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Imagine you have 1 whole pizza and 1 slice left over. Your friend brings you 2 whole pizzas and 2 more slices!

How can we put all of our pizza together to find the total?

A **mixed number** is an amount made of a whole number and a fraction side by side, like $1\frac{1}{4}$.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Adding Mixed Numbers with Like Denominators</title>
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <script src="{{VENDOR_CDN}}/classace-diagram.js"></script>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      user-select: none;
    }
    .main-wrap {
      width: 100%;
      max-width: 540px;
      display: flex;
      flex-direction: column;
      gap: 12px;
      margin: auto 0;
    }

    /* Math Equation Display */
    .equation-bar {
      background: #ffffff;
      border-radius: 12px;
      padding: 10px 16px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      box-shadow: 0 2px 6px rgba(0,0,0,0.04);
      min-height: 54px;
    }
    .math-block {
      display: inline-flex;
      align-items: center;
      transition: opacity 0.3s ease, transform 0.3s ease;
    }
    .whole-num {
      color: #059669;
      font-weight: 700;
      transition: all 0.3s ease;
      border-radius: 6px;
      padding: 2px 4px;
    }
    .frac-num {
      color: #0284c7;
      font-weight: 700;
      transition: all 0.3s ease;
      border-radius: 6px;
      padding: 2px 4px;
    }
    .hl-whole {
      background: #d1fae5;
      box-shadow: 0 0 0 2px #10b981;
    }
    .hl-frac {
      background: #e0f2fe;
      box-shadow: 0 0 0 2px #0284c7;
    }
    .dimmed {
      opacity: 0.25;
    }

    /* Visual Models Board */
    .visual-board {
      background: #ffffff;
      border-radius: 12px;
      padding: 16px 12px;
      display: flex;
      align-items: center;
      justify-content: space-around;
      box-shadow: 0 2px 6px rgba(0,0,0,0.04);
      min-height: 180px;
      position: relative;
    }
    .term-group {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
      transition: opacity 0.3s ease;
    }
    .pies-row {
      display: flex;
      align-items: center;
      gap: 6px;
      flex-wrap: wrap;
      justify-content: center;
      max-width: 140px;
    }
    .term-label {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }
    .operator {
      font-size: 24px;
      font-weight: 700;
      color: #94a3b8;
    }

    /* Pie SVG styling */
    .pie-svg {
      width: 44px;
      height: 44px;
      transition: transform 0.3s ease, filter 0.3s ease;
    }
    .slice-empty {
      fill: #f1f5f9;
      stroke: #cbd5e1;
      stroke-width: 1.5;
    }
    .slice-whole {
      fill: #10b981;
      stroke: #059669;
      stroke-width: 1.5;
      transition: fill 0.3s ease, stroke 0.3s ease;
    }
    .slice-frac {
      fill: #0284c7;
      stroke: #0369a1;
      stroke-width: 1.5;
      transition: fill 0.3s ease, stroke 0.3s ease;
    }
    .slice-new {
      fill: #38bdf8;
      stroke: #0284c7;
      stroke-width: 1.5;
    }
    .highlight-ring {
      filter: drop-shadow(0 0 4px rgba(2, 132, 199, 0.5));
    }
    .highlight-ring-green {
      filter: drop-shadow(0 0 4px rgba(16, 185, 129, 0.5));
    }

    /* Stepper Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      flex-wrap: wrap;
    }
    .step-btn {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      color: #475569;
      padding: 6px 14px;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 6px;
      transition: background 0.2s ease, color 0.2s ease, border-color 0.2s ease;
    }
    .step-btn.active {
      background: #1e2945;
      border-color: #1e2945;
      color: #ffffff;
    }
    .play-btn {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      color: #1e2945;
      width: 34px;
      height: 34px;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      font-size: 13px;
    }
  </style>
</head>
<body>

  <div class="main-wrap">
    
    <div class="equation-bar">
      <div id="eq-term1" class="math-block"></div>
      <div class="operator">+</div>
      <div id="eq-term2" class="math-block"></div>
      <div class="operator">=</div>
      <div id="eq-result" class="math-block"></div>
    </div>

