Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 5 Lesson 5.5 Subtracting Mixed Numbers regularly and improve your accuracy in solving questions.
Spectrum Math Grade 5 Chapter 5 Lesson 5.5 Subtracting Mixed Numbers Answers Key
Rename fractions to have common denominators.
Subtract the fractions, then subtract the whole numbers.
Write the difference in simplest form.
Subtract. Write answers in simplest form.
Question 1.
a.
Answer:
4\(\frac{2}{3}\) – 2\(\frac{1}{6}\)
4 + \(\frac{2}{3}\) – 2 – \(\frac{1}{6}\)
4 – 2 = 2
\(\frac{2}{3}\) – \(\frac{1}{6}\)
LCD is 6
\(\frac{4}{6}\) – \(\frac{1}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)
2 + \(\frac{1}{2}\) = 2\(\frac{1}{2}\)
b.
Answer:
7\(\frac{7}{8}\) – 2\(\frac{3}{4}\)
7 + \(\frac{7}{8}\) – 2 – \(\frac{3}{4}\)
7 – 2 = 5
\(\frac{7}{8}\) – \(\frac{3}{4}\)
LCD is 8
\(\frac{7}{8}\) – \(\frac{6}{8}\) = \(\frac{1}{8}\)
5 + \(\frac{1}{8}\) = 5\(\frac{1}{8}\)
c.
Answer:
8\(\frac{9}{10}\) – 6\(\frac{2}{5}\)
8 + \(\frac{9}{10}\) – 6 – \(\frac{2}{5}\)
8 – 6 = 2
\(\frac{9}{10}\) – \(\frac{2}{5}\)
LCD is 10
\(\frac{9}{10}\) – \(\frac{4}{10}\) = \(\frac{5}{10}\) = \(\frac{1}{2}\)
2 + \(\frac{1}{2}\) = 2\(\frac{1}{2}\)
d.
Answer:
8\(\frac{3}{4}\) – 4\(\frac{3}{8}\)
8 + \(\frac{3}{4}\) – 4 – \(\frac{3}{8}\)
8 – 4 = 4
\(\frac{3}{4}\) – \(\frac{3}{8}\)
LCD is 8.
\(\frac{6}{8}\) – \(\frac{3}{8}\) = \(\frac{3}{8}\)
4 + \(\frac{3}{8}\) = 4\(\frac{3}{8}\)
e.
Answer:
3\(\frac{1}{3}\) – 2\(\frac{2}{9}\)
3 + \(\frac{1}{3}\) – 2 – \(\frac{2}{9}\)
3 – 2 = 1
\(\frac{1}{3}\) – \(\frac{2}{9}\)
LCD is 9.
\(\frac{3}{9}\) – \(\frac{2}{9}\) = \(\frac{1}{9}\)
1 + \(\frac{1}{9}\) = 1\(\frac{1}{9}\)
Question 2.
a.
Answer:
6\(\frac{5}{8}\) – 4\(\frac{3}{7}\)
6 + \(\frac{5}{8}\) – 4 – \(\frac{3}{7}\)
6 – 4 = 2
\(\frac{5}{8}\) – \(\frac{3}{7}\)
LCD is 56
\(\frac{35}{56}\) – \(\frac{24}{56}\) = \(\frac{11}{56}\)
2 + \(\frac{11}{56}\) = 2\(\frac{11}{56}\)
b.
Answer:
5\(\frac{1}{2}\) – 1\(\frac{1}{6}\)
5 + \(\frac{1}{2}\) – 1 – \(\frac{1}{6}\)
5 – 1 = 4
\(\frac{1}{2}\) – \(\frac{1}{6}\)
LCD is 6.
\(\frac{3}{6}\) – \(\frac{1}{6}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)
4 + \(\frac{1}{3}\) = 4\(\frac{1}{3}\)
c.
Answer:
9\(\frac{7}{8}\) – 4\(\frac{2}{5}\)
9 + \(\frac{7}{8}\) – 4 – \(\frac{2}{5}\)
9 – 4 = 5
\(\frac{7}{8}\) – \(\frac{2}{5}\)
LCD is 40
\(\frac{35}{40}\) – \(\frac{16}{40}\) = \(\frac{19}{40}\)
5 + \(\frac{19}{40}\) = 5\(\frac{19}{40}\)
d.
Answer:
9\(\frac{5}{9}\) – 3\(\frac{1}{3}\)
9 + \(\frac{5}{9}\) – 3 – \(\frac{1}{3}\)
9 – 3 = 6
\(\frac{5}{9}\) – \(\frac{1}{3}\)
LCD is 9
\(\frac{5}{9}\) – \(\frac{3}{9}\) = \(\frac{2}{9}\)
6 + \(\frac{2}{9}\) = 6\(\frac{2}{9}\)
e.
Answer:
7\(\frac{7}{10}\) – 4\(\frac{4}{7}\)
7 + \(\frac{7}{10}\) – 4 – \(\frac{4}{7}\)
7 – 4 = 3
\(\frac{7}{10}\) – \(\frac{4}{7}\)
LCD is 70.
