This handy Spectrum Math Grade 7 Answer Key Chapter 1 Lesson 1.4 Adding Fractions and Mixed Numbers provides detailed answers for the workbook questions.
Spectrum Math Grade 7 Chapter 1 Lesson 1.4 Adding Fractions and Mixed Numbers Answers Key
To add fractions or mixed numbers when the denominators are different, rename the fractions so the denominators are the same.
Add. Write each answer in simplest form.
Question 1.
a.
Answer: \(\frac{11}{8}\) = 1\(\frac{3}{8}\)
\(\frac{3}{4}\) +\(\frac{5}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{4}\) x \(\frac{8}{8}\)] + [\(\frac{5}{8}\) x \(\frac{4}{4}\)]
= \(\frac{24}{32}\) + \(\frac{20}{32}\)
= \(\frac{24 + 20}{32}\)
After simplification, the result is given by,
= \(\frac{44}{32}\) = \(\frac{11}{8}\) (by simplification)
= 1\(\frac{12}{32}\) = 1\(\frac{3}{8}\) (by simplification)
b.
Answer: \(\frac{5}{6}\) = 0\(\frac{5}{6}\)
\(\frac{1}{2}\) +\(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{2}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\) x \(\frac{2}{2}\)]
= \(\frac{3}{6}\) + \(\frac{2}{6}\)
= \(\frac{3 + 2}{6}\)
After simplification, the result is given by,
= \(\frac{5}{6}\)
= 0\(\frac{5}{6}\)
c.
Answer: \(\frac{23}{20}\) = 1\(\frac{3}{20}\)
\(\frac{3}{4}\) +\(\frac{2}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{4}\) x \(\frac{5}{5}\)] + [\(\frac{2}{5}\) x \(\frac{4}{4}\)]
= \(\frac{15}{20}\) + \(\frac{8}{20}\)
= \(\frac{15 + 8}{20}\)
After simplification, the result is given by,
= \(\frac{23}{20}\)
= 1\(\frac{3}{20}\)
d.
Answer: \(\frac{1}{2}\) = 0\(\frac{1}{2}\)
\(\frac{1}{6}\) +\(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{6}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\) x \(\frac{6}{6}\)]
= \(\frac{3}{18}\) + \(\frac{6}{18}\)
= \(\frac{3 + 6}{18}\)
After simplification, the result is given by,
= \(\frac{9}{18}\) = \(\frac{1}{2}\) (by simplification)
= 0\(\frac{9}{18}\) = 0\(\frac{1}{2}\) (by simplification)
Question 2.
a.
Answer: \(\frac{47}{40}\) = 1\(\frac{7}{40}\)
\(\frac{3}{8}\) +\(\frac{4}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{8}\) x \(\frac{5}{5}\)] + [\(\frac{4}{5}\) x \(\frac{8}{8}\)]
= \(\frac{15}{40}\) + \(\frac{32}{40}\)
= \(\frac{15 + 32}{40}\)
After simplification, the result is given by,
= \(\frac{47}{40}\)
= 1\(\frac{7}{40}\)
b.
Answer: \(\frac{4}{5}\) = 0\(\frac{4}{5}\)
\(\frac{1}{2}\) +\(\frac{3}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{2}\) x \(\frac{10}{10}\)] + [\(\frac{3}{10}\) x \(\frac{2}{2}\)]
= \(\frac{10}{20}\) + \(\frac{6}{20}\)
= \(\frac{10 + 6}{20}\)
After simplification, the result is given by,
= \(\frac{16}{20}\) = \(\frac{4}{5}\) (by simplification)
= 0\(\frac{16}{20}\) = 0\(\frac{4}{5}\) (by simplification)
c.
Answer: \(\frac{11}{12}\) = 0\(\frac{11}{12}\)
\(\frac{2}{3}\) +\(\frac{3}{12}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{2}{3}\) x \(\frac{12}{12}\)] + [\(\frac{3}{12}\) x \(\frac{3}{3}\)]
= \(\frac{24}{36}\) + \(\frac{9}{36}\)
= \(\frac{24 + 9}{36}\)
After simplification, the result is given by,
= \(\frac{33}{36}\) = \(\frac{11}{12}\) (by simplification)
= 0\(\frac{33}{36}\) = 0\(\frac{11}{12}\) (by simplification)
d.
Answer: \(\frac{29}{20}\) = 1\(\frac{9}{20}\)
\(\frac{3}{4}\) +\(\frac{7}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{4}\) x \(\frac{10}{10}\)] + [\(\frac{7}{10}\) x \(\frac{4}{4}\)]
= \(\frac{30}{40}\) + \(\frac{28}{40}\)
= \(\frac{30 + 28}{40}\)
After simplification, the result is given by,
= \(\frac{58}{40}\) = \(\frac{29}{20}\) (by simplification)
= 1\(\frac{18}{40}\) = 1\(\frac{9}{20}\) (by simplification)
Question 3.
a.
