Questions On Addition And Subtraction Of Unlike Fractions

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Fractions are an essential part of mathematics, and understanding how to add and subtract unlike fractions is crucial for problem-solving. Unlike fractions have different denominators, making their calculations slightly more complex than like fractions.

This topic provides questions and answers to help students grasp the concept of addition and subtraction of unlike fractions step by step.

1. What Are Unlike Fractions?

Unlike fractions are fractions with different denominators. For example:

  • frac{2}{5} and frac{3}{7} are unlike fractions because 5 and 7 are different denominators.

To perform addition or subtraction, we must first convert them into like fractions by finding a common denominator.

2. How to Add Unlike Fractions?

To add unlike fractions, follow these steps:

  1. Find the Least Common Denominator (LCD) of both fractions.
  2. Convert the fractions by making the denominators the same.
  3. Add the numerators while keeping the denominator the same.
  4. Simplify the fraction if needed.

Example Question

Solve: frac{3}{4} + frac{2}{5}

Solution:

  1. Find the LCD of 4 and 5: The least common multiple of 4 and 5 is 20.
  2. Convert the fractions:
    • frac{3}{4} = frac{15}{20}
    • frac{2}{5} = frac{8}{20}
  3. Add the numerators:
    • $15 + 8 = 23$
  4. The result is frac{23}{20} , which is an improper fraction.
    • Converting to a mixed number: **1 frac{3}{20} **

Final Answer: $1 frac{3}{20}$

3. How to Subtract Unlike Fractions?

To subtract unlike fractions, the steps are similar to addition:

  1. Find the LCD of both fractions.
  2. Convert the fractions so that they have the same denominator.
  3. Subtract the numerators while keeping the denominator the same.
  4. Simplify the fraction if necessary.

Example Question

Solve: frac{5}{6} – frac{1}{4}

Solution:

  1. Find the LCD of 6 and 4: The least common multiple of 6 and 4 is 12.
  2. Convert the fractions:
    • frac{5}{6} = frac{10}{12}
    • frac{1}{4} = frac{3}{12}
  3. Subtract the numerators:
    • $10 – 3 = 7$
  4. The result is frac{7}{12} .

Final Answer: frac{7}{12}

4. Practice Questions on Addition and Subtraction of Unlike Fractions

Addition Problems

  1. frac{2}{3} + frac{1}{5} = ?
  2. frac{4}{7} + frac{3}{9} = ?
  3. frac{1}{6} + frac{5}{8} = ?
  4. frac{7}{10} + frac{2}{15} = ?
  5. frac{5}{9} + frac{2}{4} = ?

Subtraction Problems

  1. frac{5}{8} – frac{2}{6} = ?
  2. frac{7}{12} – frac{3}{5} = ?
  3. frac{9}{10} – frac{1}{4} = ?
  4. frac{6}{11} – frac{2}{7} = ?
  5. frac{3}{5} – frac{1}{8} = ?

5. Word Problems on Addition and Subtraction of Unlike Fractions

Question 1: Baking Recipe

Sarah is baking a cake. She uses ** frac{3}{4} cup of sugar** and later adds ** frac{1}{3} cup more**. How much sugar does she use in total?

Solution:

  • LCD of 4 and 3 is 12.
  • Convert the fractions:
    • frac{3}{4} = frac{9}{12}
    • frac{1}{3} = frac{4}{12}
  • Add the numerators:
    • $9 + 4 = 13$
  • Final Answer: ** frac{13}{12} = 1 frac{1}{12} ** cups of sugar.

Question 2: Distance Travelled

James walks ** frac{5}{6} miles** in the morning and ** frac{1}{4} miles** in the evening. How much does he walk in total?

Solution:

  • LCD of 6 and 4 is 12.
  • Convert the fractions:
    • frac{5}{6} = frac{10}{12}
    • frac{1}{4} = frac{3}{12}
  • Add the numerators:
    • $10 + 3 = 13$
  • Final Answer: ** frac{13}{12} = 1 frac{1}{12} ** miles.

Question 3: Water in a Tank

A tank contains ** frac{7}{9} ** of its capacity filled with water. After using ** frac{2}{5} ** of it, how much water remains?

Solution:

  • LCD of 9 and 5 is 45.
  • Convert the fractions:
    • frac{7}{9} = frac{35}{45}
    • frac{2}{5} = frac{18}{45}
  • Subtract the numerators:
    • $35 – 18 = 17$
  • Final Answer: ** frac{17}{45} ** of the tank remains full.

6. Common Mistakes When Adding and Subtracting Unlike Fractions

  1. Not finding the correct LCD – Using the wrong denominator leads to incorrect answers.
  2. Forgetting to adjust numerators – Both fractions must be adjusted before adding or subtracting.
  3. Not simplifying the final answer – Always check if the fraction can be simplified.
  4. Confusing addition and subtraction – Always double-check the operation being performed.

Adding and subtracting unlike fractions requires finding a common denominator before performing calculations. By following the correct steps and practicing regularly, students can master these concepts easily.

With the provided questions, answers, and word problems, learners can strengthen their understanding and improve their problem-solving skills in fraction operations.