This handy **Spectrum Math Grade 7 Answer Key**** Chapter 1 Lesson 1.7 Subtracting Fractions and Mixed Numbers** provides detailed answers for the workbook questions.

## Spectrum Math Grade 7 Chapter 1 Lesson 1.7 Subtracting Fractions and Mixed Numbers Answers Key

To subtract fractions or mixed numbers when the denominators are different, rename the fractions so the denominators are the same.

**Subtract. Write each answer in simplest form.**

Question 1.

a.

Answer: \(\frac{7}{20}\)

\(\frac{3}{5}\) – \(\frac{1}{4}\)

To subtract 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.

= [\(\frac{3}{5}\) x \(\frac{4}{4}\)] – [\(\frac{1}{4}\) x \(\frac{5}{5}\)]

= \(\frac{12}{20}\) – \(\frac{5}{20}\)

= \(\frac{12 – 5}{20}\)

After simplification, the result is given by,

= \(\frac{7}{20}\)

b.

Answer: \(\frac{1}{5}\)

\(\frac{1}{2}\) – \(\frac{3}{10}\)

To subtract 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,

= \(\frac{4}{20}\)

= \(\frac{1}{5}\)

c.

Answer: \(\frac{3}{8}\)

\(\frac{7}{8}\) – \(\frac{1}{2}\)

To subtract 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.

= [\(\frac{7}{8}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\) x \(\frac{8}{8}\)]

= \(\frac{14}{16}\) – \(\frac{8}{16}\)

= \(\frac{14 – 8}{16}\)

After simplification, the result is given by,

= \(\frac{6}{16}\)

= \(\frac{3}{8}\)

d.

Answer: \(\frac{7}{15}\)

\(\frac{4}{5}\) – \(\frac{1}{3}\)

To subtract 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.

= [\(\frac{4}{5}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\) x \(\frac{5}{5}\)]

= \(\frac{12}{15}\) – \(\frac{5}{15}\)

= \(\frac{12 – 5}{15}\)

After simplification, the result is given by,

= \(\frac{7}{15}\)

Question 2.

a.

Answer: \(\frac{1}{2}\)

\(\frac{5}{6}\) – \(\frac{1}{3}\)

To subtract 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.

= [\(\frac{5}{6}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\) x \(\frac{6}{6}\)]

= \(\frac{15}{18}\) – \(\frac{6}{18}\)

= \(\frac{15 – 6}{18}\)

After simplification, the result is given by,

= \(\frac{9}{18}\)

= \(\frac{1}{2}\)

b.

Answer: \(\frac{7}{15}\)

\(\frac{2}{3}\) – \(\frac{1}{5}\)

To subtract 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,

= \(\frac{7}{15}\)

c.

Answer: \(\frac{11}{24}\)

\(\frac{5}{8}\) – \(\frac{1}{6}\)

To subtract 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.

= [\(\frac{5}{8}\) x \(\frac{6}{6}\)] – [\(\frac{1}{6}\) x \(\frac{8}{8}\)]

= \(\frac{30}{48}\) – \(\frac{8}{48}\)

= \(\frac{30 – 8}{48}\)

After simplification, the result is given by,

= \(\frac{22}{48}\)

= \(\frac{11}{24}\)

d.

Answer: \(\frac{7}{20}\)

\(\frac{7}{10}\) – \(\frac{1}{2}\)

To subtract 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.

= [\(\frac{7}{10}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\) x \(\frac{7}{10}\)]

= \(\frac{14}{20}\) – \(\frac{7}{20}\)

= \(\frac{14 – 7}{20}\)

After simplification, the result is given by,

= \(\frac{7}{20}\)

Question 3.

a.

Answer: \(\frac{1}{12}\)

\(\frac{3}{4}\) – \(\frac{2}{3}\)

To subtract 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 \(\frac{3}{3}\)] – [\(\frac{2}{3}\) x \(\frac{4}{4}\)]

= \(\frac{9}{12}\) – \(\frac{8}{12}\)

= \(\frac{9 – 8}{12}\)

After simplification, the result is given by,

= \(\frac{1}{12}\)

b.

Answer: \(\frac{1}{18}\)

\(\frac{5}{9}\) – \(\frac{1}{2}\)

To subtract 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.

= [\(\frac{5}{9}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\) x \(\frac{9}{9}\)]

= \(\frac{10}{18}\) – \(\frac{9}{18}\)

= \(\frac{10 – 9}{18}\)

After simplification, the result is given by,

= \(\frac{1}{18}\)

c.

Answer: \(\frac{1}{6}\)

\(\frac{1}{2}\) – \(\frac{1}{3}\)

To subtract 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,

= \(\frac{1}{6}\)

d.

Answer: \(\frac{41}{99}\)

\(\frac{7}{11}\) – \(\frac{2}{9}\)

To subtract 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.

