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2026-01-01
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<p>Last updated on<strong>October 28, 2025</strong></p>
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<p>Last updated on<strong>October 28, 2025</strong></p>
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<p>The subtraction property of equality states that if two expressions are equal, subtracting the same value from both sides preserves the equality. If a = b, then subtracting the same quantity c from both sides results in a-c = b-c. This principle is fundamental in the process of solving equations.</p>
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<p>The subtraction property of equality states that if two expressions are equal, subtracting the same value from both sides preserves the equality. If a = b, then subtracting the same quantity c from both sides results in a-c = b-c. This principle is fundamental in the process of solving equations.</p>
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<h2>What is the Subtraction Property of Equality</h2>
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<h2>What is the Subtraction Property of Equality</h2>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<h2>Subtraction Property of Equality Formula</h2>
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<h2>Subtraction Property of Equality Formula</h2>
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<p>The subtraction property of equality shows that when you subtract the same<a></a><a>number</a>from both sides of an equation, it stays equal.</p>
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<p>The subtraction property of equality shows that when you subtract the same<a></a><a>number</a>from both sides of an equation, it stays equal.</p>
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<p>If \(x = y\), then subtracting a<a>real number</a>c gives: \(x - c = y - c\).</p>
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<p>If \(x = y\), then subtracting a<a>real number</a>c gives: \(x - c = y - c\).</p>
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<p>Let’s say \(x = y\), and both are equal to 10. Let \(c = 4\). \(x - c = 10 - 4 = 6\) \(y - c = 10 - 4 = 6\)</p>
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<p>Let’s say \(x = y\), and both are equal to 10. Let \(c = 4\). \(x - c = 10 - 4 = 6\) \(y - c = 10 - 4 = 6\)</p>
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<p>Since \(x = y\), subtracting the same number yields the same result: \(x - c = y - c = 6\)</p>
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<p>Since \(x = y\), subtracting the same number yields the same result: \(x - c = y - c = 6\)</p>
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<h2>Verification of Subtraction Property of Equality</h2>
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<h2>Verification of Subtraction Property of Equality</h2>
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<p>Let us check the subtraction property of equality using a few examples now that we are aware of it.</p>
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<p>Let us check the subtraction property of equality using a few examples now that we are aware of it.</p>
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<p>We know that arithmetically, \(12 + 8 = 20\). Subtracting 5 from each side of the equation.</p>
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<p>We know that arithmetically, \(12 + 8 = 20\). Subtracting 5 from each side of the equation.</p>
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<p>Now, we have: \(12 + 8 - 5 = 20 - 5\) \(⇒ 15 = 15\)</p>
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<p>Now, we have: \(12 + 8 - 5 = 20 - 5\) \(⇒ 15 = 15\)</p>
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<p>This shows when the same number is subtracted from both the sides of an equation, but the equality still holds.</p>
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<p>This shows when the same number is subtracted from both the sides of an equation, but the equality still holds.</p>
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<p>Now, let’s take another example to understand the application of the property.</p>
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<p>Now, let’s take another example to understand the application of the property.</p>
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<p>Let’s consider an<a>algebraic equation</a> \( x + 4 = 40\).</p>
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<p>Let’s consider an<a>algebraic equation</a> \( x + 4 = 40\).</p>
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<p>Now, to find the value of x, we need to subtract 4 from both the sides of the equation. So, we have: x + 4 = 40 ⇒ x + 4 - 4 = 40 - 4 ⇒ x = 36</p>
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<p>Now, to find the value of x, we need to subtract 4 from both the sides of the equation. So, we have: x + 4 = 40 ⇒ x + 4 - 4 = 40 - 4 ⇒ x = 36</p>
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<p>So, solving the<a>algebraic equations</a>is one of the important applications of the subtraction property of equality. </p>
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<p>So, solving the<a>algebraic equations</a>is one of the important applications of the subtraction property of equality. </p>
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<h2>Subtraction Property of Equality, Including Fractions.</h2>
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<h2>Subtraction Property of Equality, Including Fractions.</h2>
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<p>We will now apply the subtraction property of equality to equations involving<a></a><a>fractions</a>, since we are familiar with the idea.</p>
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<p>We will now apply the subtraction property of equality to equations involving<a></a><a>fractions</a>, since we are familiar with the idea.</p>
