This handy Spectrum Math Grade 7 Answer Key Chapter 2 Lesson 2.4 Dividing Fractions and Mixed Numbers provides detailed answers for the workbook questions.
Spectrum Math Grade 7 Chapter 2 Lesson 2.4 Dividing Fractions and Mixed Numbers Answers Key
To divide by a fraction, multiply by its reciprocal.
\(\frac{2}{3}\) ÷ \(\frac{5}{8}\) = \(\frac{2}{3}\) × \(\frac{8}{5}\) = \(\frac{16}{15}\) = 1\(\frac{1}{15}\)
Divide. Write each answer in simplest form.
Question 1.
a. 3\(\frac{1}{2}\) ÷ \(\frac{2}{3}\) = ______
Answer: \(\frac{21}{4}\) = 5\(\frac{1}{4}\)
3\(\frac{1}{2}\) ÷ \(\frac{2}{3}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{7}{2}\) ÷ \(\frac{2}{3}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\)
So, \(\frac{7}{2}\) × \(\frac{3}{2}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{7 × 3}{2 × 2}\)
= \(\frac{21}{4}\)
= 5\(\frac{1}{4}\)
Therefore, 3\(\frac{1}{2}\) ÷ \(\frac{2}{3}\) = \(\frac{21}{4}\) = 5\(\frac{1}{4}\)
b. 4\(\frac{3}{4}\) ÷ 1\(\frac{7}{8}\) = ______
Answer: \(\frac{38}{15}\) = 2\(\frac{8}{15}\)
4\(\frac{3}{4}\) ÷ 1\(\frac{7}{8}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{19}{4}\) ÷ \(\frac{15}{8}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{15}{8}\) is \(\frac{8}{15}\)
So, \(\frac{19}{4}\) × \(\frac{8}{15}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{19 × 8}{4 × 15}\)
Divide the 8 in numerator and 4 in denominator by 4, which is a common factor.
= \(\frac{19 × 2}{1 × 15}\)
= \(\frac{38}{15}\)
= 2\(\frac{8}{15}\)
Therefore, 4\(\frac{3}{4}\) ÷ 1\(\frac{7}{8}\) = \(\frac{38}{15}\) = 2\(\frac{8}{15}\)
c. \(\frac{3}{4}\) ÷ \(\frac{1}{2}\) = ______
Answer: \(\frac{3}{2}\) = 1\(\frac{1}{2}\)
\(\frac{3}{4}\) ÷ \(\frac{1}{2}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{1}{2}\) is \(\frac{2}{1}\)
So, \(\frac{3}{4}\) × \(\frac{2}{1}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{3 × 2}{4 × 1}\)
Divide the 2 in numerator and 4 in denominator by 2, which is a common factor.
= \(\frac{3 × 1}{2 × 1}\)
= \(\frac{3}{2}\)
= 1\(\frac{1}{2}\)
Therefore, \(\frac{3}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)
d. 2\(\frac{2}{3}\) ÷ \(\frac{1}{8}\) = ______
Answer: \(\frac{64}{3}\) = 21\(\frac{1}{3}\)
2\(\frac{2}{3}\) ÷ \(\frac{1}{8}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{8}{3}\) ÷ \(\frac{1}{8}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{1}{8}\) is \(\frac{8}{1}\)
So, \(\frac{8}{3}\) × \(\frac{8}{1}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{8 × 8}{3 × 1}\)
= \(\frac{64}{3}\)
= 21\(\frac{1}{3}\)
Therefore, 2\(\frac{2}{3}\) ÷ \(\frac{1}{8}\) = \(\frac{64}{3}\) = 21\(\frac{1}{3}\)
Question 2.
