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Imagine you have a shiny juice box that costs $1.40 and an apple that costs $0.50. How do you find the total price without getting mixed up?

The little dot between the numbers is called a **decimal point**, and it separates whole dollars from parts of a dollar.

<!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 Decimals</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
    }

    body {
      background-color: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    .main-layout {
      width: 100%;
      max-width: 420px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 16px;
    }

    /* Place value header */
    .grid-board {
      display: grid;
      grid-template-columns: 28px 48px 16px 48px 48px;
      column-gap: 4px;
      row-gap: 6px;
      align-items: center;
      text-align: center;
      background: #ffffff;
      padding: 16px 20px;
      border-radius: 16px;
      box-shadow: 0 4px 16px rgba(0, 0, 0, 0.06);
    }

    .header-cell {
      font-size: 11px;
      font-weight: 700;
      color: #64748b;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding-bottom: 4px;
    }

    .cell {
      font-size: 26px;
      font-weight: 600;
      height: 44px;
      display: flex;
      align-items: center;
      justify-content: center;
      border-radius: 8px;
      transition: background-color 0.3s ease, color 0.3s ease;
    }

    .cell.op {
      font-size: 22px;
      color: #94a3b8;
    }

    .cell.dot {
      font-size: 28px;
      color: #2563eb;
      font-weight: 800;
    }

    .carry-row {
      height: 20px;
      font-size: 14px;
      font-weight: 700;
      color: #ef4444;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .carry-cell {
      opacity: 0;
      transform: translateY(4px);
      transition: opacity 0.3s ease, transform 0.3s ease;
    }
    .carry-cell.visible {
      opacity: 1;
      transform: translateY(0);
    }

    .line {
      grid-column: 1 / -1;
      height: 2px;
      background-color: #cbd5e1;
      margin: 2px 0;
    }

    /* Column active highlights */
    .col-highlight {
      background-color: #eff6ff;
      color: #2563eb;
      font-weight: 700;
    }

    .dot-highlight {
      background-color: #dbeafe;
      border-radius: 6px;
    }

    .ans-digit {
      opacity: 0;
      transform: scale(0.6);
      transition: opacity 0.3s ease, transform 0.3s ease;
    }
    .ans-digit.visible {
      opacity: 1;
      transform: scale(1);
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
    }

    .btn {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      color: #1e2945;
      padding: 8px 16px;
      border-radius: 10px;
      font-size: 14px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 6px;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.04);
      transition: background-color 0.2s, border-color 0.2s;
    }
    .btn:hover {
      background: #f8fafc;
      border-color: #cbd5e1;
    }
    .btn:active {
      background: #f1f5f9;
    }

    .step-pills {
      display: flex;
      gap: 6px;
    }

    .pill {
      width: 28px;
      height: 28px;
      border-radius: 50%;
      background: #f1f5f9;
      border: 1px solid #e2e8f0;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 12px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .pill.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #2563eb;
      box-shadow: 0 2px 6px rgba(37, 99, 235, 0.3);
    }
  </style>
</head>
<body>

  <div class="main-layout">
    <div class="grid-board">
      
      <div class="header-cell"></div>
      <div class="header-cell">Units</div>
      <div class="header-cell"></div>
      <div class="header-cell">Tenths</div>
      <div class="header-cell">Hundredths</div>

      
      <div class="carry-row"></div>
      <div class="carry-row"></div>
      <div class="carry-row"></div>
      <div class="carry-row"><span id="carry1" class="carry-cell">1</span></div>
      <div class="carry-row"></div>

      
      <div class="cell op"></div>
      <div class="cell" id="n1-u">3</div>
      <div class="cell dot" id="n1-d">.</div>
      <div class="cell" id="n1-t">4</div>
      <div class="cell" id="n1-h">8</div>

      
      <div class="cell op">+</div>
      <div class="cell" id="n2-u">2</div>
      <div class="cell dot" id="n2-d">.</div>
      <div class="cell" id="n2-t">1</div>
      <div class="cell" id="n2-h">5</div>

