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McGraw-Hill Math Grade 7 Answer Key Lesson 6.5 Adding or Subtracting Fractions with Unlike Denominators
Exercises Add or Subtract
Question 1.
\(\frac{1}{4}\) + \(\frac{1}{5}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 20.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{1}{4}\) = (1 x 5)/(4 x 5) = \(\frac{5}{20}\)
\(\frac{1}{5}\) = (1 x 4)/(5 x 4) = \(\frac{4}{20}\)
Third add the fractions.
\(\frac{5}{20}\) +\(\frac{4}{20}\) = \(\frac{9}{20}\)
\(\frac{1}{4}\) + \(\frac{1}{5}\) = \(\frac{9}{20}\)
Question 2.
\(\frac{2}{7}\) + \(\frac{2}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 21.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{2}{7}\) = (2 x 3)/(7 x 3) = \(\frac{6}{21}\)
\(\frac{2}{3}\) = (2 x 7)/(3 x 7) = \(\frac{14}{21}\)
Third add the fractions.
\(\frac{6}{21}\) +\(\frac{14}{21}\) = \(\frac{20}{21}\)
\(\frac{2}{7}\) + \(\frac{2}{3}\) = \(\frac{20}{21}\)
Question 3.
\(\frac{21}{20}\) + \(\frac{1}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 60.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{21}{20}\) = (21 x 3)/(20 x 3) = \(\frac{63}{60}\)
\(\frac{1}{3}\) = (1 x 20)/(3 x 20) = \(\frac{20}{60}\)
Third add the fractions.
\(\frac{63}{60}\) +\(\frac{20}{60}\) = \(\frac{83}{60}\)
\(\frac{21}{20}\) + \(\frac{1}{3}\) = \(\frac{83}{60}\)
Question 4.
\(\frac{12}{13}\) – \(\frac{1}{2}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 26.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{12}{13}\) = (12 x 2)/(13 x 2) = \(\frac{24}{26}\)
\(\frac{1}{2}\) = (1 x 13)/(2 x 13) = \(\frac{13}{26}\)
Third subtract the fractions.
\(\frac{24}{26}\) – \(\frac{13}{26}\) = \(\frac{11}{26}\)
\(\frac{12}{13}\) – \(\frac{1}{2}\) = \(\frac{11}{26}\)
Question 5.
\(\frac{3}{4}\) – \(\frac{1}{7}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 28.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{3}{4}\) = (3 x 7)/(4 x 7) = \(\frac{21}{28}\)
\(\frac{1}{7}\) = (1 x 4)/(7 x 4) = \(\frac{4}{28}\)
Third subtract the fractions.
\(\frac{21}{28}\) – \(\frac{4}{28}\) = \(\frac{17}{28}\)
\(\frac{3}{4}\) – \(\frac{1}{7}\) = \(\frac{17}{28}\)
Question 6.
\(\frac{23}{21}\) + \(\frac{1}{5}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 105.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{23}{21}\) = (23 x 5)/(21 x 5) = \(\frac{115}{105}\)
\(\frac{1}{5}\) = (1 x 21)/(5 x 21) = \(\frac{21}{105}\)
Third add the fractions.
\(\frac{115}{105}\) +\(\frac{21}{105}\) = \(\frac{136}{105}\)
\(\frac{23}{21}\) + \(\frac{1}{5}\) = \(\frac{136}{105}\)
Question 7.
\(\frac{32}{11}\) – \(\frac{2}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 33.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{32}{11}\) = (32 x 3)/(11 x 3) = \(\frac{96}{33}\)
\(\frac{2}{3}\) = (2 x 11)/(3 x 11) = \(\frac{22}{33}\)
Third subtract the fractions.
\(\frac{96}{33}\) – \(\frac{22}{33}\) = \(\frac{74}{33}\)
\(\frac{32}{11}\) – \(\frac{2}{3}\) = \(\frac{74}{33}\)
Question 8.