a. 7 ÷ \(\frac{3}{5}\) = ______
Answer: \(\frac{35}{3}\) = 11\(\frac{2}{3}\)
7 ÷ \(\frac{3}{5}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{7}{1}\) ÷ \(\frac{3}{5}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{3}{5}\) is \(\frac{5}{3}\)
So, \(\frac{7}{1}\) × \(\frac{5}{3}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{7 × 5}{1 × 3}\)
= \(\frac{35}{3}\)
= 11\(\frac{2}{3}\)
Therefore, 7 ÷ \(\frac{3}{5}\) = \(\frac{35}{3}\) = 11\(\frac{2}{3}\)
b. 2\(\frac{1}{12}\) ÷ 1\(\frac{1}{3}\) = ______
Answer: \(\frac{25}{16}\) = 1\(\frac{9}{16}\)
2\(\frac{1}{12}\) ÷ 1\(\frac{1}{3}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{25}{12}\) ÷ \(\frac{4}{3}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{4}{3}\) is \(\frac{3}{4}\)
So, \(\frac{25}{12}\) × \(\frac{3}{4}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{25 × 3}{12 × 4}\)
Divide the 3 in numerator and 12 in denominator by 3, which is a common factor.
= \(\frac{25 × 1}{4 × 4}\)
= \(\frac{25}{16}\)
= 1\(\frac{9}{16}\)
Therefore, 2\(\frac{1}{12}\) ÷ 1\(\frac{1}{3}\) = \(\frac{25}{16}\) = 1\(\frac{9}{16}\)
c. 2\(\frac{1}{7}\) ÷ \(\frac{3}{4}\) = ______
Answer: \(\frac{20}{7}\) = 2\(\frac{6}{7}\)
2\(\frac{1}{7}\) ÷ \(\frac{3}{4}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{15}{7}\) ÷ \(\frac{3}{4}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\)
So, \(\frac{15}{7}\) × \(\frac{4}{3}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{15 × 4}{7 × 3}\)
Divide the 15 in numerator and 3 in denominator by 3, which is a common factor.
= \(\frac{5 × 4}{7 × 1}\)
= \(\frac{20}{7}\)
= 2\(\frac{6}{7}\)
Therefore, 2\(\frac{1}{7}\) ÷ \(\frac{3}{4}\) = \(\frac{20}{7}\) = 2\(\frac{6}{7}\)
d. 3 ÷ 5 = ______
Answer: \(\frac{3}{5}\)
3 ÷ 5
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{3}{1}\) ÷ \(\frac{5}{1}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{5}{1}\) is \(\frac{1}{5}\)
So, \(\frac{3}{1}\) × \(\frac{1}{5}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{3 × 1}{1 × 5}\)
= \(\frac{3}{5}\)
Therefore, 3 ÷ 5 = \(\frac{3}{5}\)
Question 3.
a. 1\(\frac{1}{8}\) ÷ \(\frac{1}{10}\) = ______
Answer: \(\frac{45}{4}\) = 11\(\frac{1}{4}\)
1\(\frac{1}{8}\) ÷ \(\frac{1}{10}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{9}{8}\) ÷ \(\frac{1}{10}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{1}{10}\) is \(\frac{10}{1}\)
So, \(\frac{9}{8}\) × \(\frac{10}{1}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{9 × 10}{8 × 1}\)
Divide the 10 in numerator and 8 in denominator by 2, which is a common factor.
= \(\frac{9 × 5}{4 × 1}\)
= \(\frac{45}{4}\)
= 11\(\frac{1}{4}\)
Therefore, 1\(\frac{1}{8}\) ÷ \(\frac{1}{10}\) = \(\frac{45}{4}\) = 11\(\frac{1}{4}\)
b. 1\(\frac{2}{5}\) ÷ 2\(\frac{1}{3}\) = ______
Answer: \(\frac{3}{5}\)
1\(\frac{2}{5}\) ÷ 2\(\frac{1}{3}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{7}{5}\) ÷ \(\frac{7}{3}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{7}{3}\) is \(\frac{3}{7}\)
So, \(\frac{7}{5}\) × \(\frac{3}{7}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{7 × 3}{5 × 7}\)
Divide the 7 in numerator and 7 in denominator by 7, which is a common factor.
