1.75 \times 1.75 \times 1.75+1.25 \times 1.25 \times 1.25}{1.75 \times 1.75-1.75 \times 1.25+1.25 \times 1.25} \)

A). 3

B). 6

C). 4

D). 5

5). \( \Large \frac{2+2 \times 2}{2 \div 2 \times 2} \div \frac{\frac{1}{2} \div \frac{1}{2}\ of\ \frac{1}{2}}{\frac{1}{2}+\frac{1}{2}\ of\ \frac{1}{2}} \)

A). \( \Large \frac{9}{8} \)

B). \( \Large \frac{9}{4} \)

C). \( \Large \frac{9}{2} \)

D). None of these

6). Solve: \( \Large \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} \)

A). \( \Large 4+\sqrt{15} \)

B). \( \Large 2+\sqrt{15} \)

C). \( \Large 2\sqrt{5}+2\sqrt{3} \)

D). \( \Large 4+2\sqrt{15} \)

7). \( \Large 16 \times \left(12\frac{5}{12} \times 15\frac{1}{4}\right)-5\frac{1}{2} \times 4\frac{1}{2} \)

A). 3005

B). 3200

C). 2400

D). 3280

8). The value of \( \LARGE \frac{1}{3+\frac{2}{2+\frac{1}{2}}} \)is

A). 45

B). \( \Large \frac{5}{4} \)

C). \( \Large \frac{5}{19} \)

D). \( \Large \frac{19}{5} \)

9). What fraction must be subtracted from the sum \( \Large \frac{1}{4} \) and \( \Large \frac{1}{6} \) to have an average of \( \Large \frac{1}{12} \) of all three fraction

A). \( \Large \frac{1}{2} \)

B). \( \Large \frac{1}{3} \)

C). \( \Large \frac{1}{4} \)

D). \( \Large \frac{1}{6} \)

10). A was asked to find \( \Large \frac{4}{9} \) of a fraction. He made a mistake of dividing the fraction by \( \Large \frac{4}{9} \) and so got an answer which exceeded the correct answer by \( \Large \frac{13}{18} \). The correct answer is.

A). \( \Large \frac{8}{45} \)

B). \( \Large \frac{7}{45} \)

C). \( \Large \frac{6}{39} \)

D). \( \Large \frac{1}{20} \)