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Spectrum Math Grade 5 Chapter 5 Posttest Answers Key
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Add or subtract. Write answers in simplest form.
Question 1.
a.
Answer:
To add fractions with like denominators, add the numerators and use the common denominator.
\(\frac{4}{6}\) + \(\frac{1}{6}\) = \(\frac{4+1}{6}\) = \(\frac{5}{6}\)
b.
Answer:
To add fractions with like denominators, add the numerators and use the common denominator.
\(\frac{3}{7}\) + \(\frac{2}{7}\) = \(\frac{3+2}{7}\) = \(\frac{5}{7}\)
c.
Answer:
To add fractions with like denominators, add the numerators and use the common denominator.
\(\frac{2}{9}\) + \(\frac{6}{9}\) = \(\frac{2+6}{9}\) = \(\frac{8}{9}\)
d.
Answer:
To add fractions with like denominators, add the numerators and use the common denominator.
\(\frac{7}{8}\) + \(\frac{2}{8}\) = \(\frac{7+2}{8}\) = \(\frac{9}{8}\)
Question 2.
a.
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.
LCD of 12 and 5 is 60.
\(\frac{7}{12}\) + \(\frac{3}{5}\)
\(\frac{35}{60}\) + \(\frac{36}{60}\) = \(\frac{71}{60}\) = 1\(\frac{11}{60}\)
b.
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.
LCD of 5 and 10 is 10
\(\frac{2}{5}\) + \(\frac{9}{10}\)
\(\frac{4}{10}\) + \(\frac{9}{10}\) = \(\frac{13}{10}\) = 1\(\frac{3}{10}\)
c.
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.
5\(\frac{2}{5}\) + 7\(\frac{2}{3}\)
5 + \(\frac{2}{5}\) + 7 + \(\frac{2}{3}\)
5 + 7 = 12
\(\frac{2}{5}\)+ \(\frac{2}{3}\)
LCD is 15.
\(\frac{6}{15}\) + \(\frac{10}{15}\) = \(\frac{16}{15}\) = 1\(\frac{1}{15}\)
12 + 1\(\frac{1}{15}\) = 13\(\frac{1}{15}\)
d.
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.
8\(\frac{3}{10}\) + 9\(\frac{3}{10}\)
8 + \(\frac{3}{10}\) + 9 + \(\frac{3}{10}\)
8 + 9 = 17
\(\frac{3}{10}\)+ \(\frac{2}{4}\)
LCD is 20.
\(\frac{6}{20}\) + \(\frac{10}{20}\) = \(\frac{16}{20}\) = \(\frac{4}{5}\)
17 + \(\frac{4}{5}\) = 17\(\frac{4}{5}\)
Question 3.
a.
Answer:
To subtract fractions with like denominators, subtract the numerators and use the common denominator.
\(\frac{5}{9}\) – \(\frac{2}{9}\) = \(\frac{5-2}{9}\) = \(\frac{3}{9}\) = \(\frac{1}{3}\)
b.
Answer:
To subtract fractions with like denominators, subtract the numerators and use the common denominator.
\(\frac{6}{7}\) – \(\frac{5}{7}\) = \(\frac{6-5}{7}\) = \(\frac{1}{7}\)
c.
Answer:
When subtracting fractions that have different denominators, rename fractions to have a common denominator.
\(\frac{5}{8}\) – \(\frac{1}{4}\)
LCD is 8.
\(\frac{5}{8}\) – \(\frac{2}{8}\) = \(\frac{3}{8}\)
d.
Answer:
When subtracting fractions that have different denominators, rename fractions to have a common denominator.
\(\frac{5}{6}\) – \(\frac{7}{12}\)
LCD is 12
\(\frac{10}{12}\) – \(\frac{7}{12}\) = \(\frac{3}{12}\) = \(\frac{1}{4}\)
Question 4.
a.
Answer:
4 – \(\frac{5}{6}\) = 3\(\frac{1}{6}\)
b.
Answer:
6\(\frac{2}{3}\) – 4\(\frac{1}{3}\)
6 + \(\frac{2}{3}\) – 4 – \(\frac{1}{3}\)
6 – 4 = 2
\(\frac{2}{3}\) – \(\frac{1}{3}\) = \(\frac{1}{3}\)
2 + \(\frac{1}{3}\) = 2\(\frac{1}{3}\)
c.
Answer:
5\(\frac{2}{7}\) – 4\(\frac{1}{4}\)
5 + \(\frac{2}{7}\) – 4 – \(\frac{1}{4}\)
5 – 4 = 1
\(\frac{2}{7}\) – \(\frac{1}{4}\)
LCD is 28
\(\frac{8}{28}\) – \(\frac{7}{28}\) = \(\frac{1}{28}\)
1 + \(\frac{1}{28}\) = 1\(\frac{1}{28}\)
d.