\(\frac{49}{70}\) – \(\frac{40}{70}\) = \(\frac{9}{70}\)
3 + \(\frac{9}{70}\) = 3\(\frac{9}{70}\)
Question 3.
a.
Answer:
8\(\frac{8}{12}\) – 2\(\frac{3}{4}\)
8 + \(\frac{8}{12}\) – 2 – \(\frac{3}{4}\)
8 – 2 = 6
\(\frac{8}{12}\) – \(\frac{3}{4}\)
LCD is 12
\(\frac{8}{12}\) – \(\frac{9}{12}\) = –\(\frac{1}{12}\)
6 – \(\frac{1}{12}\) = 5\(\frac{11}{12}\)
b.
Answer:
9\(\frac{3}{10}\) – 6\(\frac{1}{8}\)
9 + \(\frac{3}{10}\) – 6 – \(\frac{1}{8}\)
9 – 6 = 3
\(\frac{3}{10}\) – \(\frac{1}{8}\)
LCD is 40
\(\frac{12}{40}\) – \(\frac{5}{40}\) = \(\frac{7}{40}\)
3 + \(\frac{7}{40}\) = 3\(\frac{7}{40}\)
c.
Answer:
8\(\frac{4}{6}\) – 5\(\frac{2}{8}\)
8 + \(\frac{4}{6}\) – 5 – \(\frac{2}{8}\)
8 – 5 = 3
\(\frac{4}{6}\) – \(\frac{2}{8}\)
LCD is 24
\(\frac{16}{24}\) – \(\frac{6}{24}\) = \(\frac{10}{24}\) = \(\frac{5}{12}\)
3 + \(\frac{5}{12}\) = 3\(\frac{5}{12}\)
d.
Answer:
6\(\frac{6}{7}\) – 3\(\frac{3}{5}\)
6 + \(\frac{6}{7}\) – 3 – \(\frac{3}{5}\)
6 – 3 = 3
\(\frac{6}{7}\) – \(\frac{3}{5}\)
LCD is 35
\(\frac{30}{35}\) – \(\frac{21}{35}\) = \(\frac{9}{35}\)
3 + \(\frac{9}{35}\) = 3\(\frac{9}{35}\)
e.
Answer:
5\(\frac{5}{6}\) – 3\(\frac{1}{12}\)
5 + \(\frac{5}{6}\) – 3 – \(\frac{1}{12}\)
5 – 3 = 2
\(\frac{5}{6}\) – \(\frac{1}{12}\)
LCD is 6.
\(\frac{5}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)
2 + \(\frac{1}{3}\) = 2\(\frac{1}{3}\)
Subtract. Write answers in simplest form.
Question 1.
a.
Answer:
4 – \(\frac{3}{8}\) = 3\(\frac{5}{8}\)
b.
Answer:
5\(\frac{5}{6}\) – 1\(\frac{1}{3}\)
5 + \(\frac{5}{6}\) – 1 – \(\frac{1}{3}\)
5 – 1 = 4
\(\frac{5}{6}\) – \(\frac{1}{3}\)
LCD is 6.
\(\frac{5}{6}\) – \(\frac{2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)
4 + \(\frac{1}{2}\) = 4\(\frac{1}{2}\)
c.
Answer:
8 – 3\(\frac{5}{8}\)
8 – 3 – \(\frac{5}{8}\)
8 – 3 = 5
5 – \(\frac{5}{8}\) = 4\(\frac{3}{8}\)
d.
Answer:
4\(\frac{3}{5}\) – \(\frac{3}{10}\)
4 + \(\frac{3}{5}\) – \(\frac{3}{10}\)
\(\frac{3}{5}\) – \(\frac{3}{10}\)
LCD is 10
\(\frac{6}{10}\) – \(\frac{3}{10}\) = \(\frac{3}{10}\)
4 + \(\frac{3}{10}\) = 4\(\frac{3}{10}\)
Question 2.
a.
Answer:
5\(\frac{3}{4}\) – 4\(\frac{5}{8}\)
5 + \(\frac{3}{4}\) – 4 – \(\frac{5}{8}\)
5 – 4 = 1
\(\frac{3}{4}\) – \(\frac{5}{8}\)
LCD is 8.
\(\frac{6}{8}\) – \(\frac{5}{8}\) = \(\frac{1}{8}\)
1 + \(\frac{1}{8}\) = 1\(\frac{1}{8}\)
b.
Answer:
8\(\frac{2}{3}\) – 4\(\frac{1}{6}\)
8 + \(\frac{2}{3}\) – 4 – \(\frac{1}{6}\)
8 – 4 = 4
\(\frac{2}{3}\) – \(\frac{1}{6}\)
LCD is 6
\(\frac{4}{6}\) – \(\frac{1}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)
4 + \(\frac{1}{2}\) = 4\(\frac{1}{2}\)
c.
Answer:
5\(\frac{5}{6}\) – 3\(\frac{3}{4}\)
5 + \(\frac{5}{6}\) – 3 – \(\frac{3}{4}\)
5 – 3 = 2
\(\frac{5}{6}\) – \(\frac{3}{4}\)
LCD is 12
\(\frac{10}{12}\) – \(\frac{9}{12}\) = \(\frac{1}{12}\)
2 + \(\frac{1}{12}\) = 2\(\frac{1}{12}\)
d.
