McGraw Hill Math Grade 8 Lesson 4.2 Answer Key Multiplying Two Fractions: Reciprocals

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 4.2 Multiplying Two Fractions: Reciprocals to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 4.2 Multiplying Two Fractions: Reciprocals

Exercises Multiply

Question 1.
\(\frac{3}{2}\) × \(\frac{4}{9}\)
Answer:
\(\frac{2}{3}\),

Explanation:
When we multiply \(\frac{3}{2}\) X \(\frac{4}{9}\), We get \(\frac{3 X 4}{2 X 9}\) = \(\frac{12}{18}\) both goes by 6 we get  \(\frac{6 X 2}{6 X 3}\) = \(\frac{2}{3}\).

Question 2.
\(\frac{5}{9}\) × \(\frac{12}{30}\)
Answer:
\(\frac{2}{9}\),

Explanation:
When we multiply \(\frac{5}{9}\) X \(\frac{12}{30}\) we get \(\frac{5 X 12}{9 X 30}\) = \(\frac{60}{270}\) both goes by 30, So \(\frac{2 X 30}{9 X 30}\) = \(\frac{2}{9}\).

Question 3.
\(\frac{15}{21}\) × \(\frac{6}{25}\)
Answer:
\(\frac{6}{35}\),

Explanation:
When we multiply \(\frac{15}{21}\) X \(\frac{6}{25}\) we get
\(\frac{15 X 6}{21 X 25}\) = \(\frac{90}{525}\) both goes by 15, So \(\frac{6 X 15}{35 X 15}\) = \(\frac{6}{35}\),

Question 4.
\(\frac{1}{2}\) × \(\frac{1}{2}\)
Answer:
\(\frac{1}{4}\),

Explanation:
When we multiply \(\frac{1}{2}\) X \(\frac{1}{2}\) we get \(\frac{1 X 1}{2 X 2}\) = \(\frac{1}{4}\).

Question 5.
\(\frac{2}{3}\) × \(\frac{3}{4}\)
Answer:
\(\frac{1}{2}\),

Explanation:
When we multiply \(\frac{2}{3}\) X \(\frac{3}{4}\) we get
\(\frac{2 X 3}{3 X 4}\) = \(\frac{6}{12}\) both goes by 6, So
\(\frac{1 X 6}{2 X 6}\) = \(\frac{1}{2}\).

Question 6.
\(\frac{5}{4}\) × \(\frac{16}{35}\)
Answer:
\(\frac{4}{7}\),

Explanation:
When we multiply \(\frac{5}{4}\) X \(\frac{16}{35}\) we get
\(\frac{5 X 16}{4 X 35}\) = \(\frac{80}{140}\) both goes by 20, So
\(\frac{4 X 20}{7 X 20}\) = \(\frac{4}{7}\),

Question 7.
\(\frac{5}{18}\) × \(\frac{9}{25}\)
Answer:
\(\frac{1}{10}\),

Explanation:
When we multiply \(\frac{5}{18}\) X \(\frac{9}{25}\) we get \(\frac{5 X 9}{18 X 25}\) = \(\frac{45}{450}\) both goes by 45, So
\(\frac{1 X 45}{10 X 45}\) = \(\frac{1}{10}\).

Question 8.
\(\frac{4}{14}\) × \(\frac{28}{64}\)
Answer:
\(\frac{1}{8}\),

Explanation:
When we multiply \(\frac{4}{14}\) X \(\frac{28}{64}\) we get
\(\frac{4 X 28}{14 X 64}\) = \(\frac{112}{896}\) both goes by 112, So \(\frac{1}{8}\).

Question 9.
\(\frac{13}{22}\) × \(\frac{11}{13}\)
Answer:
\(\frac{1}{2}\),

Explanation:
When we multiply \(\frac{13}{22}\) X \(\frac{11}{13}\) we get
\(\frac{13 X 11}{22 X 13}\) = \(\frac{143}{286}\) both goes by 143,
So \(\frac{1 X 143}{2 X 286}\).