    
    <div class="visual-board">
      
      <div class="term-group" id="group-t1">
        <div class="pies-row">
          
          <svg class="pie-svg svg-whole" viewBox="0 0 40 40">
            <circle cx="20" cy="20" r="17" class="slice-whole" />
          </svg>
          
          <svg class="pie-svg svg-frac" viewBox="0 0 40 40">
            
            <path d="M 20 20 L 20 3 A 17 17 0 0 1 37 20 Z" class="slice-frac" />
            
            <path d="M 20 20 L 37 20 A 17 17 0 0 1 20 37 Z" class="slice-empty" />
            
            <path d="M 20 20 L 20 37 A 17 17 0 0 1 3 20 Z" class="slice-empty" />
            
            <path d="M 20 20 L 3 20 A 17 17 0 0 1 20 3 Z" class="slice-empty" />
          </svg>
        </div>
        <div class="term-label" id="lbl-t1">1 ¼</div>
      </div>

      <div class="operator">+</div>

      
      <div class="term-group" id="group-t2">
        <div class="pies-row">
          
          <svg class="pie-svg svg-whole" viewBox="0 0 40 40">
            <circle cx="20" cy="20" r="17" class="slice-whole" />
          </svg>
          <svg class="pie-svg svg-whole" viewBox="0 0 40 40">
            <circle cx="20" cy="20" r="17" class="slice-whole" />
          </svg>
          
          <svg class="pie-svg svg-frac" viewBox="0 0 40 40">
            
            <path d="M 20 20 L 20 3 A 17 17 0 0 1 37 20 Z" class="slice-frac" />
            
            <path d="M 20 20 L 37 20 A 17 17 0 0 1 20 37 Z" class="slice-frac" />
            
            <path d="M 20 20 L 20 37 A 17 17 0 0 1 3 20 Z" class="slice-empty" />
            
            <path d="M 20 20 L 3 20 A 17 17 0 0 1 20 3 Z" class="slice-empty" />
          </svg>
        </div>
        <div class="term-label" id="lbl-t2">2 ²⁄₄</div>
      </div>

      <div class="operator">=</div>

      
      <div class="term-group" id="group-res">
        <div class="pies-row">
          
          <svg class="pie-svg svg-whole" viewBox="0 0 40 40">
            <circle cx="20" cy="20" r="17" class="slice-whole" />
          </svg>
          <svg class="pie-svg svg-whole" viewBox="0 0 40 40">
            <circle cx="20" cy="20" r="17" class="slice-whole" />
          </svg>
          <svg class="pie-svg svg-whole" viewBox="0 0 40 40">
            <circle cx="20" cy="20" r="17" class="slice-whole" />
          </svg>
          
          <svg class="pie-svg svg-frac" viewBox="0 0 40 40">
            
            <path d="M 20 20 L 20 3 A 17 17 0 0 1 37 20 Z" class="slice-frac" />
            
            <path d="M 20 20 L 37 20 A 17 17 0 0 1 20 37 Z" class="slice-frac" />
            <path d="M 20 20 L 20 37 A 17 17 0 0 1 3 20 Z" class="slice-frac" />
            
            <path d="M 20 20 L 3 20 A 17 17 0 0 1 20 3 Z" class="slice-empty" />
          </svg>
        </div>
        <div class="term-label" id="lbl-res">3 ¾</div>
      </div>
    </div>

    
    <div class="controls">
      <button class="step-btn active" data-step="0">1. Problem</button>
      <button class="step-btn" data-step="1">2. Wholes</button>
      <button class="step-btn" data-step="2">3. Fractions</button>
      <button class="step-btn" data-step="3">4. Total</button>
      <button id="playBtn" class="play-btn" aria-label="Play/Pause">⏸</button>
    </div>
  </div>

