# Adding and Subtracting Fractions With Like Denominators
Section A: Multiple Choice Questions
Q1: What is \(\frac{2}{5} + \frac{1}{5}\)? (a) \(\frac{3}{10}\) (b) \(\frac{3}{5}\) (c) \(\frac{2}{5}\) (d) \(\frac{1}{5}\)
Solution:
Ans: (b) Explanation: When adding fractions with the same denominator, we add the numerators and keep the denominator the same. So \(\frac{2}{5} + \frac{1}{5} = \frac{2+1}{5} = \frac{3}{5}\). Option (a) is incorrect because it changes the denominator. Options (c) and (d) do not show addition.
Q2: What is \(\frac{7}{8} - \frac{3}{8}\)? (a) \(\frac{4}{0}\) (b) \(\frac{10}{8}\) (c) \(\frac{4}{8}\) (d) \(\frac{4}{16}\)
Solution:
Ans: (c) Explanation: When subtracting fractions with the same denominator, we subtract the numerators and keep the denominator the same. So \(\frac{7}{8} - \frac{3}{8} = \frac{7-3}{8} = \frac{4}{8}\). Option (a) is incorrect because we cannot have 0 in the denominator. Option (b) shows addition instead of subtraction. Option (d) incorrectly multiplies the denominators.
Q3: Which fraction is in simplest form? (a) \(\frac{4}{8}\) (b) \(\frac{6}{10}\) (c) \(\frac{3}{7}\) (d) \(\frac{2}{6}\)
Solution:
Ans: (c) Explanation: A fraction is in simplest form when the numerator and denominator have no common factors other than 1. \(\frac{3}{7}\) cannot be simplified further. Option (a) simplifies to \(\frac{1}{2}\), option (b) simplifies to \(\frac{3}{5}\), and option (d) simplifies to \(\frac{1}{3}\).
Q4: What is \(\frac{5}{6} + \frac{1}{6}\)? (a) \(\frac{6}{6}\) (b) \(\frac{5}{12}\) (c) \(\frac{6}{12}\) (d) \(\frac{4}{6}\)
Solution:
Ans: (a) Explanation: Adding fractions with like denominators: \(\frac{5}{6} + \frac{1}{6} = \frac{5+1}{6} = \frac{6}{6}\), which equals 1 whole. Option (b) and (c) incorrectly change the denominator to 12. Option (d) shows subtraction instead of addition.
Ans: (a) Explanation: Subtracting the numerators: \(9 - 4 = 5\), and keeping the denominator the same gives \(\frac{5}{10}\). Option (b) shows addition instead of subtraction. Option (c) has an impossible denominator of 0. Option (d) incorrectly multiplies denominators.
Q6: What is \(\frac{3}{12} + \frac{5}{12}\) in simplest form? (a) \(\frac{8}{12}\) (b) \(\frac{2}{3}\) (c) \(\frac{8}{24}\) (d) \(\frac{4}{6}\)
Solution:
Ans: (b) Explanation: First add: \(\frac{3}{12} + \frac{5}{12} = \frac{8}{12}\). Then simplify by dividing both numerator and denominator by their greatest common factor of 4: \(\frac{8÷4}{12÷4} = \frac{2}{3}\). Option (a) is correct but not in simplest form. Options (c) and (d) are incorrect calculations.
Q7: What is \(\frac{11}{12} - \frac{7}{12}\)? (a) \(\frac{18}{12}\) (b) \(\frac{4}{12}\) (c) \(\frac{4}{24}\) (d) \(\frac{5}{12}\)
Solution:
Ans: (b) Explanation: Subtract the numerators: \(11 - 7 = 4\), and keep the denominator: \(\frac{4}{12}\). Option (a) shows addition. Option (c) incorrectly multiplies denominators. Option (d) has an incorrect numerator calculation.
