Free. Exclusive. Just for you.
Four unique services that make learning easier, faster, and smarter - only on our website.

Math worksheet for practicing addition of improper fractions with unlike denominators.

Worksheet titled "Operations with Unlike Denominators" featuring 18 math problems involving addition of improper fractions with different denominators.

Worksheet titled "Operations with Unlike Denominators" featuring 18 math problems involving addition of improper fractions with different denominators.

PNG 416×539 12 KB Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #812206
Show Answer Key & Explanations Step-by-step solution for: Operations with Unlike Fractions Worksheets - 15 Worksheets Library
To solve the problems involving addition of improper fractions with unlike denominators, we need to follow these steps:

Steps:


1. Find a Common Denominator: The least common denominator (LCD) is the smallest number that is a multiple of all the denominators involved.
2. Adjust the Fractions: Rewrite each fraction with the common denominator by multiplying both the numerator and the denominator by the necessary factor.
3. Add the Numerators: Once the denominators are the same, add the numerators while keeping the denominator unchanged.
4. Simplify the Result: Reduce the resulting fraction to its simplest form if possible.

Let's solve each problem step by step.

---

Problem 1: $\frac{9}{5} + \frac{15}{10}$



1. Find the LCD: The denominators are 5 and 10. The LCD is 10.
2. Adjust the fractions:
- $\frac{9}{5} = \frac{9 \times 2}{5 \times 2} = \frac{18}{10}$
- $\frac{15}{10}$ remains $\frac{15}{10}$.
3. Add the numerators:
$$
\frac{18}{10} + \frac{15}{10} = \frac{18 + 15}{10} = \frac{33}{10}
$$
4. Simplify: $\frac{33}{10}$ is already in simplest form.

Answer: $\boxed{\frac{33}{10}}$

---

Problem 2: $\frac{18}{4} + \frac{7}{5}$



1. Find the LCD: The denominators are 4 and 5. The LCD is 20.
2. Adjust the fractions:
- $\frac{18}{4} = \frac{18 \times 5}{4 \times 5} = \frac{90}{20}$
- $\frac{7}{5} = \frac{7 \times 4}{5 \times 4} = \frac{28}{20}$
3. Add the numerators:
$$
\frac{90}{20} + \frac{28}{20} = \frac{90 + 28}{20} = \frac{118}{20}
$$
4. Simplify: Divide numerator and denominator by their greatest common divisor (GCD), which is 2:
$$
\frac{118}{20} = \frac{59}{10}
$$

Answer: $\boxed{\frac{59}{10}}$

---

Problem 3: $\frac{15}{6} + \frac{19}{12}$



1. Find the LCD: The denominators are 6 and 12. The LCD is 12.
2. Adjust the fractions:
- $\frac{15}{6} = \frac{15 \times 2}{6 \times 2} = \frac{30}{12}$
- $\frac{19}{12}$ remains $\frac{19}{12}$.
3. Add the numerators:
$$
\frac{30}{12} + \frac{19}{12} = \frac{30 + 19}{12} = \frac{49}{12}
$$
4. Simplify: $\frac{49}{12}$ is already in simplest form.

Answer: $\boxed{\frac{49}{12}}$

---

Problem 4: $\frac{21}{15} + \frac{12}{5}$



1. Find the LCD: The denominators are 15 and 5. The LCD is 15.
2. Adjust the fractions:
- $\frac{21}{15}$ remains $\frac{21}{15}$.
- $\frac{12}{5} = \frac{12 \times 3}{5 \times 3} = \frac{36}{15}$
3. Add the numerators:
$$
\frac{21}{15} + \frac{36}{15} = \frac{21 + 36}{15} = \frac{57}{15}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 3:
$$
\frac{57}{15} = \frac{19}{5}
$$

Answer: $\boxed{\frac{19}{5}}$

---

Problem 5: $\frac{18}{12} + \frac{21}{9}$



1. Find the LCD: The denominators are 12 and 9. The LCD is 36.
2. Adjust the fractions:
- $\frac{18}{12} = \frac{18 \times 3}{12 \times 3} = \frac{54}{36}$
- $\frac{21}{9} = \frac{21 \times 4}{9 \times 4} = \frac{84}{36}$
3. Add the numerators:
$$
\frac{54}{36} + \frac{84}{36} = \frac{54 + 84}{36} = \frac{138}{36}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 6:
$$
\frac{138}{36} = \frac{23}{6}
$$

Answer: $\boxed{\frac{23}{6}}$

---

Problem 6: $\frac{25}{15} + \frac{20}{3}$



1. Find the LCD: The denominators are 15 and 3. The LCD is 15.
2. Adjust the fractions:
- $\frac{25}{15}$ remains $\frac{25}{15}$.
- $\frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15}$
3. Add the numerators:
$$
\frac{25}{15} + \frac{100}{15} = \frac{25 + 100}{15} = \frac{125}{15}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 5:
$$
\frac{125}{15} = \frac{25}{3}
$$