Answer:
9 \(\frac{1}{9}\) – 1 \(\frac{4}{5}\)
9 + \(\frac{1}{9}\) – 1 – \(\frac{4}{5}\)
9 – 1 = 8
\(\frac{1}{9}\) – \(\frac{4}{5}\)
LCD is 45
\(\frac{5}{45}\) – \(\frac{36}{45}\) = – \(\frac{31}{45}\)
8 – \(\frac{31}{45}\) = 7\(\frac{14}{45}\)
Solve each problem. Show your work.
Question 5.
Lauren practiced tennis twice last week. On Tuesday, she practiced 2\(\frac{4}{8}\) hours. On Thursday, she practiced 1\(\frac{2}{6}\) hours. How much longer did Lauren practice on Tuesday?
Lauren practiced _____________ hours longer on Tuesday.
Answer:
Given,
Lauren practiced tennis twice last week. On Tuesday, she practiced 2\(\frac{4}{8}\) hours. On Thursday, she practiced 1\(\frac{2}{6}\) hours.
2\(\frac{4}{8}\) – 1\(\frac{2}{6}\)
2 + \(\frac{4}{8}\) – 1 – \(\frac{2}{6}\)
2 – 1 = 1
\(\frac{4}{8}\) – \(\frac{2}{6}\)
LCD is 24
\(\frac{12}{24}\) – \(\frac{8}{24}\) = \(\frac{4}{24}\) = \(\frac{1}{6}\)
1 + \(\frac{1}{6}\) = 1\(\frac{1}{6}\)
Lauren practiced 1\(\frac{1}{6}\) hours longer on Tuesday.
Question 6.
Mr. Daniels’ chili recipe calls for 5 cups of diced tomatoes and \(\frac{1}{4}\) cup of diced green chilies. How many cups of tomatoes and green chilies does Mr. Daniels need altogether?
Mr. Daniels needs _____________ cups of tomatoes and green chilies altogether.
Answer:
Given,
Mr. Daniels’ chili recipe calls for 5 cups of diced tomatoes and \(\frac{1}{4}\) cup of diced green chilies.
5 + \(\frac{1}{4}\) = 5\(\frac{1}{4}\)
Mr. Daniels needs 5\(\frac{1}{4}\) cups of tomatoes and green chilies altogether.
Question 7.
Ben watched a baseball game for 2\(\frac{1}{5}\) hours. Drew watched a football game for 2\(\frac{2}{8}\) hours. How much time altogether did Ben and Drew spend watching the games?
They spent _______________ hours watching the games.
Answer:
Given,
Ben watched a baseball game for 2\(\frac{1}{5}\) hours.
Drew watched a football game for 2\(\frac{2}{8}\) hours.
2\(\frac{1}{5}\) + 2\(\frac{2}{8}\)
2 + \(\frac{1}{5}\) + 2 + \(\frac{2}{8}\)
2 + 2 = 4
\(\frac{1}{5}\) + \(\frac{2}{8}\)
LCD is 40
\(\frac{8}{40}\) + \(\frac{10}{40}\) = \(\frac{18}{40}\) = \(\frac{9}{20}\)
4 + \(\frac{9}{20}\) = 4\(\frac{9}{20}\)
They spent 4\(\frac{9}{20}\) hours watching the games.
Question 8.
The Rizzo’s farm has 9\(\frac{1}{2}\) acres of corn. The Johnson’s farm has 7\(\frac{1}{3}\) acres of corn. How many more acres of corn does the Rizzo’s farm have?
The Rizzo’s farm has ______________ more acres of corn.
Answer:
Given,
The Rizzo’s farm has 9\(\frac{1}{2}\) acres of corn. The Johnson’s farm has 7\(\frac{1}{3}\) acres of corn.
9\(\frac{1}{2}\) – 7\(\frac{1}{3}\)
9 + \(\frac{1}{2}\) – 7 – \(\frac{1}{3}\)
9 – 7 = 2
\(\frac{1}{2}\) – \(\frac{1}{3}\)
LCD is 6
\(\frac{3}{6}\) – \(\frac{2}{6}\) = \(\frac{1}{6}\)
2 + \(\frac{1}{6}\) = 2\(\frac{1}{6}\)
The Rizzo’s farm has 2\(\frac{1}{6}\) more acres of corn.
Question 9.
Jeremy cleans his house in 2\(\frac{1}{2}\) hours. Hunter cleans his house in 3\(\frac{1}{4}\) hours. How much longer does it take Hunter to clean a house than Jeremy?
It takes Hunter _______________ hours longer to clean his house.
Answer:
Given,
Jeremy cleans his house in 2\(\frac{1}{2}\) hours. Hunter cleans his house in 3\(\frac{1}{4}\) hours.
3\(\frac{1}{4}\) – 2\(\frac{1}{2}\)
3 + \(\frac{1}{4}\) – 2 – \(\frac{1}{2}\)
3 – 2 = 1
\(\frac{1}{4}\) – \(\frac{1}{2}\)
LCD is 4
\(\frac{1}{4}\) – \(\frac{2}{4}\) = –\(\frac{1}{4}\)
1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)
It takes Hunter \(\frac{3}{4}\) hours longer to clean his house.