= [\(\frac{7}{11}\) x \(\frac{9}{9}\)] – [\(\frac{2}{9}\) x \(\frac{11}{11}\)]

= \(\frac{63}{99}\) – \(\frac{22}{99}\)

= \(\frac{63 – 22}{99}\)

After simplification, the result is given by,

= \(\frac{41}{99}\)

Question 4.

a.

Answer: 1\(\frac{1}{8}\)

2\(\frac{3}{8}\) – 1\(\frac{2}{9}\)

Partition the fractions and whole numbers to subtract them separately.

= (2- 1) + [\(\frac{3}{8}\) – \(\frac{2}{9}\)]

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.

= 1 + [\(\frac{3}{8}\) x \(\frac{9}{9}\)] – [\(\frac{2}{9}\) x \(\frac{8}{8}\)]

= 1 + \(\frac{27}{72}\) – \(\frac{18}{72}\)

= 1 + \(\frac{27 – 18}{72}\)

After simplification,

= 1 + \(\frac{9}{72}\)

= 1 + \(\frac{1}{8}\)

Therefore, the result is given by,

= 1\(\frac{1}{8}\)

b.

Answer: 1\(\frac{11}{12}\)

3\(\frac{1}{4}\) – 1\(\frac{1}{3}\)

Partition the fractions and whole numbers to subtract them separately.

= (3- 1) + [\(\frac{1}{4}\) – \(\frac{1}{3}\)]

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.

= 2 + [\(\frac{1}{4}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\) x \(\frac{4}{4}\)]

= 2 + \(\frac{3}{12}\) – \(\frac{4}{12}\)

= 1 + \(\frac{15}{12}\) – \(\frac{4}{12}\)

= 1 + \(\frac{15 – 4}{12}\)

After simplification,

= 1 + \(\frac{11}{12}\)

Therefore, the result is given by,

= 1\(\frac{11}{12}\)

c.

Answer: 0\(\frac{3}{4}\)

4\(\frac{1}{2}\) – 3\(\frac{3}{4}\)

Partition the fractions and whole numbers to subtract them separately.

= (4- 3) + [\(\frac{1}{2}\) – \(\frac{3}{4}\)]

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.

= 1 + [\(\frac{1}{2}\) x \(\frac{4}{4}\)] – [\(\frac{3}{4}\) x \(\frac{2}{2}\)]

= 1 + \(\frac{4}{8}\) – \(\frac{6}{8}\)

= 0 + \(\frac{12}{8}\) – \(\frac{6}{8}\)

= 0 + \(\frac{12 – 6}{8}\)

After simplification,

= 0 + \(\frac{6}{8}\)

= 0 + \(\frac{3}{4}\)

Therefore, the result is given by,

= 0\(\frac{3}{4}\)

d.

Answer: 1\(\frac{43}{56}\)

6\(\frac{5}{8}\) – 4\(\frac{6}{7}\)

Partition the fractions and whole numbers to subtract them separately.

= (6 – 4) + [\(\frac{5}{8}\) – \(\frac{6}{7}\)]

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.

= 2 + [\(\frac{5}{8}\) x \(\frac{7}{7}\)] – [\(\frac{6}{7}\) x \(\frac{8}{8}\)]

= 2 + \(\frac{35}{56}\) – \(\frac{48}{56}\)

= 1 + \(\frac{91}{56}\) – \(\frac{48}{56}\)

= 1 + \(\frac{91 – 48}{56}\)

After simplification,

= 1 + \(\frac{43}{56}\)

Therefore, the result is given by,

= 1\(\frac{43}{56}\)

Question 5.

a.

Answer: 1\(\frac{49}{88}\)

3\(\frac{2}{11}\) – 1\(\frac{5}{8}\)

Partition the fractions and whole numbers to subtract them separately.

= (3 – 1) + [\(\frac{2}{11}\) – \(\frac{5}{8}\)]

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.

= 2 + [\(\frac{2}{11}\) x \(\frac{8}{8}\)] – [\(\frac{5}{8}\) x \(\frac{11}{11}\)]

= 2 + \(\frac{16}{88}\) – \(\frac{55}{88}\)

= 1 + \(\frac{104}{88}\) – \(\frac{55}{88}\)

= 1 + \(\frac{104 – 55}{88}\)

After simplification,

= 1 + \(\frac{49}{88}\)

Therefore, the result is given by,

= 1\(\frac{49}{88}\)

b.

Answer: 4\(\frac{4}{15}\)

7\(\frac{2}{3}\) – 3\(\frac{2}{5}\)

Partition the fractions and whole numbers to subtract them separately.

= (7 – 3) + [\(\frac{2}{3}\) – \(\frac{2}{5}\)]

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.

= 4 + [\(\frac{2}{3}\) x \(\frac{5}{5}\)] – [\(\frac{2}{5}\) x \(\frac{3}{3}\)]

= 4 + \(\frac{10}{15}\) – \(\frac{6}{15}\)

= 4 + \(\frac{10 – 6}{15}\)

After simplification,

= 4 + \(\frac{4}{15}\)

Therefore, the result is given by,

= 4\(\frac{4}{15}\)

c.