      
      <div class="line"></div>

      
      <div class="cell op"></div>
      <div class="cell" id="ans-u"><span class="ans-digit" id="ans-u-val">5</span></div>
      <div class="cell dot" id="ans-d"><span class="ans-digit" id="ans-d-val">.</span></div>
      <div class="cell" id="ans-t"><span class="ans-digit" id="ans-t-val">6</span></div>
      <div class="cell" id="ans-h"><span class="ans-digit" id="ans-h-val">3</span></div>
    </div>

    <div class="controls">
      <button class="btn" id="prevBtn">◀</button>
      <div class="step-pills">
        <button class="pill active" data-step="0">1</button>
        <button class="pill" data-step="1">2</button>
        <button class="pill" data-step="2">3</button>
        <button class="pill" data-step="3">4</button>
        <button class="pill" data-step="4">5</button>
      </div>
      <button class="btn" id="nextBtn">▶</button>
    </div>
  </div>

  <script>
    let step = 0;
    const totalSteps = 5;
    let timer = null;

    const el = id => document.getElementById(id);
    const pills = document.querySelectorAll('.pill');

    function updateStep(newStep) {
      step = (newStep + totalSteps) % totalSteps;

      // Update pills
      pills.forEach((p, idx) => {
        p.classList.toggle('active', idx === step);
      });

      // Clear column highlights
      ['n1-u', 'n2-u', 'ans-u', 'n1-t', 'n2-t', 'ans-t', 'n1-h', 'n2-h', 'ans-h'].forEach(id => {
        el(id).classList.remove('col-highlight');
      });
      ['n1-d', 'n2-d', 'ans-d'].forEach(id => {
        el(id).classList.remove('dot-highlight');
      });

      // Reset values visibility based on step
      el('carry1').classList.toggle('visible', step >= 2);
      el('ans-h-val').classList.toggle('visible', step >= 1);
      el('ans-t-val').classList.toggle('visible', step >= 2);
      el('ans-d-val').classList.toggle('visible', step >= 3);
      el('ans-u-val').classList.toggle('visible', step >= 4);

      // Apply step-specific highlight
      if (step === 0) {
        // Step 1: Align decimal points
        el('n1-d').classList.add('dot-highlight');
        el('n2-d').classList.add('dot-highlight');
      } else if (step === 1) {
        // Step 2: Hundredths (8 + 5 = 13)
        el('n1-h').classList.add('col-highlight');
        el('n2-h').classList.add('col-highlight');
        el('ans-h').classList.add('col-highlight');
      } else if (step === 2) {
        // Step 3: Tenths (1 + 4 + 1 = 6)
        el('n1-t').classList.add('col-highlight');
        el('n2-t').classList.add('col-highlight');
        el('ans-t').classList.add('col-highlight');
      } else if (step === 3) {
        // Step 4: Drop decimal point down
        el('n1-d').classList.add('dot-highlight');
        el('n2-d').classList.add('dot-highlight');
        el('ans-d').classList.add('dot-highlight');
      } else if (step === 4) {
        // Step 5: Units (3 + 2 = 5)
        el('n1-u').classList.add('col-highlight');
        el('n2-u').classList.add('col-highlight');
        el('ans-u').classList.add('col-highlight');
      }
    }

    function resetTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        updateStep(step + 1);
      }, 3500);
    }

    // Controls
    el('prevBtn').addEventListener('click', () => {
      updateStep(step - 1);
      resetTimer();
    });

    el('nextBtn').addEventListener('click', () => {
      updateStep(step + 1);
      resetTimer();
    });

    pills.forEach(p => {
      p.addEventListener('click', () => {
        updateStep(parseInt(p.dataset.step, 10));
        resetTimer();
      });
    });

    // Initial render & autoplay
    updateStep(0);
    resetTimer();
  </script>
</body>
</html>

So how do we add two decimal numbers together when they have the same number of digits after the dot?

The golden rule is **column addition**: write the numbers on top of each other so their decimal points make a straight vertical line.

Once your dots are lined up, add the digits from right to left just like regular numbers, and bring the dot straight down into your answer.