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<p>Now, find the following equation,\(\frac {a}{b} = \frac{x}{y}\). The equation remains balanced when the same fraction \(\frac{c}{d}\) is subtracted from both sides.</p>
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<p>Now, find the following equation,\(\frac {a}{b} = \frac{x}{y}\). The equation remains balanced when the same fraction \(\frac{c}{d}\) is subtracted from both sides.</p>
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<p>\(\frac{a } {b} = \frac{x}{ y}\)</p>
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<p>\(\frac{a } {b} = \frac{x}{ y}\)</p>
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<p>⇒ \(\frac{a}{b} - \frac{c} {d} = \frac{x}{y} - \frac{c}{d}\)</p>
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<p>⇒ \(\frac{a}{b} - \frac{c} {d} = \frac{x}{y} - \frac{c}{d}\)</p>
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<p>Thus, the subtraction property of equality works the same way for fractions and in<a></a><a>geometry</a>as well.</p>
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<p>Thus, the subtraction property of equality works the same way for fractions and in<a></a><a>geometry</a>as well.</p>
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<h2>Tips and Tricks to Master Subtraction Property of Equality</h2>
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<h2>Tips and Tricks to Master Subtraction Property of Equality</h2>
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<p>The subtraction property of equality is a key tool in solving equations. Here are some simple tips and tricks for students to master the subtraction property of equality. </p>
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<p>The subtraction property of equality is a key tool in solving equations. Here are some simple tips and tricks for students to master the subtraction property of equality. </p>
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<ul><li><strong>Always subtract from both sides: </strong>A common mistake is subtracting from only one side of the equation. To keep things valid, remember: whatever you do to one side, you must do to the other.</li>
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<ul><li><strong>Always subtract from both sides: </strong>A common mistake is subtracting from only one side of the equation. To keep things valid, remember: whatever you do to one side, you must do to the other.</li>
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<li><strong>Identify the<a>constant</a>you need to subtract: </strong>Look at the equation and spot the<a>term</a>that is added (or sometimes subtracted) that you need to remove to isolate the<a>variable</a>. For example, \(x +4=40\), you subtract 4 from both sides.</li>
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<li><strong>Identify the<a>constant</a>you need to subtract: </strong>Look at the equation and spot the<a>term</a>that is added (or sometimes subtracted) that you need to remove to isolate the<a>variable</a>. For example, \(x +4=40\), you subtract 4 from both sides.</li>
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<li><strong>Keep track of signs: </strong>When subtracting, especially with negatives in the equation, be very careful. For example, with \(x-3=-5\), you add 3 to both sides, which is equivalent to subtract -3, to get \(x=-2\).</li>
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<li><strong>Keep track of signs: </strong>When subtracting, especially with negatives in the equation, be very careful. For example, with \(x-3=-5\), you add 3 to both sides, which is equivalent to subtract -3, to get \(x=-2\).</li>
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<li><strong>Simplify after you subtract:</strong> Once you perform the subtraction on both sides, simplify each side fully so you clearly see the isolated variable. If you skip simplification, you might misread the answer.</li>
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<li><strong>Simplify after you subtract:</strong> Once you perform the subtraction on both sides, simplify each side fully so you clearly see the isolated variable. If you skip simplification, you might misread the answer.</li>
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<li><strong>Use it with fractions or complex<a>expressions</a>too:</strong> The property applies not just to simple whole-number equations, but also when fractions or composite expressions are involved: if \(\frac{a}{b}=\frac{x}{y}\), then subtracting the same fraction from both sides yields a valid equation. </li>
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<li><strong>Use it with fractions or complex<a>expressions</a>too:</strong> The property applies not just to simple whole-number equations, but also when fractions or composite expressions are involved: if \(\frac{a}{b}=\frac{x}{y}\), then subtracting the same fraction from both sides yields a valid equation. </li>
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</ul><h2>Common Mistakes of the Subtraction Property of Equality And How to Avoid Them</h2>
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</ul><h2>Common Mistakes of the Subtraction Property of Equality And How to Avoid Them</h2>
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<p>The subtraction property of equality can be a difficult concept to understand for some students, leading to mistakes. In this section, we will look at some common mistakes and ways to avoid them. </p>
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<p>The subtraction property of equality can be a difficult concept to understand for some students, leading to mistakes. In this section, we will look at some common mistakes and ways to avoid them. </p>
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<h2>Real-Life Applications of the Subtraction Property of Equality</h2>
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<h2>Real-Life Applications of the Subtraction Property of Equality</h2>