Answer:
7\(\frac{4}{5}\) – 2\(\frac{1}{2}\)
7 + \(\frac{4}{5}\) – 2 – \(\frac{1}{2}\)
7 – 2 = 5
\(\frac{4}{5}\) – \(\frac{1}{2}\)
LCD is 10
\(\frac{8}{10}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)
5 + \(\frac{3}{10}\) = 5\(\frac{3}{10}\)
Question 3.
a.
Answer:
5\(\frac{3}{8}\) – 2\(\frac{7}{8}\)
5 + \(\frac{3}{8}\) – 2 – \(\frac{7}{8}\)
5 – 2 = 3
\(\frac{3}{8}\) – \(\frac{7}{8}\) = –\(\frac{1}{2}\)
3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\)
b.
Answer:
3\(\frac{1}{4}\) – 2\(\frac{3}{4}\)
3 + \(\frac{1}{4}\) – 2 – \(\frac{3}{4}\)
3 – 2 = 1
\(\frac{1}{4}\) – \(\frac{3}{4}\) = –\(\frac{1}{2}\)
1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)
c.
Answer:
8\(\frac{2}{5}\) – 3\(\frac{4}{5}\)
8 + \(\frac{2}{5}\) – 3 – \(\frac{4}{5}\)
8 – 3 = 5
\(\frac{2}{5}\) – \(\frac{4}{5}\) = –\(\frac{2}{5}\)
5 – \(\frac{2}{5}\) = 4\(\frac{3}{5}\)
d.
Answer:
1\(\frac{1}{3}\) – \(\frac{2}{3}\)
1 + \(\frac{1}{3}\) – \(\frac{2}{3}\)
\(\frac{1}{3}\) – \(\frac{2}{3}\) = –\(\frac{1}{3}\)
1 – \(\frac{1}{3}\) = \(\frac{2}{3}\)
Question 4.
a.
Answer:
4\(\frac{3}{4}\) – 2\(\frac{7}{8}\)
4 + \(\frac{3}{4}\) – 2 – \(\frac{7}{8}\)
4 – 2 = 2
\(\frac{3}{4}\) – \(\frac{7}{8}\)
LCD is 8
\(\frac{6}{8}\) – \(\frac{7}{8}\) = –\(\frac{1}{8}\)
2 – \(\frac{1}{8}\) = 1\(\frac{7}{8}\)
b.
Answer:
6\(\frac{1}{2}\) – 3\(\frac{2}{3}\)
6 + \(\frac{1}{2}\) – 3 – \(\frac{2}{3}\)
6 – 3 = 3
\(\frac{1}{2}\) – \(\frac{2}{3}\)
LCD is 6.
\(\frac{3}{6}\) – \(\frac{4}{6}\) = –\(\frac{1}{6}\)
3 – \(\frac{1}{6}\) = 2\(\frac{5}{6}\)
c.
Answer:
5 – 2\(\frac{3}{3}\)
5 – 3 = 2
d.
Answer:
3 – \(\frac{5}{6}\) = 2\(\frac{1}{6}\)
Question 5.
a.
Answer:
2\(\frac{1}{2}\) – 1\(\frac{4}{11}\)
2 + \(\frac{1}{2}\) – 1 – \(\frac{4}{11}\)
2 – 1 = 1
\(\frac{1}{2}\) – \(\frac{4}{11}\)
\(\frac{11}{22}\) – \(\frac{8}{22}\) = \(\frac{3}{22}\)
1 + \(\frac{3}{22}\) = 1\(\frac{3}{22}\)
b.
Answer:
5\(\frac{7}{10}\) – 2\(\frac{3}{8}\)
5 + \(\frac{7}{10}\) – 2 – \(\frac{3}{8}\)
5 – 2 = 3
\(\frac{7}{10}\) – \(\frac{3}{8}\)
LCD is 40
\(\frac{28}{40}\) – \(\frac{15}{40}\) = \(\frac{13}{40}\)
3 + \(\frac{13}{40}\) = 3\(\frac{13}{40}\)
c.
Answer:
9\(\frac{7}{8}\) – 8\(\frac{2}{9}\)
9 + \(\frac{7}{8}\) – 8 – \(\frac{2}{9}\)
9 – 8 = 1
\(\frac{7}{8}\) – \(\frac{2}{9}\)
LCD is 72
\(\frac{63}{72}\) – \(\frac{16}{72}\) = \(\frac{47}{72}\)
1 + \(\frac{47}{72}\) = 1\(\frac{47}{72}\)
d.
Answer:
7\(\frac{3}{4}\) – 6\(\frac{7}{12}\)
7 + \(\frac{3}{4}\) – 6 – \(\frac{7}{12}\)
7 – 6 = 1
\(\frac{3}{4}\) – \(\frac{7}{12}\)
LCD is 12
\(\frac{9}{12}\) – \(\frac{7}{12}\) = \(\frac{2}{12}\) = \(\frac{1}{6}\)
1 + \(\frac{1}{6}\) = 1\(\frac{1}{6}\)