<!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 Decimals</title>
<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;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
    padding: 16px;
  }

  .diagram-area {
    width: 100%;
    max-width: 420px;
    display: flex;
    flex-direction: column;
    align-items: center;
    gap: 16px;
  }

  /* Math grid container */
  .grid-card {
    background: #ffffff;
    border-radius: 16px;
    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);
    padding: 20px 24px;
    width: 100%;
    display: flex;
    flex-direction: column;
    align-items: center;
    position: relative;
  }

  /* Column Headers */
  .col-headers {
    display: grid;
    grid-template-columns: 32px 48px 20px 48px;
    gap: 4px;
    font-size: 13px;
    font-weight: 600;
    color: #6b7280;
    text-align: center;
    margin-bottom: 8px;
    width: 100%;
    justify-content: center;
  }

  /* Math rows */
  .math-rows {
    display: flex;
    flex-direction: column;
    gap: 6px;
    position: relative;
    width: 100%;
    align-items: center;
  }

  .math-row {
    display: grid;
    grid-template-columns: 32px 48px 20px 48px;
    gap: 4px;
    align-items: center;
    justify-content: center;
    font-size: 32px;
    font-weight: 700;
    font-variant-numeric: tabular-nums;
    height: 48px;
  }

  .cell {
    display: flex;
    align-items: center;
    justify-content: center;
    border-radius: 8px;
    height: 44px;
    transition: background 0.3s ease, color 0.3s ease, transform 0.3s ease;
  }

  .cell.op {
    font-size: 26px;
    color: #6b7280;
  }

  .cell.dot {
    font-size: 32px;
    font-weight: 900;
    color: #2563eb;
    position: relative;
  }

  .divider {
    width: 160px;
    height: 3px;
    background: #1e2945;
    border-radius: 2px;
    margin: 4px 0;
  }

  /* Alignment guide line */
  .alignment-line {
    position: absolute;
    top: -4px;
    bottom: -4px;
    left: calc(50% - 2px);
    width: 4px;
    background: rgba(37, 99, 235, 0.25);
    border-radius: 2px;
    pointer-events: none;
    transition: opacity 0.3s ease;
    opacity: 0;
  }
  .alignment-line.visible {
    opacity: 1;
  }

  /* Highlight states */
  .hl-col-right {
    background: #e0e7ff;
    color: #1d4ed8;
  }
  .hl-col-left {
    background: #e0e7ff;
    color: #1d4ed8;
  }
  .hl-dot {
    background: #dbeafe;
    color: #2563eb;
  }

  .hidden-cell {
    opacity: 0;
    transform: scale(0.6);
  }
  .shown-cell {
    opacity: 1;
    transform: scale(1);
  }

  /* Explanatory indicator badge */
  .badge {
    height: 32px;
    display: flex;
    align-items: center;
    justify-content: center;
    font-size: 14px;
    font-weight: 600;
    color: #2563eb;
    background: #eff6ff;
    border-radius: 20px;
    padding: 0 16px;
    letter-spacing: 0.2px;
  }

  /* Interactive Controls */
  .controls {
    display: flex;
    align-items: center;
    gap: 8px;
    width: 100%;
    justify-content: center;
  }

  .btn {
    border: none;
    background: #ffffff;
    color: #1e2945;
    font-size: 14px;
    font-weight: 600;
    padding: 8px 14px;
    border-radius: 10px;
    box-shadow: 0 2px 6px rgba(0, 0, 0, 0.06);
    cursor: pointer;
    transition: background 0.2s, box-shadow 0.2s;
    user-select: none;
    -webkit-tap-highlight-color: transparent;
  }
  .btn:hover {
    background: #f1f5f9;
  }
  .btn:active {
    box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.1);
  }

  .step-pills {
    display: flex;
    gap: 6px;
  }

  .pill {
    width: 32px;
    height: 32px;
    border-radius: 50%;
    border: 2px solid transparent;
    background: #e2e8f0;
    color: #64748b;
    font-weight: 700;
    font-size: 13px;
    display: flex;
    align-items: center;
    justify-content: center;
    cursor: pointer;
    transition: all 0.2s ease;
  }
  .pill.active {
    background: #2563eb;
    color: #ffffff;
  }
</style>
</head>
<body>