  <script>
    // Render KaTeX Math Expressions
    function renderMath(step) {
      const wHl = step === 1 ? 'hl-whole' : '';
      const fHl = step === 2 ? 'hl-frac' : '';
      const wDim = step === 2 ? 'dimmed' : '';
      const fDim = step === 1 ? 'dimmed' : '';

      const t1Html = `<span class="whole-num ${wHl} ${wDim}">1</span><span class="frac-num ${fHl} ${fDim}">${katex.renderToString('\\frac{1}{4}')}</span>`;
      const t2Html = `<span class="whole-num ${wHl} ${wDim}">2</span><span class="frac-num ${fHl} ${fDim}">${katex.renderToString('\\frac{2}{4}')}</span>`;
      
      let resHtml = '';
      if (step === 0) {
        resHtml = `<span class="math-block" style="color:#94a3b8; font-weight:700; font-size:20px;">?</span>`;
      } else if (step === 1) {
        resHtml = `<span class="whole-num hl-whole">3</span><span class="frac-num dimmed" style="color:#94a3b8;">${katex.renderToString('\\frac{?}{4}')}</span>`;
      } else if (step === 2) {
        resHtml = `<span class="whole-num dimmed">3</span><span class="frac-num hl-frac">${katex.renderToString('\\frac{3}{4}')}</span>`;
      } else {
        resHtml = `<span class="whole-num hl-whole">3</span><span class="frac-num hl-frac">${katex.renderToString('\\frac{3}{4}')}</span>`;
      }

      document.getElementById('eq-term1').innerHTML = t1Html;
      document.getElementById('eq-term2').innerHTML = t2Html;
      document.getElementById('eq-result').innerHTML = resHtml;
    }

    function updateVisuals(step) {
      renderMath(step);

      const wholeSvgs = document.querySelectorAll('.svg-whole');
      const fracSvgs = document.querySelectorAll('.svg-frac');
      const groupRes = document.getElementById('group-res');

      // Reset styles
      wholeSvgs.forEach(el => {
        el.classList.remove('dimmed', 'highlight-ring-green');
      });
      fracSvgs.forEach(el => {
        el.classList.remove('dimmed', 'highlight-ring');
      });
      groupRes.classList.remove('dimmed');

      if (step === 0) {
        // Problem Overview
        groupRes.classList.add('dimmed');
      } else if (step === 1) {
        // Adding Wholes (1 + 2 = 3)
        fracSvgs.forEach(el => el.classList.add('dimmed'));
        wholeSvgs.forEach(el => el.classList.add('highlight-ring-green'));
      } else if (step === 2) {
        // Adding Fractions (1/4 + 2/4 = 3/4)
        wholeSvgs.forEach(el => el.classList.add('dimmed'));
        fracSvgs.forEach(el => el.classList.add('highlight-ring'));
      } else if (step === 3) {
        // Full Combined Total
        wholeSvgs.forEach(el => el.classList.add('highlight-ring-green'));
        fracSvgs.forEach(el => el.classList.add('highlight-ring'));
      }
    }

    // Initialize Stepper
    let currentStep = 0;
    const totalSteps = 4;
    let isPlaying = true;
    let timer = null;

    function goToStep(stepIndex) {
      currentStep = stepIndex;
      document.querySelectorAll('.step-btn').forEach((btn, idx) => {
        btn.classList.toggle('active', idx === currentStep);
      });
      updateVisuals(currentStep);
    }

    function nextStep() {
      goToStep((currentStep + 1) % totalSteps);
    }

    function startAutoPlay() {
      if (timer) clearInterval(timer);
      timer = setInterval(nextStep, 3500);
      isPlaying = true;
      document.getElementById('playBtn').textContent = '⏸';
    }

    function pauseAutoPlay() {
      if (timer) clearInterval(timer);
      isPlaying = false;
      document.getElementById('playBtn').textContent = '▶';
    }

    // Event Listeners
    document.querySelectorAll('.step-btn').forEach(btn => {
      btn.addEventListener('click', (e) => {
        const step = parseInt(e.currentTarget.getAttribute('data-step'), 10);
        pauseAutoPlay();
        goToStep(step);
      });
    });

    document.getElementById('playBtn').addEventListener('click', () => {
      if (isPlaying) {
        pauseAutoPlay();
      } else {
        nextStep();
        startAutoPlay();
      }
    });

    // Initial run
    goToStep(0);
    startAutoPlay();
  </script>
</body>
</html>

How do we combine two mixed numbers when their pizza slices are the exact same size?

