How to Balance the Scales: Inequalities with Addition and Subtraction of Mixed Numbers
Mixed numbers, which consist of a whole number and a fraction, often appear in real-world scenarios.

When dealing with inequalities involving mixed numbers, understanding the impact of addition and subtraction is essential. In this guide, we’ll explore the intricacies of inequalities when adding or subtracting mixed numbers.
Step-by-step Guide:
1. Basics of Inequalities:
Inequalities use symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) to compare two values.
2. Understanding Mixed Numbers:
A mixed number is a combination of a whole number and a fraction. For instance, 213 is a mixed number.
3. Impact of Addition on Inequalities:
When you add the same mixed number to both sides of an inequality, the relationship between the two sides remains unchanged.
Example: If a>b, then a+c>b+c for any mixed number c.
4. Impact of Subtraction on Inequalities:
Similarly, when you subtract the same mixed number from both sides of an inequality, the relationship remains unchanged.
Example: If a<b, then a–c<b–c for any mixed number c.
5. Working with Mixed Numbers:
When adding or subtracting mixed numbers in inequalities:
– First, perform the operation on the whole numbers.
– Then, perform the operation on the fractions. If necessary, find a common denominator for the fractions.
Example 1:
Given 314<412, what happens when we add 134 to both sides?
Solution:
Adding 134 to both sides:
314+134<412+134
5<614
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Example 2:
Given 523>413, what is the result when we subtract 213 from both sides?
Solution:
Subtracting 213 from both sides:
523–213>413–213
313>2
Practice Questions:
1. If 435>325, what is the inequality after adding 215 to both sides?
2. Given 647<737, what happens when we subtract 327 from both sides?
3. If 818>738, what is the result when we add 128 to both sides?
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Answers:
1. 645>535
2. 327<417
3. 938>858
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