<div class="diagram-area">
  <div class="grid-card">
    <div class="col-headers">
      <div></div>
      <div>Ones</div>
      <div></div>
      <div>Tenths</div>
    </div>

    <div class="math-rows">
      <div id="guideLine" class="alignment-line"></div>

      
      <div class="math-row">
        <div class="cell"></div>
        <div id="u1" class="cell">3</div>
        <div id="d1" class="cell dot">.</div>
        <div id="t1" class="cell">4</div>
      </div>

      
      <div class="math-row">
        <div class="cell op">+</div>
        <div id="u2" class="cell">1</div>
        <div id="d2" class="cell dot">.</div>
        <div id="t2" class="cell">2</div>
      </div>

      <div class="divider"></div>

      
      <div class="math-row">
        <div class="cell"></div>
        <div id="ansU" class="cell hidden-cell">4</div>
        <div id="ansD" class="cell dot hidden-cell">.</div>
        <div id="ansT" class="cell hidden-cell">6</div>
      </div>
    </div>
  </div>

  <div id="badgeLabel" class="badge">Step 1: Line up dots</div>

  <div class="controls">
    <button class="btn" id="prevBtn">◀</button>
    <div class="step-pills">
      <button class="pill active" data-step="0">1</button>
      <button class="pill" data-step="1">2</button>
      <button class="pill" data-step="2">3</button>
      <button class="pill" data-step="3">4</button>
    </div>
    <button class="btn" id="nextBtn">▶</button>
  </div>
</div>

<script>
  const steps = [
    {
      label: "1. Line up decimal dots",
      line: true,
      tHl: false,
      dHl: true,
      uHl: false,
      showT: false,
      showD: false,
      showU: false
    },
    {
      label: "2. Add tenths (4 + 2 = 6)",
      line: false,
      tHl: true,
      dHl: false,
      uHl: false,
      showT: true,
      showD: false,
      showU: false
    },
    {
      label: "3. Bring dot straight down",
      line: true,
      tHl: false,
      dHl: true,
      uHl: false,
      showT: true,
      showD: true,
      showU: false
    },
    {
      label: "4. Add ones (3 + 1 = 4)",
      line: false,
      tHl: false,
      dHl: false,
      uHl: true,
      showT: true,
      showD: true,
      showU: true
    }
  ];

  let currentStep = 0;
  let timer = null;

  const guideLine = document.getElementById("guideLine");
  const badgeLabel = document.getElementById("badgeLabel");
  const pills = document.querySelectorAll(".pill");

  const t1 = document.getElementById("t1");
  const t2 = document.getElementById("t2");
  const ansT = document.getElementById("ansT");

  const d1 = document.getElementById("d1");
  const d2 = document.getElementById("d2");
  const ansD = document.getElementById("ansD");

  const u1 = document.getElementById("u1");
  const u2 = document.getElementById("u2");
  const ansU = document.getElementById("ansU");

  function render(stepIdx) {
    const s = steps[stepIdx];

    badgeLabel.textContent = s.label;

    pills.forEach((p, idx) => {
      p.classList.toggle("active", idx === stepIdx);
    });

    guideLine.classList.toggle("visible", s.line);

    // Tenths column
    t1.classList.toggle("hl-col-right", s.tHl);
    t2.classList.toggle("hl-col-right", s.tHl);
    ansT.classList.toggle("hl-col-right", s.tHl);
    ansT.className = `cell ${s.tHl ? "hl-col-right " : ""}${s.showT ? "shown-cell" : "hidden-cell"}`;

    // Dots
    d1.classList.toggle("hl-dot", s.dHl);
    d2.classList.toggle("hl-dot", s.dHl);
    ansD.classList.toggle("hl-dot", s.dHl);
    ansD.className = `cell dot ${s.dHl ? "hl-dot " : ""}${s.showD ? "shown-cell" : "hidden-cell"}`;