\(\frac{12}{7}\) + \(\frac{2}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 21.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{12}{7}\) = (12 x 3)/(7 x 3) = \(\frac{36}{21}\)
\(\frac{2}{3}\) = (2 x 7)/(3 x 7) = \(\frac{14}{21}\)
Third add the fractions.
\(\frac{36}{21}\) +\(\frac{14}{21}\) = \(\frac{50}{21}\)
\(\frac{12}{7}\) + \(\frac{2}{3}\) = \(\frac{50}{21}\)
Question 9.
\(\frac{8}{15}\) – \(\frac{1}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 15.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{8}{15}\) = (8 x 1)/(15 x 1) = \(\frac{8}{15}\)
\(\frac{1}{3}\) = (1 x 5)/(3 x 5) = \(\frac{5}{15}\)
Third subtract the fractions.
\(\frac{8}{15}\) – \(\frac{5}{15}\) = \(\frac{3}{15}\)
\(\frac{8}{15}\) – \(\frac{1}{3}\) = \(\frac{3}{15}\) or \(\frac{1}{5}\)
Question 10.
\(\frac{7}{8}\) – \(\frac{2}{5}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 40.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{7}{8}\) = (7 x 5)/(8 x 5) = \(\frac{35}{40}\)
\(\frac{2}{5}\) = (2 x 8)/(5 x 8) = \(\frac{16}{40}\)
Third subtract the fractions.
\(\frac{35}{40}\) – \(\frac{16}{40}\) = \(\frac{19}{40}\)
\(\frac{7}{8}\) – \(\frac{2}{5}\) = \(\frac{19}{40}\)
Question 11.
Answer:
Explanation:
First find the common multiple for both the denominators. The common multiple is 77.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{54}{11}\) = (54 x 7)/(11 x 7) = \(\frac{378}{77}\)
\(\frac{2}{7}\) = (2 x 11)/(7 x 11) = \(\frac{22}{77}\)
Third add the fractions.
\(\frac{378}{77}\) + \(\frac{22}{77}\) = \(\frac{400}{77}\)
Question 12.
Answer:
Explanation:
First find the common multiple for both the denominators. The common multiple is 60.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{13}{12}\) = (13 x 5)/(12 x 5) = \(\frac{65}{60}\)
\(\frac{4}{5}\) = (4 x 12)/(5 x 12) = \(\frac{48}{60}\)
Third subtract the fractions.
\(\frac{65}{60}\) – \(\frac{48}{60}\) = \(\frac{17}{60}\)
Question 13.
Answer:
Explanation:
First find the common multiple for both the denominators. The common multiple is 39.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{56}{13}\) = (56 x 3)/(13 x 3) = \(\frac{168}{39}\)
\(\frac{2}{3}\) = (2 x 13)/(3 x 13) = \(\frac{26}{39}\)
Third subtract the fractions.
\(\frac{168}{39}\) – \(\frac{26}{39}\) = \(\frac{142}{39}\)
Question 14.
Answer:
Explanation:
First find the common multiple for both the denominators. The common multiple is 20.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{3}{4}\) = (3 x 5)/(4 x 5) = \(\frac{15}{20}\)
\(\frac{2}{5}\) = (2 x 4)/(5 x 4) = \(\frac{8}{20}\)
Third subtract the fractions.
\(\frac{15}{20}\) – \(\frac{8}{20}\) = \(\frac{7}{20}\)
Question 15.
Answer:
Explanation:
First find the common multiple for both the denominators. The common multiple is 4.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{21}{4}\) = (21 x 1)/(4 x 1) = \(\frac{21}{4}\)
\(\frac{5}{2}\) = (5 x 2)/(2 x 2) = \(\frac{10}{4}\)
Third subtract the fractions.
\(\frac{21}{4}\) – \(\frac{10}{4}\) = \(\frac{11}{4}\)