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<p>The subtraction property of equality shows an equation stays balanced. Let us see some real-life examples of the subtraction property of equality. </p>
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<p>The subtraction property of equality shows an equation stays balanced. Let us see some real-life examples of the subtraction property of equality. </p>
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<ul><li><strong>Nature:</strong>If there are 50 birds in a tree and 20 fly away, we subtract to find how many are left: 50 - 20 = 30 birds remaining. </li>
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<ul><li><strong>Nature:</strong>If there are 50 birds in a tree and 20 fly away, we subtract to find how many are left: 50 - 20 = 30 birds remaining. </li>
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</ul><ul><li><strong>Architecture:</strong>To determine the usable floor space, subtract the thickness of the walls from the total building area. </li>
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</ul><ul><li><strong>Architecture:</strong>To determine the usable floor space, subtract the thickness of the walls from the total building area. </li>
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</ul><ul><li><strong>Biology:</strong>To calculate a temperature difference, subtract the normal body temperature from the current reading. For example, 101°F - 98.6°F = 2.4°F above normal. </li>
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</ul><ul><li><strong>Biology:</strong>To calculate a temperature difference, subtract the normal body temperature from the current reading. For example, 101°F - 98.6°F = 2.4°F above normal. </li>
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</ul><ul><li><strong>Art and Design:</strong>When adjusting<a>proportions</a>in a design, subtract unwanted elements. For example, excess measurements or dimensions to refine the final layout.</li>
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</ul><ul><li><strong>Art and Design:</strong>When adjusting<a>proportions</a>in a design, subtract unwanted elements. For example, excess measurements or dimensions to refine the final layout.</li>
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</ul><ul><li><strong>Cooking:</strong>If a recipe calls for 5 grams of salt and 2 grams are already added, subtract 2 from 5 to know how much more to add: 5 - 2 = 3 grams. </li>
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</ul><ul><li><strong>Cooking:</strong>If a recipe calls for 5 grams of salt and 2 grams are already added, subtract 2 from 5 to know how much more to add: 5 - 2 = 3 grams. </li>
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</ul><h3>Problem 1</h3>
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</ul><h3>Problem 1</h3>
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<p>x + 7 = 12</p>
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<p>x + 7 = 12</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>x = 5 </p>
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<p>x = 5 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We must subtract the same number from both sides to solve the equation correctly.</p>
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<p>We must subtract the same number from both sides to solve the equation correctly.</p>
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<p>we have, \(x+7=12\)</p>
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<p>we have, \(x+7=12\)</p>
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<p>we can subtract the same number from both sides. </p>
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<p>we can subtract the same number from both sides. </p>
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<p>\(x +7-7=12-7\)</p>
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<p>\(x +7-7=12-7\)</p>
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<p>\(x =5\) </p>
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<p>\(x =5\) </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A fish tank had 18 fish. After removing 10 fish, how many fish are left?</p>
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<p>A fish tank had 18 fish. After removing 10 fish, how many fish are left?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The number is 8. </p>
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<p>The number is 8. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Subtracting 10 from 18 gives the answer 8. </p>
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<p>Subtracting 10 from 18 gives the answer 8. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Jay added 4 to a number and got 9. What was the number?</p>
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<p>Jay added 4 to a number and got 9. What was the number?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> The number was 5.</p>
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<p> The number was 5.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> Subtracting 4 from 9 gives the result 5. </p>
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<p> Subtracting 4 from 9 gives the result 5. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>A student had a number, and when he added 6, the total became 15. What was his starting number?</p>
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<p>A student had a number, and when he added 6, the total became 15. What was his starting number?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The number was 9. </p>
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<p>The number was 9. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> We need to subtract 6 from 15, our answer will be 9. </p>
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<p> We need to subtract 6 from 15, our answer will be 9. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>A number and 12 together become 25. What is the number?</p>