    // Ones column
    u1.classList.toggle("hl-col-left", s.uHl);
    u2.classList.toggle("hl-col-left", s.uHl);
    ansU.classList.toggle("hl-col-left", s.uHl);
    ansU.className = `cell ${s.uHl ? "hl-col-left " : ""}${s.showU ? "shown-cell" : "hidden-cell"}`;
  }

  function setStep(idx) {
    currentStep = (idx + steps.length) % steps.length;
    render(currentStep);
    resetAutoPlay();
  }

  function nextStep() {
    setStep(currentStep + 1);
  }

  function prevStep() {
    setStep(currentStep - 1);
  }

  function resetAutoPlay() {
    if (timer) clearInterval(timer);
    timer = setInterval(() => {
      currentStep = (currentStep + 1) % steps.length;
      render(currentStep);
    }, 3600);
  }

  document.getElementById("prevBtn").addEventListener("click", prevStep);
  document.getElementById("nextBtn").addEventListener("click", nextStep);

  pills.forEach((pill) => {
    pill.addEventListener("click", () => {
      const target = parseInt(pill.dataset.step, 10);
      setStep(target);
    });
  });

  render(0);
  resetAutoPlay();
</script>

</body>
</html>

That was smooth! But what should you do if the numbers in one column add up to 10 or more?

When a column makes 10 or more, you **regroup** by carrying the extra ten to the next column on the left.

Let's add $3.7 + 2.5$. In the tenths place, $7 + 5 = 12$ tenths, which is 1 whole and 2 tenths.

<!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">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif; }
    
    body {
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      padding: 16px;
    }

    .main-grid {
      display: flex;
      gap: 20px;
      align-items: center;
      justify-content: center;
      width: 100%;
      max-width: 520px;
    }

    /* Column math layout */
    .math-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 14px;
      padding: 18px 24px;
      box-shadow: 0 4px 12px rgba(0,0,0,0.04);
      display: flex;
      flex-direction: column;
      align-items: center;
    }

    .grid-table {
      display: grid;
      grid-template-columns: 24px 44px 16px 44px;
      font-size: 28px;
      font-weight: 700;
      line-height: 1.4;
      text-align: center;
      align-items: center;
    }

    .header-row {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      margin-bottom: 6px;
    }

    .carry-box {
      height: 28px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .carry-digit {
      background: #eff6ff;
      color: #2563eb;
      border: 1.5px solid #bfdbfe;
      border-radius: 6px;
      width: 26px;
      height: 26px;
      font-size: 15px;
      display: flex;
      align-items: center;
      justify-content: center;
      opacity: 0;
      transform: translateY(6px);
      transition: all 0.3s ease;
    }

    .carry-digit.visible {
      opacity: 1;
      transform: translateY(0);
    }

    .divider {
      grid-column: 1 / -1;
      height: 3px;
      background: #1e2945;
      border-radius: 2px;
      margin: 4px 0;
    }

    .col-highlight {
      border-radius: 8px;
      transition: background 0.3s ease;
    }

    .col-highlight.active-tenths {
      background: #fef3c7;
      color: #d97706;
    }

    .col-highlight.active-ones {
      background: #dbeafe;
      color: #2563eb;
    }

    .ans-digit {
      opacity: 0;
      transform: scale(0.6);
      transition: all 0.3s cubic-bezier(0.34, 1.56, 0.64, 1);
    }

    .ans-digit.visible {
      opacity: 1;
      transform: scale(1);
    }

    /* Place value disks visual */
    .vis-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 14px;
      padding: 16px;
      box-shadow: 0 4px 12px rgba(0,0,0,0.04);
      flex: 1;
      min-width: 220px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }

    .vis-section {
      display: flex;
      flex-direction: column;
      gap: 6px;
    }

    .vis-title {
      font-size: 12px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      display: flex;
      justify-content: space-between;
    }

    .vis-title.ones-lbl { color: #2563eb; }
    .vis-title.tenths-lbl { color: #d97706; }