Answer: $\boxed{\frac{25}{3}}$

---

Problem 7: $\frac{9}{5} + \frac{10}{3}$



1. Find the LCD: The denominators are 5 and 3. The LCD is 15.
2. Adjust the fractions:
- $\frac{9}{5} = \frac{9 \times 3}{5 \times 3} = \frac{27}{15}$
- $\frac{10}{3} = \frac{10 \times 5}{3 \times 5} = \frac{50}{15}$
3. Add the numerators:
$$
\frac{27}{15} + \frac{50}{15} = \frac{27 + 50}{15} = \frac{77}{15}
$$
4. Simplify: $\frac{77}{15}$ is already in simplest form.

Answer: $\boxed{\frac{77}{15}}$

---

Problem 8: $\frac{14}{9} + \frac{5}{3}$



1. Find the LCD: The denominators are 9 and 3. The LCD is 9.
2. Adjust the fractions:
- $\frac{14}{9}$ remains $\frac{14}{9}$.
- $\frac{5}{3} = \frac{5 \times 3}{3 \times 3} = \frac{15}{9}$
3. Add the numerators:
$$
\frac{14}{9} + \frac{15}{9} = \frac{14 + 15}{9} = \frac{29}{9}
$$
4. Simplify: $\frac{29}{9}$ is already in simplest form.

Answer: $\boxed{\frac{29}{9}}$

---

Problem 9: $\frac{2}{15} + \frac{12}{5}$



1. Find the LCD: The denominators are 15 and 5. The LCD is 15.
2. Adjust the fractions:
- $\frac{2}{15}$ remains $\frac{2}{15}$.
- $\frac{12}{5} = \frac{12 \times 3}{5 \times 3} = \frac{36}{15}$
3. Add the numerators:
$$
\frac{2}{15} + \frac{36}{15} = \frac{2 + 36}{15} = \frac{38}{15}
$$
4. Simplify: $\frac{38}{15}$ is already in simplest form.

Answer: $\boxed{\frac{38}{15}}$

---

Problem 10: $\frac{15}{9} + \frac{9}{5}$



1. Find the LCD: The denominators are 9 and 5. The LCD is 45.
2. Adjust the fractions:
- $\frac{15}{9} = \frac{15 \times 5}{9 \times 5} = \frac{75}{45}$
- $\frac{9}{5} = \frac{9 \times 9}{5 \times 9} = \frac{81}{45}$
3. Add the numerators:
$$
\frac{75}{45} + \frac{81}{45} = \frac{75 + 81}{45} = \frac{156}{45}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 3:
$$
\frac{156}{45} = \frac{52}{15}
$$

Answer: $\boxed{\frac{52}{15}}$

---

Problem 11: $\frac{18}{10} + \frac{14}{5}$



1. Find the LCD: The denominators are 10 and 5. The LCD is 10.
2. Adjust the fractions:
- $\frac{18}{10}$ remains $\frac{18}{10}$.
- $\frac{14}{5} = \frac{14 \times 2}{5 \times 2} = \frac{28}{10}$
3. Add the numerators:
$$
\frac{18}{10} + \frac{28}{10} = \frac{18 + 28}{10} = \frac{46}{10}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 2:
$$
\frac{46}{10} = \frac{23}{5}
$$

Answer: $\boxed{\frac{23}{5}}$

---

Problem 12: $\frac{12}{9} + \frac{4}{3}$



1. Find the LCD: The denominators are 9 and 3. The LCD is 9.
2. Adjust the fractions:
- $\frac{12}{9}$ remains $\frac{12}{9}$.
- $\frac{4}{3} = \frac{4 \times 3}{3 \times 3} = \frac{12}{9}$
3. Add the numerators:
$$
\frac{12}{9} + \frac{12}{9} = \frac{12 + 12}{9} = \frac{24}{9}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 3:
$$
\frac{24}{9} = \frac{8}{3}
$$

Answer: $\boxed{\frac{8}{3}}$

---

Problem 13: $\frac{21}{15} + \frac{17}{10}$



1. Find the LCD: The denominators are 15 and 10. The LCD is 30.
2. Adjust the fractions:
- $\frac{21}{15} = \frac{21 \times 2}{15 \times 2} = \frac{42}{30}$
- $\frac{17}{10} = \frac{17 \times 3}{10 \times 3} = \frac{51}{30}$
3. Add the numerators:
$$
\frac{42}{30} + \frac{51}{30} = \frac{42 + 51}{30} = \frac{93}{30}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 3:
$$
\frac{93}{30} = \frac{31}{10}
$$

