Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators

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Spectrum Math Grade 5 Chapter 5 Lesson 5.2 Adding Fractions with Unlike Denominators Answers Key

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.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 1
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.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 2
If necessary, change improper fractions to mixed numerals in simplest form.

Add each fraction. Write answers in simplest form.

Question 1.
a.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 3
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.
\(\frac{3}{5}\) + \(\frac{1}{4}\)
\(\frac{12}{20}\) + \(\frac{5}{20}\) = \(\frac{17}{20}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-3

b.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 4
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.
\(\frac{14}{21}\) + \(\frac{6}{21}\) = \(\frac{20}{21}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-4

c.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 5
Answer:
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
\(\frac{7}{35}\) + \(\frac{5}{35}\) = \(\frac{12}{35}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-5

d.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 6
Answer:
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
\(\frac{9}{24}\) + \(\frac{4}{24}\) = \(\frac{13}{24}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-6

e.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 7
Answer:
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
\(\frac{3}{6}\) + \(\frac{2}{6}\) = \(\frac{5}{6}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-7

Question 2.
a.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 8
Answer:
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.
\(\frac{16}{72}\) + \(\frac{45}{72}\) = \(\frac{61}{72}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-8

b.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 9
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\(\frac{4}{21}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-9

c.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 10
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\(\frac{4}{35}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-10

d.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 11
Answer:
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\(\frac{1}{30}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-11

e.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 12
Answer:
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
\(\frac{24}{56}\) + \(\frac{7}{56}\) = \(\frac{31}{56}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-12

Question 3.
a.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 13
Answer:
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
\(\frac{10}{15}\) + \(\frac{3}{15}\) = \(\frac{13}{15}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-13

b.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 14
Answer:
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\(\frac{8}{63}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-14

c.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 15
Answer:
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\(\frac{1}{20}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-15

d.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 16
Answer:
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\(\frac{11}{40}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-16

e.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 17
Answer:
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\(\frac{47}{63}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-17

Add. Write answers in simplest form.

Question 1.
a.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 18
Answer:
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\(\frac{1}{4}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-18

b.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 19
Answer:
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\(\frac{1}{10}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-19

c.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 20
Answer:
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\(\frac{7}{12}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-20

d.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 21
Answer:
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\(\frac{1}{6}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-21

e.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 22
Answer:
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
\(\frac{8}{12}\) + \(\frac{1}{12}\) = \(\frac{9}{12}\) = \(\frac{3}{4}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-22

Question 2.
a.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 23
Answer:
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
\(\frac{3}{8}\) + \(\frac{2}{8}\) = \(\frac{5}{8}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-23

b.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 24
Answer:
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\(\frac{2}{9}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-24

c.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 25
Answer:
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\(\frac{7}{24}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-25

d.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 26
Answer:
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\(\frac{1}{5}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-26

e.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 27
Answer:
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\(\frac{7}{12}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-27

Question 3.
a.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 28
Answer:
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
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-28

b.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 29
Answer:
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\(\frac{1}{24}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-29

c.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 30
Answer:
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\(\frac{21}{40}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-30

d.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 31
Answer:
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\(\frac{5}{36}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-31

e.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 32
Answer:
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\(\frac{13}{18}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-32

Question 4.
a.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 33
Answer:
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
\(\frac{6}{10}\) + \(\frac{1}{10}\) = \(\frac{7}{10}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-33

b.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 34
Answer:
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\(\frac{1}{2}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-34

c.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 35
Answer:
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\(\frac{1}{12}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-35

d.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 36
Answer:
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
\(\frac{9}{24}\) + \(\frac{2}{24}\) = \(\frac{11}{24}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-36

e.
Spectrum Math Grade 5 Chapter 5 Lesson 2 Answer Key Adding Fractions with Unlike Denominators 37
Answer:
To add fractions, the denominators must be the same. When you have unlike denominators, find the least common multiple (LCM) and rename the fractions.
\(\frac{2}{5}\) + \(\frac{2}{7}\)
LCD = 35
\(\frac{14}{35}\) + \(\frac{10}{35}\) = \(\frac{24}{35}\)
Spectrum-Math-Grade-5-Chapter-5-Lesson-2-Answer-Key-Adding-Fractions-with-Unlike-Denominators-37

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