To add $1\frac{1}{4} + 2\frac{2}{4}$, we do it in two easy steps: first add the whole numbers, then add the fractions.

First, add the big whole numbers together: $1 + 2 = 3$ whole pizzas.

Next, add the fraction pieces: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ of a pizza.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Adding Mixed Numbers</title>
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <script src="{{VENDOR_CDN}}/classace-diagram.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      user-select: none;
    }

    /* Step Navigation */
    .nav-bar {
      display: flex;
      gap: 6px;
      width: 100%;
      max-width: 440px;
      justify-content: center;
      margin-bottom: 8px;
    }
    .step-btn {
      flex: 1;
      padding: 6px 4px;
      font-size: 13px;
      font-weight: 600;
      border: 1px solid #e2e8f0;
      background: #ffffff;
      color: #64748b;
      border-radius: 8px;
      cursor: pointer;
      text-align: center;
      transition: all 0.25s ease;
    }
    .step-btn.active {
      background: #22b7ff;
      color: #ffffff;
      border-color: #22b7ff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.3);
    }

    /* Equation Display */
    .math-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-size: 20px;
      background: #ffffff;
      padding: 8px 16px;
      border-radius: 12px;
      border: 1px solid #e2e8f0;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
      min-height: 48px;
      margin-bottom: 8px;
    }
    .hl-whole {
      color: #2563eb;
      font-weight: 700;
      padding: 2px 4px;
      border-radius: 4px;
      transition: background 0.3s;
    }
    .hl-frac {
      color: #d97706;
      font-weight: 700;
      padding: 2px 4px;
      border-radius: 4px;
      transition: background 0.3s;
    }
    .hl-active-whole { background: #dbeafe; }
    .hl-active-frac { background: #fef3c7; }

    /* Visual Arena */
    .stage {
      width: 100%;
      max-width: 440px;
      flex: 1;
      display: flex;
      flex-direction: column;
      justify-content: center;
      gap: 10px;
      background: #ffffff;
      border-radius: 12px;
      border: 1px solid #e2e8f0;
      padding: 12px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
      position: relative;
    }

    .group-row {
      display: flex;
      align-items: center;
      justify-content: space-around;
      position: relative;
      transition: opacity 0.3s ease, transform 0.3s ease;
    }

    .item-group {
      display: flex;
      align-items: center;
      gap: 6px;
      padding: 6px 8px;
      border-radius: 10px;
      border: 1.5px solid transparent;
      transition: all 0.3s ease;
    }
    .item-group.highlight-whole {
      border-color: #3b82f6;
      background: #eff6ff;
    }
    .item-group.highlight-frac {
      border-color: #f59e0b;
      background: #fffbeb;
    }

    .pizza-box {
      width: 52px;
      height: 52px;
      position: relative;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    svg.pizza {
      width: 100%;
      height: 100%;
      filter: drop-shadow(0 2px 3px rgba(0,0,0,0.08));
    }
    .slice-whole { fill: #38bdf8; stroke: #ffffff; stroke-width: 1.5; }
    .slice-frac { fill: #fbbf24; stroke: #ffffff; stroke-width: 1.5; }
    .slice-empty { fill: #f1f5f9; stroke: #e2e8f0; stroke-width: 1.5; stroke-dasharray: 2,2; }

    .op-sign {
      font-size: 22px;
      font-weight: 700;
      color: #94a3b8;
    }

    /* Sub-labels */
    .badge-label {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 2px 8px;
      border-radius: 999px;
      display: inline-block;
      margin-bottom: 2px;
    }
    .badge-whole { background: #dbeafe; color: #1d4ed8; }
    .badge-frac { background: #fef3c7; color: #b45309; }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      gap: 12px;
      margin-top: 8px;
    }
    .play-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #334155;
      padding: 5px 14px;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
      transition: background 0.2s;
    }
    .play-btn:hover { background: #f1f5f9; }
  </style>
</head>
<body>

