This handy Spectrum Math Grade 4 Answer Key Chapter 6 Lesson 6.11 Adding Mixed Numerals with Like Denominators provides detailed answers for the workbook questions.
Spectrum Math Grade 4 Chapter 6 Lesson 6.11 Adding Mixed Numerals with Like Denominators Answers Key
Add the fractions.
\(\frac{4}{9}\) + \(\frac{2}{9}\) = \(\frac{6}{9}\)
Add the whole numbers.
3 + 2 = 5
Reduce to simplest form. \(\frac{6}{9} \div \frac{3}{3}\) = \(\frac{2}{3}\)
Add. Write answers in simplest form.
Question 1.
a.
Answer:
9
Explanation:
Add the fractions.
\(\frac{4}{7}\) + \(\frac{3}{7}\) = \(\frac{7}{7}\) = 1
Add the whole numbers.
3 + 5 = 8
Therefore, 8 + 1 = 9
b.
Answer:
15
Explanation:
Add the fractions.
\(\frac{4}{9}\) + \(\frac{5}{9}\) = \(\frac{9}{9}\) = 1
Add the whole numbers.
6 + 8 = 14
Hence, 14 + 1 = 15
c.
Answer:
10\(\frac{1}{3}\)
Explanation:
Add the fractions.
\(\frac{1}{6}\) + \(\frac{1}{6}\) = \(\frac{2}{6}\)
Add the whole numbers.
7 + 3 = 10
Reduce to simplest form.
\(\frac{2}{6} \div \frac{2}{2}\) = \(\frac{1}{3}\)
Hence, 10\(\frac{1}{3}\)
d.
Answer:
7\(\frac{1}{5}\)
Explanation:
Add the fractions.
\(\frac{2}{5}\) + \(\frac{4}{5}\) = \(\frac{6}{5}\)
Add the whole numbers.
2 + 4 = 6
6 \(\frac{6}{5}\) = \(\frac{36}{5}\)
Reduce to simplest form.
7\(\frac{1}{5}\)
e.
Answer:
11\(\frac{10}{11}\)
Explanation:
Add the fractions.
\(\frac{2}{11}\) + \(\frac{8}{11}\) = \(\frac{10}{11}\)
Add the whole numbers.
3 + 8 = 11
Hence, 11 \(\frac{10}{11}\)
Question 2.
a.
Answer:
12\(\frac{1}{5}\)
Explanation:
Add the fractions.
\(\frac{3}{10}\) + \(\frac{9}{10}\) = \(\frac{12}{10}\)
\(\frac{12}{10} \div \frac{2}{2}\) = \(\frac{6}{5}\)
Add the whole numbers.
9 + 2 = 11
Reduce to simplest form.
11\(\frac{6}{5}\) = \(\frac{61}{5}\) = 12\(\frac{1}{5}\)
b.
Answer:
9\(\frac{1}{4}\)
Explanation:
Add the fractions.
\(\frac{1}{8}\) + \(\frac{3}{8}\) = \(\frac{4}{8}\)
Add the whole numbers.
5 + 4 = 9
Reduce to simplest form.
\(\frac{4}{8} \div \frac{4}{4}\) = \(\frac{1}{4}\)
Hence, 9 \(\frac{1}{4}\)
c.
Answer:
5\(\frac{1}{7}\)
Explanation:
Add the fractions.
\(\frac{6}{7}\) + \(\frac{2}{7}\) = \(\frac{8}{7}\)
Add the whole numbers.
1 + 3 = 4
So, 4 \(\frac{8}{7}\) = \(\frac{36}{7}\)
Reduce to simplest form.
5 \(\frac{1}{7}\)
d.
Answer:
15\(\frac{1}{2}\)
Explanation:
Add the fractions.
\(\frac{3}{4}\) + \(\frac{3}{4}\) = \(\frac{6}{4}\)
Reduce to simplest form.
\(\frac{6}{4} \div \frac{2}{2}\) = \(\frac{3}{2}\)
Add the whole numbers.
8 + 6 = 14
So, 14\(\frac{3}{2}\) = \(\frac{31}{2}\)
Reduce to simplest form.
15\(\frac{1}{2}\)
e.