Q8: Maria has \(\frac{7}{8}\) of a pizza. She eats \(\frac{2}{8}\) of it. How much pizza does she have left? (a) \(\frac{9}{8}\) (b) \(\frac{5}{8}\) (c) \(\frac{9}{16}\) (d) \(\frac{5}{16}\)
Solution:
Ans: (b) Explanation: This is a subtraction problem: \(\frac{7}{8} - \frac{2}{8} = \frac{5}{8}\). Option (a) shows addition. Options (c) and (d) incorrectly change the denominator to 16.
Section B: Fill in the Blanks
Q9: When adding fractions with the same denominator, we add the __________ and keep the denominator the same.
Solution:
Ans: numerators Explanation: In fractions with like denominators, only the numerators (top numbers) are added while the denominator (bottom number) stays the same.
Q10: The fraction \(\frac{6}{6}\) is equal to the whole number __________.
Solution:
Ans: 1 Explanation: When the numerator and denominator are the same, the fraction equals 1 whole because you have all the parts that make up one complete unit.
Ans: 6 Explanation: Add the numerators: \(4 + 2 = 6\). The denominator remains 9, so the answer is \(\frac{6}{9}\).
Q12: The simplified form of \(\frac{6}{8}\) is __________.
Solution:
Ans: \(\frac{3}{4}\) Explanation: To simplify, divide both the numerator and denominator by their greatest common factor, which is 2: \(\frac{6÷2}{8÷2} = \frac{3}{4}\).
Ans: 7 Explanation: Subtract the numerators: \(10 - 3 = 7\). The denominator stays as 11, giving \(\frac{7}{11}\).
Q14: Fractions that have the same denominator are called fractions with __________ denominators.
Solution:
Ans: like (or common) Explanation: When fractions share the same denominator, they are called fractions with like denominators or common denominators, which makes them easier to add or subtract.
Section C: Word Problems
Q15: Sarah walked \(\frac{2}{7}\) of a mile to school and then \(\frac{3}{7}\) of a mile to the library. How many miles did she walk in total?
Q16: Tom had \(\frac{9}{10}\) of a candy bar. He gave \(\frac{4}{10}\) of the candy bar to his friend. What fraction of the candy bar does Tom have left?
Solution:
Ans: \(\frac{9}{10} - \frac{4}{10} = \frac{9-4}{10} = \frac{5}{10}\) Simplified: \(\frac{5}{10} = \frac{1}{2}\) Final Answer: \(\frac{5}{10}\) or \(\frac{1}{2}\) of the candy bar
Q17: Emma drank \(\frac{3}{8}\) of a gallon of water in the morning and \(\frac{2}{8}\) of a gallon in the afternoon. How much water did she drink altogether?
Q18: A recipe calls for \(\frac{5}{6}\) cup of flour. Jason has already added \(\frac{2}{6}\) cup of flour. How much more flour does he need to add?
Solution:
Ans: \(\frac{5}{6} - \frac{2}{6} = \frac{5-2}{6} = \frac{3}{6}\) Simplified: \(\frac{3}{6} = \frac{1}{2}\) Final Answer: \(\frac{3}{6}\) or \(\frac{1}{2}\) cup
Q19: Lisa colored \(\frac{4}{12}\) of a drawing on Monday and \(\frac{5}{12}\) of the drawing on Tuesday. What fraction of the drawing has she colored so far? Write your answer in simplest form.
Solution:
Ans: \(\frac{4}{12} + \frac{5}{12} = \frac{4+5}{12} = \frac{9}{12}\) Simplified: \(\frac{9÷3}{12÷3} = \frac{3}{4}\) Final Answer: \(\frac{3}{4}\) of the drawing
Q20: A bucket was \(\frac{11}{12}\) full of water. David used \(\frac{7}{12}\) of the bucket for watering plants. What fraction of the bucket still has water?
Solution:
Ans: \(\frac{11}{12} - \frac{7}{12} = \frac{11-7}{12} = \frac{4}{12}\) Simplified: \(\frac{4÷4}{12÷4} = \frac{1}{3}\) Final Answer: \(\frac{4}{12}\) or \(\frac{1}{3}\) of the bucket
The document Worksheet (with Solutions): Adding and Subtracting Fractions With Like Denominators is a part of the Grade 4 Course Math Grade 4.
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