  
  <div class="nav-bar">
    <button class="step-btn active" id="btn0">1. Problem</button>
    <button class="step-btn" id="btn1">2. Wholes</button>
    <button class="step-btn" id="btn2">3. Fractions</button>
    <button class="step-btn" id="btn3">4. Total</button>
  </div>

  
  <div class="math-bar" id="equation"></div>

  
  <div class="stage" id="stage">
    
    <div class="group-row" id="row-split">
      
      <div class="item-group" id="grp-a">
        <div class="pizza-box" id="p-w1"></div>
        <div class="pizza-box" id="p-f1"></div>
      </div>

      <div class="op-sign" id="main-op">+</div>

      
      <div class="item-group" id="grp-b">
        <div class="pizza-box" id="p-w2a"></div>
        <div class="pizza-box" id="p-w2b"></div>
        <div class="pizza-box" id="p-f2"></div>
      </div>
    </div>

    
    <div class="group-row" id="row-result" style="display: none; border-top: 1px dashed #e2e8f0; padding-top: 8px;">
      <div class="item-group" id="grp-res" style="background: #f0fdf4; border-color: #86efac;">
        <div class="pizza-box" id="p-rw1"></div>
        <div class="pizza-box" id="p-rw2"></div>
        <div class="pizza-box" id="p-rw3"></div>
        <div class="pizza-box" id="p-rf"></div>
      </div>
    </div>
  </div>

  
  <div class="controls">
    <button class="play-btn" id="togglePlay">
      <span id="playIcon">⏸</span> Auto-play
    </button>
  </div>

  <script>
    // SVG Pizza Helpers (4 slices: Top-Right, Bottom-Right, Bottom-Left, Top-Left)
    function createPizzaSVG(filledCount, isFraction = false) {
      const cls = isFraction ? 'slice-frac' : 'slice-whole';
      const paths = [
        'M 26 26 L 26 3 A 23 23 0 0 1 49 26 Z', // Q1: top-right
        'M 26 26 L 49 26 A 23 23 0 0 1 26 49 Z', // Q2: bottom-right
        'M 26 26 L 26 49 A 23 23 0 0 1 3 26 Z',  // Q3: bottom-left
        'M 26 26 L 3 26 A 23 23 0 0 1 26 3 Z'   // Q4: top-left
      ];

      let inner = '';
      for (let i = 0; i < 4; i++) {
        const sliceClass = (i < filledCount) ? cls : 'slice-empty';
        inner += `<path d="${paths[i]}" class="${sliceClass}" />`;
      }

      return `<svg class="pizza" viewBox="0 0 52 52">${inner}</svg>`;
    }

    // Render initial static pizzas
    document.getElementById('p-w1').innerHTML = createPizzaSVG(4);
    document.getElementById('p-f1').innerHTML = createPizzaSVG(1, true);

    document.getElementById('p-w2a').innerHTML = createPizzaSVG(4);
    document.getElementById('p-w2b').innerHTML = createPizzaSVG(4);
    document.getElementById('p-f2').innerHTML = createPizzaSVG(2, true);

    document.getElementById('p-rw1').innerHTML = createPizzaSVG(4);
    document.getElementById('p-rw2').innerHTML = createPizzaSVG(4);
    document.getElementById('p-rw3').innerHTML = createPizzaSVG(4);
    document.getElementById('p-rf').innerHTML = createPizzaSVG(3, true);

    const stepsData = [
      {
        katex: "1\\frac{1}{4} + 2\\frac{2}{4} = \\text{?}",
        highlight: 'all'
      },
      {
        katex: "\\mathbf{\\color{#2563eb}1} + \\mathbf{\\color{#2563eb}2} = \\mathbf{\\color{#2563eb}3}",
        highlight: 'wholes'
      },
      {
        katex: "\\mathbf{\\color{#d97706}\\frac{1}{4}} + \\mathbf{\\color{#d97706}\\frac{2}{4}} = \\mathbf{\\color{#d97706}\\frac{3}{4}}",
        highlight: 'fractions'
      },
      {
        katex: "1\\frac{1}{4} + 2\\frac{2}{4} = \\mathbf{\\color{#10b981}3\\frac{3}{4}}",
        highlight: 'total'
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      // Update Nav Buttons
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      }