= \(\frac{1 × 3}{5 × 1}\)
= \(\frac{3}{5}\)
Therefore, 1\(\frac{2}{5}\) ÷ 2\(\frac{1}{3}\) = \(\frac{3}{5}\)
c. 5 ÷ 1\(\frac{1}{2}\) = ______
Answer: \(\frac{10}{3}\) = 3\(\frac{1}{3}\)
5 ÷ 1\(\frac{1}{2}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{5}{1}\) ÷ \(\frac{3}{2}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{3}{2}\) is \(\frac{2}{3}\)
So, \(\frac{5}{1}\) × \(\frac{2}{3}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{5 × 2}{1 × 3}\)
= \(\frac{10}{3}\)
= 3\(\frac{1}{3}\)
Therefore, 5 ÷ 1\(\frac{1}{2}\) = \(\frac{10}{3}\) = 3\(\frac{1}{3}\)
d. 3\(\frac{1}{4}\) ÷ 1\(\frac{1}{2}\) = ______
Answer: \(\frac{13}{6}\) = 2\(\frac{1}{6}\)
3\(\frac{1}{4}\) ÷ 1\(\frac{1}{2}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{13}{4}\) ÷ \(\frac{3}{2}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{3}{2}\) is \(\frac{2}{3}\)
So, \(\frac{13}{4}\) × \(\frac{2}{3}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{13 × 2}{4 × 3}\)
Divide the 2 in numerator and 4 in denominator by 2, which is a common factor.
= \(\frac{13 × 1}{2 × 3}\)
= \(\frac{13}{6}\)
= 2\(\frac{1}{6}\)
Therefore, 3\(\frac{1}{4}\) ÷ 1\(\frac{1}{2}\) = \(\frac{13}{6}\) = 2\(\frac{1}{6}\)
Question 4.
a. 6\(\frac{2}{3}\) ÷ \(\frac{2}{3}\) = ______
Answer: \(\frac{10}{1}\)=10
6\(\frac{2}{3}\) ÷ \(\frac{2}{3}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{20}{3}\) ÷ \(\frac{2}{3}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\)
So, \(\frac{20}{3}\) × \(\frac{3}{2}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{20 × 3}{3 × 2}\)
Divide the 3 in numerator and 3 in denominator by 3, which is a common factor.
= \(\frac{20 × 1}{1 × 2}\)
Now, Divide the 20 in numerator and 2 in denominator by 2, which is a common factor.
= \(\frac{10 × 1}{1 × 1}\)
= \(\frac{10}{1}\)
=10
Therefore, 6\(\frac{2}{3}\) ÷ \(\frac{2}{3}\) = \(\frac{10}{1}\)=10
b. 3\(\frac{1}{8}\) ÷ \(\frac{2}{7}\) = ______
Answer: \(\frac{175}{16}\) = 10\(\frac{15}{16}\)
3\(\frac{1}{8}\) ÷ \(\frac{2}{7}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{25}{8}\) ÷ \(\frac{2}{7}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{2}{7}\) is \(\frac{7}{2}\)
So, \(\frac{25}{8}\) × \(\frac{7}{2}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{25 × 7}{8 × 2}\)
= \(\frac{175}{16}\)
= 10\(\frac{15}{16}\)
Therefore, 3\(\frac{1}{8}\) ÷ \(\frac{2}{7}\) = \(\frac{175}{16}\) = 10\(\frac{15}{16}\)
c. 4\(\frac{1}{4}\) ÷ \(\frac{1}{12}\) = ______
Answer: \(\frac{51}{1}\) =51
4\(\frac{1}{4}\) ÷ \(\frac{1}{12}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{17}{4}\) ÷ \(\frac{1}{12}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{1}{12}\) is \(\frac{12}{1}\)
So, \(\frac{17}{4}\) × \(\frac{12}{1}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{17 × 12}{4 × 1}\)
Divide the 12 in numerator and 4 in denominator by 4, which is a common factor.