Answer: \(\frac{5}{8}\) = 0\(\frac{5}{8}\)
\(\frac{1}{4}\) +\(\frac{3}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{4}\) x \(\frac{8}{8}\)] + [\(\frac{3}{8}\) x \(\frac{4}{4}\)]
= \(\frac{8}{32}\) + \(\frac{12}{32}\)
= \(\frac{8 + 12}{32}\)
After simplification, the result is given by,
= \(\frac{20}{32}\) = \(\frac{5}{8}\) (by simplification)
= 0\(\frac{20}{32}\) = 0\(\frac{5}{8}\) (by simplification)
b.
Answer: \(\frac{29}{35}\) = 0\(\frac{29}{35}\)
\(\frac{2}{5}\) +\(\frac{3}{7}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{2}{5}\) x \(\frac{7}{7}\)] + [\(\frac{3}{7}\) x \(\frac{5}{5}\)]
= \(\frac{14}{35}\) + \(\frac{15}{35}\)
= \(\frac{14 + 15}{35}\)
After simplification, the result is given by,
= \(\frac{29}{35}\)
= 0\(\frac{29}{35}\)
c.
Answer: \(\frac{57}{56}\) = 1\(\frac{1}{56}\)
\(\frac{1}{7}\) +\(\frac{7}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{7}\) x \(\frac{8}{8}\)] + [\(\frac{7}{8}\) x \(\frac{7}{7}\)]
= \(\frac{8}{56}\) + \(\frac{49}{56}\)
= \(\frac{8 + 49}{56}\)
After simplification, the result is given by,
= \(\frac{57}{56}\)
= 1\(\frac{1}{56}\)
d.
Answer: \(\frac{13}{15}\) = 0\(\frac{13}{15}\)
\(\frac{2}{3}\) +\(\frac{1}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{2}{3}\) x \(\frac{5}{5}\)] + [\(\frac{1}{5}\) x \(\frac{3}{3}\)]
= \(\frac{10}{15}\) + \(\frac{3}{15}\)
= \(\frac{10 + 3}{15}\)
After simplification, the result is given by,
= \(\frac{13}{15}\)
= 0\(\frac{13}{15}\)
Question 4.
a.
Answer: 3\(\frac{7}{12}\)
1\(\frac{1}{3}\) + 2\(\frac{1}{4}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 2) + \(\frac{1}{3}\) + \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{1}{3}\) x \(\frac{4}{4}\)] + [\(\frac{1}{4}\) x \(\frac{3}{3}\)]
= 3 + \(\frac{4}{12}\) + \(\frac{3}{12}\)
= 3 + \(\frac{4 + 3}{12}\)
After simplification,
= 3 + \(\frac{7}{12}\)
Therefore, the result is given by,
= 3\(\frac{7}{12}\)
b.
Answer: 10\(\frac{7}{8}\)
3\(\frac{3}{8}\) + 7\(\frac{1}{2}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 7) + \(\frac{3}{8}\) + \(\frac{1}{2}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 10 + [\(\frac{3}{8}\) x \(\frac{2}{2}\)] + [\(\frac{1}{2}\) x \(\frac{8}{8}\)]
= 10 + \(\frac{6}{16}\) + \(\frac{8}{16}\)
= 10 + \(\frac{6 + 8}{16}\)
After simplification,
= 10 + \(\frac{14}{16}\)
= 10 + \(\frac{7}{8}\) (by simplification)
Therefore, the result is given by,
= 10\(\frac{7}{8}\)
c.
Answer: 6\(\frac{13}{21}\)
4\(\frac{2}{7}\) + 2\(\frac{1}{3}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 2) + \(\frac{2}{7}\) + \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 6 + [\(\frac{2}{7}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\) x \(\frac{7}{7}\)]
= 6 + \(\frac{6}{21}\) + \(\frac{7}{21}\)
= 6 + \(\frac{6 + 7}{21}\)
After simplification,
= 6 + \(\frac{13}{21}\)
Therefore, the result is given by,
= 6\(\frac{13}{21}\)
d.
Answer: 4\(\frac{7}{10}\)
1\(\frac{2}{5}\) + 3\(\frac{3}{10}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 3) + \(\frac{2}{5}\) + \(\frac{3}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{2}{5}\) x \(\frac{10}{10}\)] + [\(\frac{3}{10}\) x \(\frac{5}{5}\)]
= 4 + \(\frac{20}{50}\) + \(\frac{15}{50}\)
= 4 + \(\frac{20 + 15}{50}\)
After simplification,
= 4 + \(\frac{35}{50}\)
= 4 + \(\frac{7}{10}\) (by simplification)
Therefore, the result is given by,
= 4\(\frac{7}{10}\)
Question 5.
a.