      // Render Math Formula
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        katex.render(stepsData[idx].katex, eqEl, { throwOnError: false });
      } else {
        eqEl.textContent = stepsData[idx].katex;
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      // Visual adjustments
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      const grpB = document.getElementById('grp-b');
      const rowSplit = document.getElementById('row-split');
      const rowResult = document.getElementById('row-result');

      const pw1 = document.getElementById('p-w1');
      const pw2a = document.getElementById('p-w2a');
      const pw2b = document.getElementById('p-w2b');
      const pf1 = document.getElementById('p-f1');
      const pf2 = document.getElementById('p-f2');

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      pw2a.style.opacity = '1';
      pw2b.style.opacity = '1';
      pf1.style.opacity = '1';
      pf2.style.opacity = '1';
      grpA.className = 'item-group';
      grpB.className = 'item-group';

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        rowResult.style.display = 'none';
        rowSplit.style.opacity = '1';
      } else if (idx === 1) {
        // Wholes focused
        rowResult.style.display = 'none';
        rowSplit.style.opacity = '1';
        grpA.classList.add('highlight-whole');
        grpB.classList.add('highlight-whole');
        pf1.style.opacity = '0.2';
        pf2.style.opacity = '0.2';
      } else if (idx === 2) {
        // Fractions focused
        rowResult.style.display = 'none';
        rowSplit.style.opacity = '1';
        grpA.classList.add('highlight-frac');
        grpB.classList.add('highlight-frac');
        pw1.style.opacity = '0.2';
        pw2a.style.opacity = '0.2';
        pw2b.style.opacity = '0.2';
      } else if (idx === 3) {
        // Total Result
        rowResult.style.display = 'flex';
        rowSplit.style.opacity = '0.35';
      }
    }

    function nextStep() {
      renderStep((currentStep + 1) % 4);
    }

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      if (timer) clearInterval(timer);
      timer = setInterval(nextStep, 3500);
      isPlaying = true;
      document.getElementById('playIcon').textContent = '⏸';
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    function stopAutoPlay() {
      if (timer) clearInterval(timer);
      timer = null;
      isPlaying = false;
      document.getElementById('playIcon').textContent = '▶';
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        stopAutoPlay();
        renderStep(i);
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        nextStep();
        startAutoPlay();
      }
    });

    // Init
    renderStep(0);
    startAutoPlay();
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</body>
</html>

What if we try this with yummy chocolate bars cut into five equal pieces?

Let's solve $2\frac{1}{5} + 1\frac{3}{5}$.

Add the fractions: $\frac{1}{5} + \frac{3}{5} = \frac{4}{5}$.

Put them together, and you get $3\frac{4}{5}$!

Remember: the bottom number, called the **denominator**, stays the same because the size of each piece never changed.

math

Adding Mixed Numbers with Like Denominators. Add mixed numbers with matching denominators by combining wholes and fractional parts.

Intro to Adding Mixed Numbers with Like Denominators

Adding and Subtracting Fractions and Mixed Numbers

Add Mixed Numbers with Like Denominators

Follow a Concrete-Pictorial-Abstract (CPA) progression. Begin by using physical fraction tiles or Cuisenaire rods to build mixed numbers, progress to drawing segmented bar models to highlight the bridging of wholes, and conclude with symbolic decomposition and regrouping equations. Emphasise estimation prior to calculation (e.g., $1\frac{4}{6} + 2\frac{5}{6} \approx 2 + 3 = 5$) to help learners detect reasonableness and prevent common arithmetic slips.

Adding Mixed Numbers with Like Denominators

What Is a Mixed Number?

Combining Wholes and Parts

Let's Try Another Example