Question
3.) \( 4 \frac{3}{4}-3 \frac{2}{3} \) 4.) \( 5 \frac{3}{6}-\frac{2}{3} \) 5) \( 3-2 \frac{3}{5} \)
Ask by Mcguire Greene. in the Philippines
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
3.) \( 4 \frac{3}{4} - 3 \frac{2}{3} = 1 \frac{1}{12} \)
4.) \( 5 \frac{3}{6} - \frac{2}{3} = 4 \frac{5}{6} \)
5.) \( 3 - 2 \frac{3}{5} = \frac{2}{5} \)
Solution
Sure, let's solve each of these subtraction problems involving mixed numbers step by step.
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### **3.) \( 4 \frac{3}{4} - 3 \frac{2}{3} \)**
**Step 1: Convert Mixed Numbers to Improper Fractions**
- \( 4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \)
- \( 3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \)
**Step 2: Find a Common Denominator**
The least common denominator (LCD) for 4 and 3 is 12.
- \( \frac{19}{4} = \frac{19 \times 3}{4 \times 3} = \frac{57}{12} \)
- \( \frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12} \)
**Step 3: Subtract the Fractions**
- \( \frac{57}{12} - \frac{44}{12} = \frac{13}{12} \)
**Step 4: Convert Back to a Mixed Number**
- \( \frac{13}{12} = 1 \frac{1}{12} \)
**Final Answer:**
\( 4 \frac{3}{4} - 3 \frac{2}{3} = 1 \frac{1}{12} \)
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### **4.) \( 5 \frac{3}{6} - \frac{2}{3} \)**
**Step 1: Simplify the Mixed Number**
- \( 5 \frac{3}{6} = 5 \frac{1}{2} \) (since \( \frac{3}{6} = \frac{1}{2} \))
**Step 2: Convert to Improper Fractions**
- \( 5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \)
- \( \frac{2}{3} \) remains the same.
**Step 3: Find a Common Denominator**
The LCD for 2 and 3 is 6.
- \( \frac{11}{2} = \frac{11 \times 3}{2 \times 3} = \frac{33}{6} \)
- \( \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \)
**Step 4: Subtract the Fractions**
- \( \frac{33}{6} - \frac{4}{6} = \frac{29}{6} \)
**Step 5: Convert Back to a Mixed Number**
- \( \frac{29}{6} = 4 \frac{5}{6} \)
**Final Answer:**
\( 5 \frac{3}{6} - \frac{2}{3} = 4 \frac{5}{6} \)
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### **5.) \( 3 - 2 \frac{3}{5} \)**
**Step 1: Convert to Improper Fractions**
- \( 2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5} \)
- \( 3 = \frac{15}{5} \) (to have the same denominator)
**Step 2: Subtract the Fractions**
- \( \frac{15}{5} - \frac{13}{5} = \frac{2}{5} \)
**Final Answer:**
\( 3 - 2 \frac{3}{5} = \frac{2}{5} \)
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I hope this helps! Let me know if you have any other questions.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
Let's delve into the fascinating world of fractions! Did you know that the concept of fractions dates back to ancient civilizations like the Egyptians, who used a unique system involving unit fractions? They had a quirky but practical approach for dividing whole quantities, which has influenced how we handle fractions today! When it comes to real-world applications, fractions pop up everywhere! From cooking to woodworking, understanding how to subtract fractions is essential. For example, if you’re baking and a recipe calls for 4 ¾ cups of flour but you want to make just 3 ⅔ cups, knowing how to subtract those fractions makes your kitchen endeavors deliciously successful!