Question 10.
\(\frac{12}{13}\) × \(\frac{52}{72}\)
Answer:
\(\frac{2}{3}\),

Explanation:
When we multiply \(\frac{12}{13}\) X \(\frac{52}{72}\) we get
\(\frac{12 X 52}{13 X 72}\) = \(\frac{624}{936}\) both goes by 312,
So \(\frac{2 X 312}{3 X 312}\) = \(\frac{2}{3}\).

Question 11.
\(\frac{2}{15}\) × \(\frac{2}{15}\)
Answer:
\(\frac{4}{225}\),

Explanation:
When we multiply \(\frac{2}{15}\) X \(\frac{2}{15}\) we get
\(\frac{2 X 2}{15 X 15}\) = \(\frac{4}{225}\).

Question 12.
\(\frac{21}{24}\) × \(\frac{8}{35}\)
Answer:
\(\frac{1}{5}\),

Explanation:
When we multiply \(\frac{21}{24}\) X \(\frac{8}{35}\) we get
\(\frac{21 X 8}{24 X 35}\) = \(\frac{168}{840}\) both goes by 168, \(\frac{1}{5}\).

Question 13.
\(\frac{48}{21}\) × \(\frac{42}{64}\)
Answer:
\(\frac{3}{2}\),

Explanation:
When we multiply \(\frac{48}{21}\) X \(\frac{42}{64}\) we get
\(\frac{48 X 42}{21 X 64}\) = \(\frac{2016}{1344}\) both goes by 672, So \(\frac{3}{2}\).

Question 14.
\(\frac{7}{9}\) × \(\frac{9}{14}\)
Answer:
\(\frac{1}{2}\),

Explanation:
When we multiply \(\frac{7}{9}\) X \(\frac{9}{14}\) we get
\(\frac{7 X 9}{9 X 14}\) = \(\frac{63}{126}\) both goes by 63, So \(\frac{1 x 63}{2 X 63}\) = \(\frac{1}{2}\).

Question 15.
\(\frac{15}{18}\) × \(\frac{9}{25}\)
Answer:
\(\frac{3}{10}\),

Explanation:
When we multiply \(\frac{15}{18}\) X \(\frac{9}{25}\) we get \(\frac{15 X 9}{18 X 25}\) = \(\frac{135}{450}\) both goes by 45, So \(\frac{3 X 45}{10 X 45}\) = \(\frac{3}{10}\).

Question 16.
\(\frac{10}{13}\) × \(\frac{26}{45}\)
Answer:
\(\frac{4}{9}\),

Explanation:
When we multiply \(\frac{10}{13}\) X \(\frac{26}{45}\) we get
\(\frac{10 X 26}{13 X 45}\) = \(\frac{260}{585}\) both goes by 65,
So \(\frac{4 X 65}{9 X 65}\) = \(\frac{4}{9}\).

Question 17.
Daisy runs on an oval track that is \(\frac{1}{4}\) of a mile long. If she runs \(\frac{5}{16}\) of the way around the track, how far did she run?
Answer:
\(\frac{5}{64}\) mile long Daisy ran on an oval track,

Explanation:
When Daisy runs we multiply \(\frac{1}{4}\) mile long track with  \(\frac{5}{16}\) way Daisy ran around the track  we get \(\frac{1 X 5}{4 X 16}\) = \(\frac{5}{64}\) mile long Daisy ran.

Question 18.
Bart’s family’s motorboat uses \(\frac{22}{6}\) gallons of gas every hour. If they run the boat for \(\frac{1}{3}\) of an hour, how much gas will they be using?
Answer:
\(\frac{11}{9}\) gallons of gas will be used every hour,

Explanation:
When we multiply Bart’s family’s motorboat uses  \(\frac{22}{6}\) gallons of gas is used every hour by Barts family’s boat  \(\frac{1}{3}\) of an hour, we get \(\frac{22 X 1}{6 X 3}\) = \(\frac{22}{18}\) both goes by 2 we get \(\frac{11 X 2}{9 X 2}\) =  \(\frac{11}{9}\) gallons of gas would be used for every hour.

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