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<p>A number and 12 together become 25. What is the number?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The number is 13. </p>
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<p>The number is 13. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Given \(x + 12 = 25\). Subtract 12 from both sides. So, \(x + 12 - 12 = 25 - 12\) \(x = 13\) </p>
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<p>Given \(x + 12 = 25\). Subtract 12 from both sides. So, \(x + 12 - 12 = 25 - 12\) \(x = 13\) </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs of the Subtraction Property of Equality</h2>
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<h2>FAQs of the Subtraction Property of Equality</h2>
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<h3>1.What is the subtraction property of equality?</h3>
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<h3>1.What is the subtraction property of equality?</h3>
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<p>The Subtraction property of equality states that subtracting the same number from both the sides of an equation and it does not change the equality. </p>
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<p>The Subtraction property of equality states that subtracting the same number from both the sides of an equation and it does not change the equality. </p>
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<h3>2.How to use the subtraction property to solve equations?</h3>
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<h3>2.How to use the subtraction property to solve equations?</h3>
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<p> We use this property to subtract the same numbers from both sides of an equation to solve the variable. For example, in x + 5 = 10, subtracting 5 from both sides gives x = 5. </p>
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<p> We use this property to subtract the same numbers from both sides of an equation to solve the variable. For example, in x + 5 = 10, subtracting 5 from both sides gives x = 5. </p>
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<h3>3. What is the difference between subtraction and the subtraction property of equality?</h3>
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<h3>3. What is the difference between subtraction and the subtraction property of equality?</h3>
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<p>Subtraction usually means taking away, but in equations, the subtraction property of equality is a rule that keeps both sides balanced when we subtract the same value. </p>
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<p>Subtraction usually means taking away, but in equations, the subtraction property of equality is a rule that keeps both sides balanced when we subtract the same value. </p>
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<h3>4. Can this property work with negative numbers?</h3>
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<h3>4. Can this property work with negative numbers?</h3>
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<h3>5. What happens when we forget to subtract from both sides?</h3>
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<h3>5. What happens when we forget to subtract from both sides?</h3>
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<p> If we don’t subtract the same value from both sides, the solution will be incorrect. </p>
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<p> If we don’t subtract the same value from both sides, the solution will be incorrect. </p>
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<h3>6.Why is the subtraction property of equality useful when solving equations?</h3>
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<h3>6.Why is the subtraction property of equality useful when solving equations?</h3>
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<ul><li>It helps isolate the unknown (variable) by undoing addition (or later, subtraction) so the equation remains balanced. </li>
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<ul><li>It helps isolate the unknown (variable) by undoing addition (or later, subtraction) so the equation remains balanced. </li>
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<li>It ensures that the solution is valid because you’re preserving equality. </li>
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<li>It ensures that the solution is valid because you’re preserving equality. </li>
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<li>For younger learners, it helps to clarify the idea of keeping balance in an equation, like a scale: if you remove weight from one side, you must remove the same from the other.</li>
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<li>For younger learners, it helps to clarify the idea of keeping balance in an equation, like a scale: if you remove weight from one side, you must remove the same from the other.</li>
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</ul><h3>7.Why should parents teach the subtraction property of equality to their children?</h3>
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</ul><h3>7.Why should parents teach the subtraction property of equality to their children?</h3>
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<p>Parents should teach the Subtraction Property of Equality because it forms a vital foundation for<a>understanding algebra</a>and logical reasoning. This property helps children grasp the idea that an equation works like a balanced scale, when you subtract the same value from both sides, the balance remains unchanged.</p>
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<p>Parents should teach the Subtraction Property of Equality because it forms a vital foundation for<a>understanding algebra</a>and logical reasoning. This property helps children grasp the idea that an equation works like a balanced scale, when you subtract the same value from both sides, the balance remains unchanged.</p>
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