Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 5 Lesson 5.2 Adding Fractions with Unlike Denominators regularly and improve your accuracy in solving questions.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
In the example, the denominators are 3 and 7, so find the LCM of 3 and 7.

Multiples of 3: 3,6,9, 12, 15, 18, 21, 24
Multiples of 7: 7, 14, 21, 28
The least common multiple of 3 and 7 is 21. To change each fraction so it has the same denominator, multiply both the numerator and denominator by the same number.

If necessary, change improper fractions to mixed numerals in simplest form.

Question 1.
a.

Answer: $$\frac{17}{20}$$
To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
LCD of 4 and 5 is 20.
$$\frac{3}{5}$$ + $$\frac{1}{4}$$
$$\frac{12}{20}$$ + $$\frac{5}{20}$$ = $$\frac{17}{20}$$

b.

Answer: $$\frac{20}{21}$$
To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{2}{3}$$ + $$\frac{2}{7}$$
LCD of 3 and 7 is 21.
$$\frac{14}{21}$$ + $$\frac{6}{21}$$ = $$\frac{20}{21}$$

c.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{1}{5}$$ + $$\frac{1}{7}$$
LCD is 35
$$\frac{7}{35}$$ + $$\frac{5}{35}$$ = $$\frac{12}{35}$$

d.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{3}{8}$$ + $$\frac{1}{6}$$
LCD is 24
$$\frac{9}{24}$$ + $$\frac{4}{24}$$ = $$\frac{13}{24}$$

e.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{1}{2}$$ + $$\frac{1}{3}$$
LCD is 6
$$\frac{3}{6}$$ + $$\frac{2}{6}$$ = $$\frac{5}{6}$$

Question 2.
a.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{2}{9}$$ + $$\frac{5}{8}$$
LCD is 72.
$$\frac{16}{72}$$ + $$\frac{45}{72}$$ = $$\frac{61}{72}$$

b.

Answer: 1 $$\frac{4}{21}$$
To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{6}{7}$$ + $$\frac{1}{3}$$
LCD = 21
$$\frac{18}{21}$$ + $$\frac{7}{21}$$ = $$\frac{25}{21}$$ = 1$$\frac{4}{21}$$

c.

Answer: 1 $$\frac{4}{35}$$
To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{2}{5}$$ + $$\frac{5}{7}$$
LCD = 35
$$\frac{14}{35}$$ + $$\frac{25}{35}$$ = $$\frac{39}{35}$$ = 1$$\frac{4}{35}$$

d.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{7}{10}$$ + $$\frac{1}{3}$$
LCD = 30
$$\frac{21}{30}$$ + $$\frac{10}{30}$$ = $$\frac{31}{30}$$ = 1$$\frac{1}{30}$$

e.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{3}{7}$$ + $$\frac{1}{8}$$
LCD = 56
$$\frac{24}{56}$$ + $$\frac{7}{56}$$ = $$\frac{31}{56}$$

Question 3.
a.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{2}{3}$$ + $$\frac{1}{5}$$
LCD = 15
$$\frac{10}{15}$$ + $$\frac{3}{15}$$ = $$\frac{13}{15}$$

b.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{4}{7}$$ + $$\frac{5}{9}$$
LCD = 63
$$\frac{36}{63}$$ + $$\frac{35}{63}$$ = $$\frac{71}{63}$$ = 1$$\frac{8}{63}$$

c.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{3}{4}$$ + $$\frac{3}{10}$$
LCD = 20
$$\frac{15}{20}$$ + $$\frac{6}{20}$$ = $$\frac{21}{20}$$ = 1$$\frac{1}{20}$$

d.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{7}{8}$$ + $$\frac{2}{5}$$
LCD = 40
$$\frac{35}{40}$$ + $$\frac{16}{40}$$ = $$\frac{51}{40}$$ = 1$$\frac{11}{40}$$

e.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{8}{9}$$ + $$\frac{6}{7}$$
LCD = 63
$$\frac{56}{63}$$ + $$\frac{54}{63}$$ = $$\frac{110}{63}$$ = 1$$\frac{47}{63}$$

