Grade 3 Math Worksheets: Comparing fractions | Worsheets library - Free Printable

Problem: Comparing Fractions with Unlike Denominators

The task involves comparing fractions that have different denominators. To compare such fractions, we need to find a common denominator or convert the fractions into decimal form. Here, we will use the method of finding a common denominator for each pair of fractions.

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Step-by-Step Solution:

#### 1. 8/20 ______ 3/6
- Find the Least Common Denominator (LCD): The denominators are 20 and 6. The LCD of 20 and 6 is 60.
- Convert each fraction to an equivalent fraction with the LCD:
- For \( \frac{8}{20} \):
\[
\frac{8}{20} = \frac{8 \times 3}{20 \times 3} = \frac{24}{60}
\]
- For \( \frac{3}{6} \):
\[
\frac{3}{6} = \frac{3 \times 10}{6 \times 10} = \frac{30}{60}
\]
- Compare the numerators:
\[
\frac{24}{60} < \frac{30}{60}
\]
- Answer: \( \frac{8}{20} < \frac{3}{6} \)

---

#### 2. 1/10 ______ 1/4
- Find the LCD: The denominators are 10 and 4. The LCD of 10 and 4 is 20.
- Convert each fraction:
- For \( \frac{1}{10} \):
\[
\frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20}
\]
- For \( \frac{1}{4} \):
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]
- Compare the numerators:
\[
\frac{2}{20} < \frac{5}{20}
\]
- Answer: \( \frac{1}{10} < \frac{1}{4} \)

---

#### 3. 1/5 ______ 5/10
- Find the LCD: The denominators are 5 and 10. The LCD of 5 and 10 is 10.
- Convert each fraction:
- For \( \frac{1}{5} \):
\[
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
\]
- For \( \frac{5}{10} \):
\[
\frac{5}{10} = \frac{5}{10}
\]
- Compare the numerators:
\[
\frac{2}{10} < \frac{5}{10}
\]
- Answer: \( \frac{1}{5} < \frac{5}{10} \)

---

#### 4. 5/15 ______ 7/12
- Find the LCD: The denominators are 15 and 12. The LCD of 15 and 12 is 60.
- Convert each fraction:
- For \( \frac{5}{15} \):
\[
\frac{5}{15} = \frac{5 \times 4}{15 \times 4} = \frac{20}{60}
\]
- For \( \frac{7}{12} \):
\[
\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}
\]
- Compare the numerators:
\[
\frac{20}{60} < \frac{35}{60}
\]
- Answer: \( \frac{5}{15} < \frac{7}{12} \)

---

#### 5. 2/4 ______ 10/49
- Find the LCD: The denominators are 4 and 49. The LCD of 4 and 49 is 196.
- Convert each fraction:
- For \( \frac{2}{4} \):
\[
\frac{2}{4} = \frac{2 \times 49}{4 \times 49} = \frac{98}{196}
\]
- For \( \frac{10}{49} \):
\[
\frac{10}{49} = \frac{10 \times 4}{49 \times 4} = \frac{40}{196}
\]
- Compare the numerators:
\[
\frac{98}{196} > \frac{40}{196}
\]
- Answer: \( \frac{2}{4} > \frac{10}{49} \)

---

#### 6. 2/6 ______ 20/50
- Simplify each fraction first:
- \( \frac{2}{6} = \frac{1}{3} \)
- \( \frac{20}{50} = \frac{2}{5} \)
- Find the LCD: The denominators are 3 and 5. The LCD of 3 and 5 is 15.
- Convert each fraction:
- For \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]
- For \( \frac{2}{5} \):
\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]
- Compare the numerators:
\[
\frac{5}{15} < \frac{6}{15}
\]
- Answer: \( \frac{2}{6} < \frac{20}{50} \)

---

#### 7. 5/5 ______ 7/10
- Simplify \( \frac{5}{5} \):
\[
\frac{5}{5} = 1
\]
- Compare:
\[
1 > \frac{7}{10}
\]
- Answer: \( \frac{5}{5} > \frac{7}{10} \)

---

#### 8. 5/12 ______ 1/2
- Find the LCD: The denominators are 12 and 2. The LCD of 12 and 2 is 12.
- Convert each fraction:
- For \( \frac{5}{12} \):
\[
\frac{5}{12} = \frac{5}{12}
\]
- For \( \frac{1}{2} \):
\[
\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}
\]
- Compare the numerators:
\[
\frac{5}{12} < \frac{6}{12}
\]
- Answer: \( \frac{5}{12} < \frac{1}{2} \)

---

#### 9. 4/6 ______ 42/48
- Simplify each fraction:
- \( \frac{4}{6} = \frac{2}{3} \)
- \( \frac{42}{48} = \frac{7}{8} \)
- Find the LCD: The denominators are 3 and 8. The LCD of 3 and 8 is 24.
- Convert each fraction:
- For \( \frac{2}{3} \):
\[
\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}
\]
- For \( \frac{7}{8} \):
\[
\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}
\]
- Compare the numerators:
\[
\frac{16}{24} < \frac{21}{24}
\]
- Answer: \( \frac{4}{6} < \frac{42}{48} \)

