Math Problem Statement

Solve exercises involving the addition, subtraction, and comparison of fractions with different denominators, as well as mixed numbers.

Solution

The image you uploaded contains a set of exercises on fractions. Let's break it down step by step.

Exercise Breakdown:

  1. Exercise 1: Convert the fractions so they have the same denominator before performing the operation. This includes fractions like 13+78\frac{1}{3} + \frac{7}{8}.

  2. Exercise 2: Similar to the first exercise, find the least common denominator (LCD) and solve the addition and subtraction of fractions.

  3. Exercise 3: This exercise involves mixed numbers and simplifying them before performing the operations.

  4. Exercise 4: Identify which fractions should be added together to get the indicated sum.

  5. Exercise 5: Find which fraction needs to be subtracted from another to achieve a given difference.

  6. Exercise 6: a) Combine the total amounts of paint from different buckets. b) After using some of the paint, calculate how much is left.

  7. Exercise 7: Calculate the proportion of students who walked during a sports day event based on the fractions provided for other activities.

Would you like me to walk through the solutions to each of these problems step by step? Let me know if you need detailed solutions for specific exercises or explanations!

Follow-up Questions:

  1. How do you find the least common denominator between two fractions?
  2. What is the process to add or subtract fractions with different denominators?
  3. How do you convert mixed numbers into improper fractions for calculation?
  4. What are some tips for simplifying fractions after an operation?
  5. How can you solve word problems involving fractions, like in exercise 6 and 7?

Tip:

Always simplify your fractions at the end of any operation to get the simplest form of the answer.

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Math Problem Analysis

Mathematical Concepts

Fractions
Least Common Denominator (LCD)
Addition of Fractions
Subtraction of Fractions
Mixed Numbers

Formulas

LCD formula to find common denominators
Improper fraction conversion
Addition: a/b + c/d = (a*d + b*c) / (b*d)
Subtraction: a/b - c/d = (a*d - b*c) / (b*d)

Theorems

Least Common Denominator
Fraction Simplification

Suitable Grade Level

Grades 4-6