Question 1.
a.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{1}{2}$$ + $$\frac{3}{4}$$
LCD = 4
$$\frac{2}{4}$$ + $$\frac{3}{4}$$ = $$\frac{5}{4}$$ = 1$$\frac{1}{4}$$

b.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{3}{3}$$ + $$\frac{1}{10}$$
LCD = 30
$$\frac{30}{30}$$ + $$\frac{3}{30}$$ = $$\frac{33}{30}$$ = 1$$\frac{1}{10}$$

c.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{5}{6}$$ + $$\frac{3}{4}$$
LCD = 12
$$\frac{10}{12}$$ + $$\frac{9}{12}$$ = $$\frac{19}{12}$$ = 1$$\frac{7}{12}$$

d.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{1}{3}$$ + $$\frac{5}{6}$$
LCD = 6
$$\frac{2}{6}$$ + $$\frac{5}{6}$$ = $$\frac{7}{6}$$ = 1$$\frac{1}{6}$$

e.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{2}{3}$$ + $$\frac{1}{12}$$
LCD = 12
$$\frac{8}{12}$$ + $$\frac{1}{12}$$ = $$\frac{9}{12}$$ = $$\frac{3}{4}$$

Question 2.
a.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{3}{8}$$ + $$\frac{1}{4}$$
LCD = 8
$$\frac{3}{8}$$ + $$\frac{2}{8}$$ = $$\frac{5}{8}$$

b.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{2}{3}$$ + $$\frac{5}{9}$$
LCD = 9
$$\frac{6}{9}$$ + $$\frac{5}{9}$$ = $$\frac{11}{9}$$ = 1$$\frac{2}{9}$$

c.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{5}{12}$$ + $$\frac{7}{8}$$
LCD = 24
$$\frac{10}{24}$$ + $$\frac{21}{24}$$ = $$\frac{31}{24}$$ = 1$$\frac{7}{24}$$

d.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{1}{2}$$ + $$\frac{7}{10}$$
LCD = 10
$$\frac{5}{10}$$ + $$\frac{7}{10}$$ = $$\frac{12}{10}$$ = 1$$\frac{1}{5}$$

e.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{5}{6}$$ + $$\frac{3}{4}$$
LCD = 12
$$\frac{10}{12}$$ + $$\frac{9}{12}$$ = $$\frac{19}{12}$$ = 1$$\frac{7}{12}$$

Question 3.
a.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{5}{7}$$ + $$\frac{4}{14}$$
LCD = 14
$$\frac{10}{14}$$ + $$\frac{4}{14}$$ = $$\frac{14}{14}$$ = 1

b.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{1}{6}$$ + $$\frac{7}{8}$$
LCD = 24
$$\frac{4}{24}$$ + $$\frac{21}{24}$$ = $$\frac{25}{24}$$ = 1$$\frac{1}{24}$$

c.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{9}{10}$$ + $$\frac{5}{8}$$
LCD = 40
$$\frac{36}{40}$$ + $$\frac{25}{40}$$ = $$\frac{61}{40}$$ = 1$$\frac{21}{40}$$

d.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{2}{9}$$ + $$\frac{11}{12}$$
LCD = 36
$$\frac{8}{36}$$ + $$\frac{33}{36}$$ = $$\frac{41}{36}$$ = 1$$\frac{5}{36}$$

e.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{5}{6}$$ + $$\frac{8}{9}$$
LCD = 18
$$\frac{15}{18}$$ + $$\frac{16}{18}$$ = $$\frac{31}{18}$$ = 1$$\frac{13}{18}$$

Question 4.
a.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{3}{5}$$ + $$\frac{1}{10}$$
LCD = 10
$$\frac{6}{10}$$ + $$\frac{1}{10}$$ = $$\frac{7}{10}$$

b.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{3}{5}$$ + $$\frac{9}{10}$$
LCD = 10
$$\frac{6}{10}$$ + $$\frac{9}{10}$$ = $$\frac{15}{10}$$ = $$\frac{3}{2}$$ = 1$$\frac{1}{2}$$

c.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{1}{4}$$ + $$\frac{5}{6}$$
LCD = 12
$$\frac{3}{12}$$ + $$\frac{10}{12}$$ = $$\frac{13}{12}$$ = 1$$\frac{1}{12}$$

d.

To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
$$\frac{3}{8}$$ + $$\frac{1}{12}$$
LCD = 24
$$\frac{9}{24}$$ + $$\frac{2}{24}$$ = $$\frac{11}{24}$$

e.

$$\frac{2}{5}$$ + $$\frac{2}{7}$$
$$\frac{14}{35}$$ + $$\frac{10}{35}$$ = $$\frac{24}{35}$$