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#### 10. 3/6 ______ 2/4
- Simplify each fraction:
- \( \frac{3}{6} = \frac{1}{2} \)
- \( \frac{2}{4} = \frac{1}{2} \)
- Compare:
\[
\frac{1}{2} = \frac{1}{2}
\]
- Answer: \( \frac{3}{6} = \frac{2}{4} \)

---

#### 11. 3/9 ______ 10/50
- Simplify each fraction:
- \( \frac{3}{9} = \frac{1}{3} \)
- \( \frac{10}{50} = \frac{1}{5} \)
- Find the LCD: The denominators are 3 and 5. The LCD of 3 and 5 is 15.
- Convert each fraction:
- For \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]
- For \( \frac{1}{5} \):
\[
\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}
\]
- Compare the numerators:
\[
\frac{5}{15} > \frac{3}{15}
\]
- Answer: \( \frac{3}{9} > \frac{10}{50} \)

---

#### 12. 10/20 ______ 4/8
- Simplify each fraction:
- \( \frac{10}{20} = \frac{1}{2} \)
- \( \frac{4}{8} = \frac{1}{2} \)
- Compare:
\[
\frac{1}{2} = \frac{1}{2}
\]
- Answer: \( \frac{10}{20} = \frac{4}{8} \)

---

#### 13. 5/8 ______ 2/6
- Find the LCD: The denominators are 8 and 6. The LCD of 8 and 6 is 24.
- Convert each fraction:
- For \( \frac{5}{8} \):
\[
\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}
\]
- For \( \frac{2}{6} \):
\[
\frac{2}{6} = \frac{2 \times 4}{6 \times 4} = \frac{8}{24}
\]
- Compare the numerators:
\[
\frac{15}{24} > \frac{8}{24}
\]
- Answer: \( \frac{5}{8} > \frac{2}{6} \)

---

#### 14. 15/60 ______ 16/20
- Simplify each fraction:
- \( \frac{15}{60} = \frac{1}{4} \)
- \( \frac{16}{20} = \frac{4}{5} \)
- Find the LCD: The denominators are 4 and 5. The LCD of 4 and 5 is 20.
- Convert each fraction:
- For \( \frac{1}{4} \):
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]
- For \( \frac{4}{5} \):
\[
\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}
\]
- Compare the numerators:
\[
\frac{5}{20} < \frac{16}{20}
\]
- Answer: \( \frac{15}{60} < \frac{16}{20} \)

---

#### 15. 6/24 ______ 2/10
- Simplify each fraction:
- \( \frac{6}{24} = \frac{1}{4} \)
- \( \frac{2}{10} = \frac{1}{5} \)
- Find the LCD: The denominators are 4 and 5. The LCD of 4 and 5 is 20.
- Convert each fraction:
- For \( \frac{1}{4} \):
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]
- For \( \frac{1}{5} \):
\[
\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}
\]
- Compare the numerators:
\[
\frac{5}{20} > \frac{4}{20}
\]
- Answer: \( \frac{6}{24} > \frac{2}{10} \)

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#### 16. 20/24 ______ 3/9
- Simplify each fraction:
- \( \frac{20}{24} = \frac{5}{6} \)
- \( \frac{3}{9} = \frac{1}{3} \)
- Find the LCD: The denominators are 6 and 3. The LCD of 6 and 3 is 6.
- Convert each fraction:
- For \( \frac{5}{6} \):
\[
\frac{5}{6} = \frac{5}{6}
\]
- For \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\]
- Compare the numerators:
\[
\frac{5}{6} > \frac{2}{6}
\]
- Answer: \( \frac{20}{24} > \frac{3}{9} \)

---

#### 17. 18/48 ______ 10/30
- Simplify each fraction:
- \( \frac{18}{48} = \frac{3}{8} \)
- \( \frac{10}{30} = \frac{1}{3} \)
- Find the LCD: The denominators are 8 and 3. The LCD of 8 and 3 is 24.
- Convert each fraction:
- For \( \frac{3}{8} \):
\[
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
\]
- For \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}
\]
- Compare the numerators:
\[
\frac{9}{24} > \frac{8}{24}
\]
- Answer: \( \frac{18}{48} > \frac{10}{30} \)

---

#### 18. 2/10 ______ 1/2
- Simplify \( \frac{2}{10} \):
\[
\frac{2}{10} = \frac{1}{5}
\]
- Find the LCD: The denominators are 5 and 2. The LCD of 5 and 2 is 10.
- Convert each fraction:
- For \( \frac{1}{5} \):
\[
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
\]
- For \( \frac{1}{2} \):
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
- Compare the numerators:
\[
\frac{2}{10} < \frac{5}{10}
\]
- Answer: \( \frac{2}{10} < \frac{1}{2} \)

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