Answer:
9\(\frac{4}{9}\)
Explanation:
Add the fractions.
\(\frac{2}{9}\) + \(\frac{2}{9}\) = \(\frac{4}{9}\)
Add the whole numbers.
2 + 7 = 9
So, 9\(\frac{4}{9}\)
Question 3.
a.
Answer:
7\(\frac{7}{11}\)
Explanation:
Add the fractions.
\(\frac{4}{11}\) + \(\frac{3}{11}\) = \(\frac{7}{11}\)
Add the whole numbers.
6 + 1 = 7
So, 7\(\frac{7}{11}\)
b.
Answer:
8
Explanation:
Add the fractions.
\(\frac{1}{10}\) + \(\frac{9}{10}\) = \(\frac{10}{10}\) = 1
Add the whole numbers.
3 + 4 = 7
So, 7 + 1 = 8
c.
Answer:
12\(\frac{2}{3}\)
Explanation:
Add the fractions.
\(\frac{5}{6}\) + \(\frac{5}{6}\) = \(\frac{10}{6}\)
Add the whole numbers.
6 + 5 = 11
So, 11 \(\frac{10}{6}\)
Reduce to simplest form.
\(\frac{76}{6}\) = 12\(\frac{2}{3}\)
d.
Answer:
13\(\frac{3}{4}\)
Explanation:
Add the fractions.
\(\frac{3}{8}\) + \(\frac{3}{8}\) = \(\frac{6}{8}\)
Add the whole numbers.
5 + 8 = 13
Reduce to simplest form.
\(\frac{6}{8} \div \frac{2}{2}\) = \(\frac{3}{4}\)
Therefore, 13\(\frac{3}{4}\)
e.
Answer:
8\(\frac{2}{7}\)
Explanation:
Add the fractions.
\(\frac{5}{7}\) + \(\frac{4}{7}\) = \(\frac{9}{7}\)
Add the whole numbers.
1 + 6 = 7
So, 7 \(\frac{9}{7}\)
Reduce to simplest form.
\(\frac{58}{7}\) = 8\(\frac{2}{7}\)
Question 4.
a.
Answer:
10\(\frac{5}{6}\)
Explanation:
Add the fractions.
\(\frac{11}{12}\) + \(\frac{11}{12}\) = \(\frac{22}{12}\)
Reduce to simplest form.
\(\frac{22}{12} \div \frac{2}{2}\) = \(\frac{11}{6}\)
Add the whole numbers.
2 + 7 = 9
Hence, 9 \(\frac{11}{6}\)
Reduce to simplest form.
\(\frac{65}{6}\) = 10\(\frac{5}{6}\)
b.
Answer:
16\(\frac{4}{5}\)
Explanation:
Add the fractions.
\(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{5}\)
Add the whole numbers.
8 + 8 = 16
So, 16\(\frac{4}{5}\)
c.
Answer:
14
Explanation:
Add the fractions.
\(\frac{5}{12}\) + \(\frac{7}{12}\) = \(\frac{12}{12}\) = 1
Add the whole numbers.
9 + 4 = 13
So, 13 + 1 = 14
d.
Answer:
8\(\frac{2}{3}\)
Explanation:
Add the fractions.
\(\frac{8}{9}\) + \(\frac{7}{9}\) = \(\frac{15}{9}\)
Add the whole numbers.
2 + 5 = 7
Reduce to simplest form.
\(\frac{15}{9} \div \frac{3}{3}\) = \(\frac{5}{3}\)
Therefore, 7\(\frac{5}{3}\)
Reduce to simplest form.
\(\frac{26}{3}\) = 8\(\frac{2}{3}\)
e.
Answer:
14\(\frac{4}{5}\)
Explanation:
Add the fractions.
\(\frac{9}{10}\) + \(\frac{9}{10}\) = \(\frac{18}{10}\)
Add the whole numbers.
7 + 6 = 13
Reduce to simplest form.
\(\frac{18}{10} \div \frac{2}{2}\) = \(\frac{9}{5}\)
So, 13\(\frac{9}{5}\)
= \(\frac{74}{5}\)
= 14\(\frac{4}{5}\)