Answer: 2\(\frac{5}{6}\)

5\(\frac{1}{3}\) – 2\(\frac{1}{2}\)

Partition the fractions and whole numbers to subtract them separately.

= (5 – 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.

= 3 + [\(\frac{1}{3}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\) x \(\frac{3}{3}\)]

= 3 + \(\frac{2}{6}\) – \(\frac{3}{6}\)

= 2 + \(\frac{8}{6}\) – \(\frac{3}{6}\)

= 2 + \(\frac{8 – 3}{6}\)

After simplification,

= 2 + \(\frac{5}{6}\)

Therefore, the result is given by,

= 2\(\frac{5}{6}\)

d.

Answer: 1\(\frac{23}{42}\)

2\(\frac{5}{6}\) – 1\(\frac{2}{7}\)

Partition the fractions and whole numbers to subtract them separately.

= (2 – 1) + [\(\frac{5}{6}\) – \(\frac{2}{7}\)]

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.

= 1 + [\(\frac{5}{6}\) x \(\frac{7}{7}\)] – [\(\frac{2}{7}\) x \(\frac{6}{6}\)]

= 1 + \(\frac{35}{42}\) – \(\frac{12}{42}\)

= 1 + \(\frac{35 – 12}{42}\)

After simplification,

= 1 + \(\frac{23}{42}\)

Therefore, the result is given by,

= 1\(\frac{23}{42}\)

Question 6.

a.

Answer: 2\(\frac{5}{9}\)

4\(\frac{7}{9}\) – 2\(\frac{2}{3}\)

Partition the fractions and whole numbers to subtract them separately.

= (4 – 2) + [\(\frac{7}{9}\) – \(\frac{2}{3}\)]

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.

= 2 + [\(\frac{7}{9}\) x \(\frac{3}{3}\)] – [\(\frac{2}{3}\) x \(\frac{9}{9}\)]

= 2 + \(\frac{21}{27}\) – \(\frac{6}{27}\)

= 2 + \(\frac{21 – 6}{27}\)

After simplification,

= 2+ \(\frac{15}{27}\)

= 2+ \(\frac{5}{9}\)

Therefore, the result is given by,

= 2\(\frac{5}{9}\)

b.

Answer: 1\(\frac{9}{20}\)

3\(\frac{1}{5}\) – 1\(\frac{3}{4}\)

Partition the fractions and whole numbers to subtract them separately.

= (3 – 1) + [\(\frac{1}{5}\) – \(\frac{3}{4}\)]

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.

= 2 + [\(\frac{1}{5}\) x \(\frac{4}{4}\)] – [\(\frac{3}{4}\) x \(\frac{5}{5}\)]

= 2 + \(\frac{4}{20}\) – \(\frac{15}{20}\)

= 1 + \(\frac{24}{20}\) – \(\frac{15}{20}\)

= 1 + \(\frac{24 – 15}{20}\)

After simplification,

= 1+ \(\frac{9}{20}\)

Therefore, the result is given by,

= 1\(\frac{9}{20}\)

c.

Answer: 2\(\frac{17}{24}\)

4\(\frac{5}{6}\) – 2\(\frac{1}{8}\)

Partition the fractions and whole numbers to subtract them separately.

= (4 – 2) + [\(\frac{5}{6}\) – \(\frac{1}{8}\)]

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.

= 2 + [\(\frac{5}{6}\) x \(\frac{8}{8}\)] – [\(\frac{1}{8}\) x \(\frac{6}{6}\)]

= 2 + \(\frac{40}{48}\) – \(\frac{6}{48}\)

= 2 + \(\frac{40 – 6}{48}\)

After simplification,

= 2 + \(\frac{34}{48}\)

= 2 + \(\frac{17}{24}\)

Therefore, the result is given by,

= 2\(\frac{17}{24}\)

d.

Answer:1\(\frac{1}{4}\)

3\(\frac{1}{8}\) – 1\(\frac{3}{4}\)

Partition the fractions and whole numbers to subtract them separately.

= (3 – 1) + [\(\frac{1}{8}\) – \(\frac{3}{4}\)]

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.

= 2 + [\(\frac{1}{8}\) x \(\frac{4}{4}\)] – [\(\frac{3}{4}\) x \(\frac{8}{8}\)]

= 2 + \(\frac{4}{32}\) – \(\frac{24}{32}\)

= 1 + \(\frac{36}{32}\) – \(\frac{24}{32}\)

= 1 + \(\frac{36 – 24}{48}\)

After simplification,

= 1 + \(\frac{12}{48}\)

= 1 + \(\frac{1}{4}\)

Therefore, the result is given by,

= 1\(\frac{1}{4}\)