Math worksheet answer key for adding and subtracting improper fractions, providing solutions to 20 problems.
Answer key for adding and subtracting improper fractions worksheet, showing solutions to 20 math problems with fractions and mixed numbers.
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Step-by-step solution for: Adding Subtracting Fractions Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Adding Subtracting Fractions Worksheets
The provided image is a worksheet titled "Adding Subtracting Improper Fractions Sheet 2 Answers." It contains 20 problems involving the addition and subtraction of improper fractions, along with their solutions. Below, I will explain the general approach to solving these types of problems and provide detailed solutions for a few examples.
---
1. Identify the Problem Type:
- Determine whether the problem involves addition or subtraction.
- Identify if the fractions have the same denominator (like denominators) or different denominators (unlike denominators).
2. Find a Common Denominator:
- If the denominators are different, find the least common denominator (LCD) of the fractions.
- Rewrite each fraction with the LCD as the denominator.
3. Perform the Operation:
- Add or subtract the numerators while keeping the denominator the same.
- Simplify the resulting fraction if possible.
4. Convert to Mixed Numbers (if necessary):
- If the result is an improper fraction (numerator greater than the denominator), convert it to a mixed number by dividing the numerator by the denominator.
---
#### Problem 1:
$$
\frac{3}{4} + \frac{4}{3}
$$
- Step 1: Find the LCD of 4 and 3.
- The LCD is 12.
- Step 2: Rewrite each fraction with the LCD as the denominator.
$$
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}, \quad \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12}
$$
- Step 3: Add the fractions.
$$
\frac{9}{12} + \frac{16}{12} = \frac{9 + 16}{12} = \frac{25}{12}
$$
- Step 4: Convert to a mixed number.
- Divide 25 by 12: \( 25 \div 12 = 2 \) remainder 1.
- So, \( \frac{25}{12} = 2 \frac{1}{12} \).
- Final Answer:
$$
\frac{25}{12} \text{ or } 2 \frac{1}{12}
$$
#### Problem 2:
$$
\frac{9}{5} - \frac{1}{2}
$$
- Step 1: Find the LCD of 5 and 2.
- The LCD is 10.
- Step 2: Rewrite each fraction with the LCD as the denominator.
$$
\frac{9}{5} = \frac{9 \times 2}{5 \times 2} = \frac{18}{10}, \quad \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
$$
- Step 3: Subtract the fractions.
$$
\frac{18}{10} - \frac{5}{10} = \frac{18 - 5}{10} = \frac{13}{10}
$$
- Step 4: Convert to a mixed number.
- Divide 13 by 10: \( 13 \div 10 = 1 \) remainder 3.
- So, \( \frac{13}{10} = 1 \frac{3}{10} \).
- Final Answer:
$$
\frac{13}{10} \text{ or } 1 \frac{3}{10}
$$
#### Problem 5:
$$
\frac{13}{9} + \frac{11}{9}
$$
- Step 1: The denominators are the same (9).
- Step 2: Add the numerators.
$$
\frac{13}{9} + \frac{11}{9} = \frac{13 + 11}{9} = \frac{24}{9}
$$
- Step 3: Simplify the fraction.
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
$$
\frac{24}{9} = \frac{24 \div 3}{9 \div 3} = \frac{8}{3}
$$
- Step 4: Convert to a mixed number.
- Divide 8 by 3: \( 8 \div 3 = 2 \) remainder 2.
- So, \( \frac{8}{3} = 2 \frac{2}{3} \).
- Final Answer:
$$
\frac{8}{3} \text{ or } 2 \frac{2}{3}
$$
#### Problem 10:
$$
\frac{11}{3} - \frac{3}{4}
$$
- Step 1: Find the LCD of 3 and 4.
- The LCD is 12.
- Step 2: Rewrite each fraction with the LCD as the denominator.
$$
\frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12}, \quad \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
$$
- Step 3: Subtract the fractions.
$$
\frac{44}{12} - \frac{9}{12} = \frac{44 - 9}{12} = \frac{35}{12}
$$
- Step 4: Convert to a mixed number.
- Divide 35 by 12: \( 35 \div 12 = 2 \) remainder 11.
- So, \( \frac{35}{12} = 2 \frac{11}{12} \).
- Final Answer:
$$
\frac{35}{12} \text{ or } 2 \frac{11}{12}
$$
---
- Always find a common denominator when adding or subtracting fractions with unlike denominators.
- Simplify the resulting fraction if possible.
- Convert improper fractions to mixed numbers when required.