Answer: $\boxed{\frac{31}{10}}$

---

Problem 14: $\frac{30}{12} + \frac{15}{4}$



1. Find the LCD: The denominators are 12 and 4. The LCD is 12.
2. Adjust the fractions:
- $\frac{30}{12}$ remains $\frac{30}{12}$.
- $\frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}$
3. Add the numerators:
$$
\frac{30}{12} + \frac{45}{12} = \frac{30 + 45}{12} = \frac{75}{12}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 3:
$$
\frac{75}{12} = \frac{25}{4}
$$

Answer: $\boxed{\frac{25}{4}}$

---

Problem 15: $\frac{19}{14} + \frac{7}{2}$



1. Find the LCD: The denominators are 14 and 2. The LCD is 14.
2. Adjust the fractions:
- $\frac{19}{14}$ remains $\frac{19}{14}$.
- $\frac{7}{2} = \frac{7 \times 7}{2 \times 7} = \frac{49}{14}$
3. Add the numerators:
$$
\frac{19}{14} + \frac{49}{14} = \frac{19 + 49}{14} = \frac{68}{14}
$$
4. Simplify: Divide numerator and denominator by their GCD, which is 2:
$$
\frac{68}{14} = \frac{34}{7}
$$

Answer: $\boxed{\frac{34}{7}}$

---

Problem 16: $\frac{15}{4} + \frac{25}{8}$



1. Find the LCD: The denominators are 4 and 8. The LCD is 8.
2. Adjust the fractions:
- $\frac{15}{4} = \frac{15 \times 2}{4 \times 2} = \frac{30}{8}$
- $\frac{25}{8}$ remains $\frac{25}{8}$.
3. Add the numerators:
$$
\frac{30}{8} + \frac{25}{8} = \frac{30 + 25}{8} = \frac{55}{8}
$$
4. Simplify: $\frac{55}{8}$ is already in simplest form.

Answer: $\boxed{\frac{55}{8}}$

---

Problem 17: $\frac{10}{7} + \frac{5}{2}$



1. Find the LCD: The denominators are 7 and 2. The LCD is 14.
2. Adjust the fractions:
- $\frac{10}{7} = \frac{10 \times 2}{7 \times 2} = \frac{20}{14}$
- $\frac{5}{2} = \frac{5 \times 7}{2 \times 7} = \frac{35}{14}$
3. Add the numerators:
$$
\frac{20}{14} + \frac{35}{14} = \frac{20 + 35}{14} = \frac{55}{14}
$$
4. Simplify: $\frac{55}{14}$ is already in simplest form.

Answer: $\boxed{\frac{55}{14}}$

---

Problem 18: $\frac{7}{3} + \frac{21}{15}$



1. Find the LCD: The denominators are 3 and 15. The LCD is 15.
2. Adjust the fractions:
- $\frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15}$
- $\frac{21}{15}$ remains $\frac{21}{15}$.
3. Add the numerators:
$$
\frac{35}{15} + \frac{21}{15} = \frac{35 + 21}{15} = \frac{56}{15}
$$
4. Simplify: $\frac{56}{15}$ is already in simplest form.

Answer: $\boxed{\frac{56}{15}}$

---

Final Answers:


1. $\boxed{\frac{33}{10}}$
2. $\boxed{\frac{59}{10}}$
3. $\boxed{\frac{49}{12}}$
4. $\boxed{\frac{19}{5}}$
5. $\boxed{\frac{23}{6}}$
6. $\boxed{\frac{25}{3}}$
7. $\boxed{\frac{77}{15}}$
8. $\boxed{\frac{29}{9}}$
9. $\boxed{\frac{38}{15}}$
10. $\boxed{\frac{52}{15}}$
11. $\boxed{\frac{23}{5}}$
12. $\boxed{\frac{8}{3}}$
13. $\boxed{\frac{31}{10}}$
14. $\boxed{\frac{25}{4}}$
15. $\boxed{\frac{34}{7}}$
16. $\boxed{\frac{55}{8}}$
17. $\boxed{\frac{55}{14}}$
18. $\boxed{\frac{56}{15}}$
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting unlike fractions worksheet.
Print Download

How to use

Click Print to open a print-ready version directly in your browser, or use Download to save the file to your device. The ⭐ Answer button generates an AI answer key instantly - useful for teachers who need a quick reference. Need a different version? Our AI Worksheet Generator lets you create a custom worksheet on any topic in seconds.

(view all adding and subtracting unlike fractions worksheet)

Fractions Worksheets | Printable Fractions Worksheets for Teachers
Subtracting Fractions with Unlike Denominators
Fractions Worksheets | Printable Fractions Worksheets for Teachers
Grade 4 Adding and subtracting unlike fractions: Free download
Subtracting Fractions Worksheets
Adding and Subtracting Fractions Visually (Different Denominators ...
Adding and Subtracting Fractions Worksheets with Answer Key
Addition and Subtraction of Dissimilar Fraction worksheet | Live ...
Operations with Unlike Fractions Worksheets - 15 Worksheets.com
Adding Subtracting Fractions Worksheets