Answer: 7\(\frac{7}{9}\)
4\(\frac{4}{9}\) + 3\(\frac{1}{3}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 3) + \(\frac{4}{9}\) + \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 7 + [\(\frac{4}{9}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\) x \(\frac{9}{9}\)]
= 7 + \(\frac{12}{27}\) + \(\frac{9}{27}\)
= 7 + \(\frac{12 + 9}{27}\)
After simplification,
= 7 + \(\frac{21}{27}\)
= 7 + \(\frac{7}{9}\) (by simplification)
Therefore, the result is given by,
= 7\(\frac{7}{9}\)
b.
Answer: 2\(\frac{33}{40}\)
1\(\frac{1}{8}\) + 1\(\frac{7}{10}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 1) + \(\frac{1}{8}\) + \(\frac{7}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{1}{8}\) x \(\frac{10}{10}\)] + [\(\frac{7}{10}\) x \(\frac{8}{8}\)]
= 2 + \(\frac{10}{80}\) + \(\frac{56}{80}\)
= 2 + \(\frac{10 + 56}{80}\)
After simplification,
= 2 + \(\frac{66}{80}\)
= 2 + \(\frac{33}{40}\) (by simplification)
Therefore, the result is given by,
= 2\(\frac{33}{40}\)
c.
Answer: 5\(\frac{19}{24}\)
2\(\frac{1}{6}\) + 3\(\frac{5}{8}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 3) + \(\frac{1}{6}\) + \(\frac{5}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 5 + [\(\frac{1}{6}\) x \(\frac{8}{8}\)] + [\(\frac{5}{8}\) x \(\frac{6}{6}\)]
= 5 + \(\frac{8}{48}\) + \(\frac{30}{48}\)
= 5 + \(\frac{8 + 30}{48}\)
After simplification,
= 5 + \(\frac{38}{48}\)
= 5 + \(\frac{19}{24}\) (by simplification)
Therefore, the result is given by,
= 5\(\frac{19}{24}\)
d.
Answer: 3\(\frac{22}{35}\)
1\(\frac{3}{7}\) + 2\(\frac{1}{5}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 2) + \(\frac{3}{7}\) + \(\frac{1}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{3}{7}\) x \(\frac{5}{5}\)] + [\(\frac{1}{5}\) x \(\frac{7}{7}\)]
= 3 + \(\frac{15}{35}\) + \(\frac{7}{35}\)
= 3 + \(\frac{15 + 7}{35}\)
After simplification,
= 3 + \(\frac{22}{35}\)
Therefore, the result is given by,
= 3\(\frac{22}{35}\)
Question 6.
a.
Answer: 5\(\frac{3}{4}\)
3\(\frac{1}{2}\) + 2\(\frac{1}{4}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 2) + \(\frac{1}{2}\) + \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 5 + [\(\frac{1}{2}\) x \(\frac{4}{4}\)] + [\(\frac{1}{4}\) x \(\frac{2}{2}\)]
= 5 + \(\frac{4}{8}\) + \(\frac{2}{8}\)
= 5 + \(\frac{4 + 2}{8}\)
After simplification,
= 5 + \(\frac{6}{8}\)
= 5 + \(\frac{3}{4}\) (by simplification)
Therefore, the result is given by,
= 5\(\frac{3}{4}\)
b.
Answer: 3\(\frac{25}{18}\)
2\(\frac{5}{6}\) + 1\(\frac{5}{9}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 1) + \(\frac{5}{6}\) + \(\frac{5}{9}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{5}{6}\) x \(\frac{9}{9}\)] + [\(\frac{5}{9}\) x \(\frac{6}{6}\)]
= 3 + \(\frac{45}{54}\) + \(\frac{30}{54}\)
= 3 + \(\frac{45 + 30}{54}\)
After simplification,
= 3 + \(\frac{75}{54}\)
= 3 + \(\frac{25}{18}\) (by simplification)
Therefore, the result is given by,
= 3\(\frac{25}{18}\)
c.
Answer: 4\(\frac{47}{70}\)
3\(\frac{4}{7}\) + 1\(\frac{1}{10}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 1) + \(\frac{4}{7}\) + \(\frac{1}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{4}{7}\) x \(\frac{10}{10}\)] + [\(\frac{1}{10}\) x \(\frac{7}{7}\)]
= 4 + \(\frac{40}{70}\) + \(\frac{7}{70}\)
= 4 + \(\frac{40 + 7}{70}\)
After simplification,
= 4 + \(\frac{47}{70}\)
Therefore, the result is given by,
= 4\(\frac{47}{70}\)
d.
Answer: 6\(\frac{5}{6}\)
4\(\frac{1}{3}\) + 2\(\frac{1}{2}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 2) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 6 + [\(\frac{1}{3}\) x \(\frac{2}{2}\)] + [\(\frac{1}{2}\) x \(\frac{3}{3}\)]
= 6 + \(\frac{2}{6}\) + \(\frac{3}{6}\)
= 6 + \(\frac{2 + 3}{6}\)
After simplification,
= 6 + \(\frac{5}{6}\)
Therefore, the result is given by,
= 6\(\frac{5}{6}\)