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Original
2026-01-01
Modified
2026-02-28
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<p>Let’s understand these steps with the help of an example:</p>
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<p>Let’s understand these steps with the help of an example:</p>
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<p><strong>Adding 2 Fractions with Different Denominators</strong></p>
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<p><strong>Adding 2 Fractions with Different Denominators</strong></p>
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<p>To add 2 fractions with different denominators, we use the same steps as discussed:</p>
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<p>To add 2 fractions with different denominators, we use the same steps as discussed:</p>
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<p>Add 3/4 + 5/8</p>
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<p>Add 3/4 + 5/8</p>
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<p>Solution: </p>
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<p>Solution: </p>
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<p><strong>Step 1:</strong>We first find the LCM of 4 and 8:</p>
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<p><strong>Step 1:</strong>We first find the LCM of 4 and 8:</p>
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<ul><li> LCM = 8</li>
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<ul><li> LCM = 8</li>
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</ul><p><strong>Step 2: </strong>Now, we make the denominators equal by converting them to 8:</p>
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</ul><p><strong>Step 2: </strong>Now, we make the denominators equal by converting them to 8:</p>
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<ul><li>Since 5/8 already has 8 as the denominator, we will only convert the denominator of 3/4. </li>
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<ul><li>Since 5/8 already has 8 as the denominator, we will only convert the denominator of 3/4. </li>
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</ul><p><strong>Step 3: </strong>Determine what, when multiplied by 4, gives 8.</p>
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</ul><p><strong>Step 3: </strong>Determine what, when multiplied by 4, gives 8.</p>
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<p><strong>Step 4:</strong>Multiply by 2 with both the numerator and denominator, resulting 6/8.</p>
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<p><strong>Step 4:</strong>Multiply by 2 with both the numerator and denominator, resulting 6/8.</p>
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<p><strong>Step 5: </strong>Now add the numerators, since the denominators are the same. </p>
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<p><strong>Step 5: </strong>Now add the numerators, since the denominators are the same. </p>
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<ul><li>3/4 + 5/8 = 6/8 + 5/8 = (6 + 5) / 8 = 11/8.</li>
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<ul><li>3/4 + 5/8 = 6/8 + 5/8 = (6 + 5) / 8 = 11/8.</li>
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</ul><p>We can express it as a<a>mixed fraction</a>of \(1^3/_8\).</p>
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</ul><p>We can express it as a<a>mixed fraction</a>of \(1^3/_8\).</p>
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<p><strong>Adding 3 Fractions with Different Denominators</strong></p>
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<p><strong>Adding 3 Fractions with Different Denominators</strong></p>
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<p>Similarly, we add three fractions with different denominators:</p>
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<p>Similarly, we add three fractions with different denominators:</p>
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<p>Add 2/3 + 4/7 + 5/7</p>
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<p>Add 2/3 + 4/7 + 5/7</p>
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<p>Solution: </p>
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<p>Solution: </p>
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<p><strong>Step1:</strong>The LCM of 3 and 7 is 21</p>
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<p><strong>Step1:</strong>The LCM of 3 and 7 is 21</p>
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<p><strong>Step 2:</strong>Now, we will multiply the fractions by appropriate factors that give 21 as the denominator:</p>
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<p><strong>Step 2:</strong>Now, we will multiply the fractions by appropriate factors that give 21 as the denominator:</p>
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<ul><li>2/3 → (2 × 7)/ (3 × 7) = 14/21</li>
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<ul><li>2/3 → (2 × 7)/ (3 × 7) = 14/21</li>
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</ul><ul><li>4/7 → (4 × 3) / (7 × 3) = 12/21</li>
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</ul><ul><li>4/7 → (4 × 3) / (7 × 3) = 12/21</li>
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</ul><ul><li>5/7 → (5 × 3) / (7 × 3) = 15/21</li>
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</ul><ul><li>5/7 → (5 × 3) / (7 × 3) = 15/21</li>
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</ul><p><strong>Step 3:</strong>Add the numerators:</p>
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</ul><p><strong>Step 3:</strong>Add the numerators:</p>
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<ul><li>(14 + 12 + 15) / 21 = 41/21</li>
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<ul><li>(14 + 12 + 15) / 21 = 41/21</li>
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</ul><p><strong>Step 4:</strong>Convert to a mixed fraction:</p>
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</ul><p><strong>Step 4:</strong>Convert to a mixed fraction:</p>
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<ul><li>41/21 = \(1^{20}/_{21}\)</li>
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<ul><li>41/21 = \(1^{20}/_{21}\)</li>
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</ul><p><strong>Adding Mixed Fractions with Unlike Denominators</strong></p>
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</ul><p><strong>Adding Mixed Fractions with Unlike Denominators</strong></p>
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<p>Before<a>adding mixed fractions</a>, we must convert them into<a>improper fractions</a>and follow similar steps. Let’s look at the steps involved using an example:</p>
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<p>Before<a>adding mixed fractions</a>, we must convert them into<a>improper fractions</a>and follow similar steps. Let’s look at the steps involved using an example:</p>
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<p>Add \(3^{2}/_{5}\) and \(2^{3}/_{4}\)</p>
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<p>Add \(3^{2}/_{5}\) and \(2^{3}/_{4}\)</p>
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<p><strong>Step 1:</strong>Convert into improper fractions:</p>
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<p><strong>Step 1:</strong>Convert into improper fractions:</p>
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<p>\(3^{2}/_{5}\) = (3 × 5 + 2) /5 = 17/5</p>
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<p>\(3^{2}/_{5}\) = (3 × 5 + 2) /5 = 17/5</p>
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<p>\(2^{3}/_{4}\) = (2 × 4 + 3)/4 = 11/4</p>
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<p>\(2^{3}/_{4}\) = (2 × 4 + 3)/4 = 11/4</p>
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<p>LCM of 4 and 5 is 20</p>
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<p>LCM of 4 and 5 is 20</p>
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<p><strong>Step 2:</strong>Now, convert the fractions to have the same denominator, 20</p>
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<p><strong>Step 2:</strong>Now, convert the fractions to have the same denominator, 20</p>
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<p>17/5 = (17 × 4) / (5 × 4) = 68/20</p>
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<p>17/5 = (17 × 4) / (5 × 4) = 68/20</p>
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<p>11/4 = (11 × 5)/ (4 × 5) = 55/20</p>
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<p>11/4 = (11 × 5)/ (4 × 5) = 55/20</p>
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<p><strong>Step 3:</strong>Add the numerators:</p>
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<p><strong>Step 3:</strong>Add the numerators:</p>
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<p>(68 + 55)/ 20 = 123/20</p>
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<p>(68 + 55)/ 20 = 123/20</p>
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<p><strong>Step 4:</strong>Convert to a mixed fraction:</p>
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<p><strong>Step 4:</strong>Convert to a mixed fraction:</p>
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<p>123/20 = \(6^{3}/_{20}\)</p>
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<p>123/20 = \(6^{3}/_{20}\)</p>
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