This handy Spectrum Math Grade 4 Answer Key Chapter 6 Lesson 6.3 Comparing Fractions Using LCM provides detailed answers for the workbook questions.
Spectrum Math Grade 4 Chapter 6 Lesson 6.3 Comparing Fractions Using LCM Answers Key
\(\frac{1}{7}\) 
\(\frac{2}{3}\)
To compare fractions without pictures, the denominators must be 3 the same. When you have unlike denominators, find the least 3 common multiple (LCM) and rename the fractions.
In the example, the denominators are 3 and 7, so find the LCM of 3 and 7.
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. Look at the numerator to determine the larger fraction.
Use <, >, or = to compare the fractions. Show your work.
Question 1.
a. \(\frac{4}{8}\) \(\frac{2}{10}\)
Answer:
\(\frac{4}{8}\) > \(\frac{2}{10}\)
Explanation:
Given,
\(\frac{4}{8}\) \(\frac{2}{10}\)
When you have unlike denominators,
find the least 8 common multiple (LCM) and rename the fractions.
we convert the fractions such that their denominators are same so that we can compare the numerators.
The least common multiple of 8 and 10 is 40.
To change each fraction so it has the same denominator,
multiply both the numerator and denominator by the same number.
Then look at the numerator to determine the larger fraction.
\(\frac{4 × 5}{8 × 5}\) > \(\frac{2 × 4}{10 × 4}\)
\(\frac{20}{40}\) > \(\frac{8}{40}\)
since the denominators are same we compare the numerators
20 > 8
So, \(\frac{20}{40}\) > \(\frac{8}{40}\)
b. \(\frac{1}{5}\) \(\frac{2}{10}\)
Answer:
\(\frac{1}{5}\) = \(\frac{2}{10}\)
Explanation:
Given,
\(\frac{1}{5}\) \(\frac{2}{10}\)
When you have unlike denominators,
find the least 5 common multiple (LCM) and rename the fractions.
we convert the fractions such that their denominators are same so that we can compare the numerators.
The least common multiple of 5 and 10 is 10.
To change each fraction so it has the same denominator,
multiply both the numerator and denominator by the same number.
Then look at the numerator to determine the larger fraction.
\(\frac{1 × 2}{5 × 2}\) = \(\frac{2 × 1}{10 × 1}\)
\(\frac{2}{10}\) = \(\frac{2}{10}\)
since the denominators and numerators are same,
both the given fractions are equivalent fractions.
So, \(\frac{1}{5}\) = \(\frac{2}{10}\)
Question 2.
a. \(\frac{3}{8}\) \(\frac{10}{12}\)
Answer:
\(\frac{3}{8}\) < \(\frac{10}{12}\)
Explanation:
Given,
\(\frac{3}{8}\) \(\frac{10}{12}\)
When you have unlike denominators,
find the least 8 common multiple (LCM) and rename the fractions.
we convert the fractions such that their denominators are same so that we can compare the numerators.
The least common multiple of 8 and 12 is 24.
To change each fraction so it has the same denominator,
multiply both the numerator and denominator by the same number.
Then look at the numerator to determine the larger fraction.
\(\frac{3 × 3}{8 × 3}\) < \(\frac{10 × 3}{12 × 3}\)
\(\frac{9}{24}\) < \(\frac{30}{24}\)
since the denominators are same we compare the numerators
9 < 30
So, \(\frac{3}{8}\) < \(\frac{10}{12}\)
b. \(\frac{3}{12}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{12}\) < \(\frac{1}{3}\)
Explanation:
Given,
\(\frac{3}{12}\) \(\frac{1}{3}\)
When you have unlike denominators,
find the least 3 common multiple (LCM) and rename the fractions.
we convert the fractions such that their denominators are same so that we can compare the numerators.
The least common multiple of 3 and 12 is 12.
To change each fraction so it has the same denominator,
multiply both the numerator and denominator by the same number.
Then look at the numerator to determine the larger fraction.
\(\frac{3 × 1}{12 × 1}\) < \(\frac{1 × 4}{3 × 4}\)
\(\frac{3}{12}\) < \(\frac{4}{12}\)
since the denominators are same we compare the numerators.
3 < 4
So, \(\frac{3}{12}\) < \(\frac{1}{3}\)
Question 3.
a. \(\frac{2}{8}\) \(\frac{1}{4}\)
Answer:
\(\frac{2}{8}\) = \(\frac{1}{4}\)
Explanation:
Given,
\(\frac{2}{8}\) \(\frac{1}{4}\)
When you have unlike denominators,
find the least 4 common multiple (LCM) and rename the fractions.
we convert the fractions such that their denominators are same so that we can compare the numerators.
The least common multiple of 8 and 4 is 8.
To change each fraction so it has the same denominator,
multiply both the numerator and denominator by the same number.
Then look at the numerator to determine the larger fraction.
\(\frac{2 × 1}{8 × 1}\) = \(\frac{1 × 2}{4 × 2}\)
\(\frac{2}{8}\) = \(\frac{2}{8}\)
Hence, both the numerators and denominators are same.
So, \(\frac{2}{8}\) = \(\frac{2}{8}\)
b. \(\frac{3}{6}\) \(\frac{4}{8}\)
Answer:
\(\frac{3}{6}\) = \(\frac{4}{8}\)
Explanation:
Given,
\(\frac{3}{6}\) \(\frac{4}{8}\)
When you have unlike denominators,
find the least 6 common multiple (LCM) and rename the fractions.
we convert the fractions such that their denominators are same so that we can compare the numerators.
The least common multiple of 8 and 6 is 24.
To change each fraction so it has the same denominator,
multiply both the numerator and denominator by the same number.
Then look at the numerator to determine the larger fraction.
\(\frac{3 × 4}{6 × 4}\) = \(\frac{4 × 3}{8 × 3}\)
\(\frac{12}{24}\) = \(\frac{12}{24}\)
Hence, the numerators and denominators are same.
So, \(\frac{3}{6}\) = \(\frac{4}{8}\)