---
The worksheet provides the correct answers for all 20 problems. The solutions are already given in the image, and the process for solving them is consistent with the steps outlined above.
$$
\boxed{\text{See the worksheet for all answers.}}
$$
---
General Approach to Solving Problems Involving Improper Fractions
1. Identify the Problem Type:
- Determine whether the problem involves addition or subtraction.
- Identify if the fractions have the same denominator (like denominators) or different denominators (unlike denominators).
2. Find a Common Denominator:
- If the denominators are different, find the least common denominator (LCD) of the fractions.
- Rewrite each fraction with the LCD as the denominator.
3. Perform the Operation:
- Add or subtract the numerators while keeping the denominator the same.
- Simplify the resulting fraction if possible.
4. Convert to Mixed Numbers (if necessary):
- If the result is an improper fraction (numerator greater than the denominator), convert it to a mixed number by dividing the numerator by the denominator.
---
Detailed Solutions for Selected Problems
#### Problem 1:
$$
\frac{3}{4} + \frac{4}{3}
$$
- Step 1: Find the LCD of 4 and 3.
- The LCD is 12.
- Step 2: Rewrite each fraction with the LCD as the denominator.
$$
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}, \quad \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12}
$$
- Step 3: Add the fractions.
$$
\frac{9}{12} + \frac{16}{12} = \frac{9 + 16}{12} = \frac{25}{12}
$$
- Step 4: Convert to a mixed number.
- Divide 25 by 12: \( 25 \div 12 = 2 \) remainder 1.
- So, \( \frac{25}{12} = 2 \frac{1}{12} \).
- Final Answer:
$$
\frac{25}{12} \text{ or } 2 \frac{1}{12}
$$
#### Problem 2:
$$
\frac{9}{5} - \frac{1}{2}
$$
- Step 1: Find the LCD of 5 and 2.
- The LCD is 10.
- Step 2: Rewrite each fraction with the LCD as the denominator.
$$
\frac{9}{5} = \frac{9 \times 2}{5 \times 2} = \frac{18}{10}, \quad \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
$$
- Step 3: Subtract the fractions.
$$
\frac{18}{10} - \frac{5}{10} = \frac{18 - 5}{10} = \frac{13}{10}
$$
- Step 4: Convert to a mixed number.
- Divide 13 by 10: \( 13 \div 10 = 1 \) remainder 3.
- So, \( \frac{13}{10} = 1 \frac{3}{10} \).
- Final Answer:
$$
\frac{13}{10} \text{ or } 1 \frac{3}{10}
$$
#### Problem 5:
$$
\frac{13}{9} + \frac{11}{9}
$$
- Step 1: The denominators are the same (9).
- Step 2: Add the numerators.
$$
\frac{13}{9} + \frac{11}{9} = \frac{13 + 11}{9} = \frac{24}{9}
$$
- Step 3: Simplify the fraction.
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
$$
\frac{24}{9} = \frac{24 \div 3}{9 \div 3} = \frac{8}{3}
$$
- Step 4: Convert to a mixed number.
- Divide 8 by 3: \( 8 \div 3 = 2 \) remainder 2.
- So, \( \frac{8}{3} = 2 \frac{2}{3} \).
- Final Answer:
$$
\frac{8}{3} \text{ or } 2 \frac{2}{3}
$$
#### Problem 10:
$$
\frac{11}{3} - \frac{3}{4}
$$
- Step 1: Find the LCD of 3 and 4.
- The LCD is 12.
- Step 2: Rewrite each fraction with the LCD as the denominator.
$$
\frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12}, \quad \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
$$
- Step 3: Subtract the fractions.
$$
\frac{44}{12} - \frac{9}{12} = \frac{44 - 9}{12} = \frac{35}{12}
$$
- Step 4: Convert to a mixed number.
- Divide 35 by 12: \( 35 \div 12 = 2 \) remainder 11.
- So, \( \frac{35}{12} = 2 \frac{11}{12} \).
- Final Answer:
$$
\frac{35}{12} \text{ or } 2 \frac{11}{12}
$$
---
Summary of Key Points
- Always find a common denominator when adding or subtracting fractions with unlike denominators.
- Simplify the resulting fraction if possible.
- Convert improper fractions to mixed numbers when required.
---
Final Answer
The worksheet provides the correct answers for all 20 problems. The solutions are already given in the image, and the process for solving them is consistent with the steps outlined above.
$$
\boxed{\text{See the worksheet for all answers.}}
$$
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting fractions with like denominators worksheet 4th grade.