= \(\frac{17 × 3 }{1 × 1}\)
= \(\frac{51}{1}\)
=51
Therefore, 4\(\frac{1}{4}\) ÷ \(\frac{1}{12}\) = \(\frac{51}{1}\) =51
d. 14 ÷ \(\frac{1}{7}\) = ______
Answer: \(\frac{98}{1}\)= 98
14 ÷ \(\frac{1}{7}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{14}{1}\) ÷ \(\frac{1}{7}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{1}{7}\) is \(\frac{7}{1}\)
So, \(\frac{14}{1}\) × \(\frac{7}{1}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{14 × 7}{1 × 1}\)
= \(\frac{98}{1}\)
= 98
Therefore, 14 ÷ \(\frac{1}{7}\) = \(\frac{98}{1}\)= 98
Question 5.
a. 2\(\frac{3}{5}\) ÷ 1\(\frac{2}{7}\) = ______
Answer: \(\frac{91}{45}\) = 2\(\frac{1}{45}\)
2\(\frac{3}{5}\) ÷ 1\(\frac{2}{7}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{13}{5}\) ÷ \(\frac{9}{7}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{9}{7}\) is \(\frac{7}{9}\)
So, \(\frac{13}{5}\) × \(\frac{7}{9}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{13 × 7}{5 × 9}\)
= \(\frac{91}{45}\)
= 2\(\frac{1}{45}\)
Therefore, 2\(\frac{3}{5}\) ÷ 1\(\frac{2}{7}\) = \(\frac{91}{45}\) = 2\(\frac{1}{45}\)
b. 1\(\frac{1}{9}\) ÷ \(\frac{7}{11}\) = ______
Answer: \(\frac{110}{63}\) = 1\(\frac{47}{63}\)
1\(\frac{1}{9}\) ÷ \(\frac{7}{11}\)
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{10}{9}\) ÷ \(\frac{7}{11}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{7}{11}\) is \(\frac{11}{7}\)
So, \(\frac{10}{9}\) × \(\frac{11}{7}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{10 × 11}{9 × 7}\)
= \(\frac{110}{63}\)
= 1\(\frac{47}{63}\)
Therefore, 1\(\frac{1}{9}\) ÷ \(\frac{7}{11}\) = \(\frac{110}{63}\) = 1\(\frac{47}{63}\)
c. 12 ÷ 15 = ______
Answer: \(\frac{4}{5}\)
12 ÷ 15
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{12}{1}\) ÷ \(\frac{15}{1}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{15}{1}\) is \(\frac{1}{15}\)
So, \(\frac{12}{1}\) × \(\frac{1}{15}\)
Reduce the above fractions into simplest form if possible. In this case, it is possible.
Then, multiply the numerators and denominators separately.
= \(\frac{12 × 1}{1 × 15}\)
Divide the 12 in numerator and 15 in denominator by 3, which is a common factor.
= \(\frac{4 × 1}{1 × 5}\)
= \(\frac{4}{5}\)
Therefore, 12 ÷ 15 = \(\frac{4}{5}\)
d. 2\(\frac{4}{5}\) ÷ 3 = ______
Answer: \(\frac{14}{15}\)
2\(\frac{4}{5}\) ÷ 3
Convert the above numbers in improper fractions to make calculations easy.
= \(\frac{14}{5}\) ÷ \(\frac{3}{1}\)
To divide by a fraction, multiply by its reciprocal.
Here, the reciprocal of \(\frac{3}{1}\) is \(\frac{1}{3}\)
So, \(\frac{14}{5}\) × \(\frac{1}{3}\)
Reduce the above fractions into simplest form if possible. In this case, it is not possible.
Then, multiply the numerators and denominators separately.
= \(\frac{14 × 1}{5 × 3}\)
= \(\frac{14}{15}\)
Therefore, 2\(\frac{4}{5}\) ÷ 3 = \(\frac{14}{15}\)