    .token-grid {
      display: flex;
      flex-wrap: wrap;
      gap: 5px;
      min-height: 48px;
      align-items: center;
      padding: 6px;
      background: #f8fafc;
      border-radius: 8px;
    }

    .token {
      width: 22px;
      height: 22px;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 11px;
      font-weight: 700;
      transition: all 0.4s ease;
    }

    .token.one {
      background: #2563eb;
      color: #ffffff;
    }

    .token.tenth {
      background: #f59e0b;
      color: #ffffff;
    }

    .token.bundled {
      background: #93c5fd;
      border: 2px dashed #2563eb;
      transform: scale(0.85);
    }

    .token.new-one {
      background: #2563eb;
      color: #ffffff;
      animation: pulse 0.5s ease;
    }

    @keyframes pulse {
      0% { transform: scale(0); }
      70% { transform: scale(1.25); }
      100% { transform: scale(1); }
    }

    /* Stepper navigation */
    .controls {
      margin-top: 18px;
      display: flex;
      align-items: center;
      gap: 8px;
    }

    .step-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #475569;
      padding: 6px 14px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .step-btn:hover {
      background: #f1f5f9;
    }

    .step-btn.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #2563eb;
    }

    .play-btn {
      width: 32px;
      height: 32px;
      border-radius: 8px;
      background: #ffffff;
      border: 1px solid #cbd5e1;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      font-size: 13px;
      color: #475569;
    }

    @media (max-width: 480px) {
      .main-grid {
        flex-direction: column;
        gap: 12px;
      }
      .math-card, .vis-card {
        width: 100%;
      }
      .grid-table {
        font-size: 24px;
      }
    }
  </style>
</head>
<body>

  <div class="main-grid">
    
    <div class="math-card">
      <div class="grid-table header-row">
        <div></div>
        <div>1s</div>
        <div></div>
        <div>0.1s</div>
      </div>

      <div class="grid-table">
        <div></div>
        <div class="carry-box">
          <div class="carry-digit" id="carry">1</div>
        </div>
        <div></div>
        <div></div>

        <div></div>
        <div id="o1" class="col-highlight">3</div>
        <div>.</div>
        <div id="t1" class="col-highlight">7</div>

        <div>+</div>
        <div id="o2" class="col-highlight">2</div>
        <div>.</div>
        <div id="t2" class="col-highlight">5</div>

        <div class="divider"></div>

        <div></div>
        <div class="ans-digit" id="ans-o">6</div>
        <div class="ans-digit" id="ans-dot">.</div>
        <div class="ans-digit" id="ans-t">2</div>
      </div>
    </div>

    
    <div class="vis-card">
      <div class="vis-section">
        <div class="vis-title tenths-lbl">
          <span>Tenths (0.1)</span>
          <span id="tenth-count">12</span>
        </div>
        <div class="token-grid" id="tenths-container"></div>
      </div>

      <div class="vis-section">
        <div class="vis-title ones-lbl">
          <span>Ones (1.0)</span>
          <span id="ones-count">5</span>
        </div>
        <div class="token-grid" id="ones-container"></div>
      </div>
    </div>
  </div>

  
  <div class="controls">
    <button class="play-btn" id="play-btn" title="Play/Pause">⏸</button>
    <button class="step-btn active" data-step="0">1. Align</button>
    <button class="step-btn" data-step="1">2. Add Tenths</button>
    <button class="step-btn" data-step="2">3. Regroup</button>
    <button class="step-btn" data-step="3">4. Total</button>
  </div>

  <script>
    let currentStep = 0;
    let autoPlay = true;
    let timer = null;

    const carryEl = document.getElementById('carry');
    const t1 = document.getElementById('t1');
    const t2 = document.getElementById('t2');
    const o1 = document.getElementById('o1');
    const o2 = document.getElementById('o2');
    const ansT = document.getElementById('ans-t');
    const ansDot = document.getElementById('ans-dot');
    const ansO = document.getElementById('ans-o');

    const tenthsBox = document.getElementById('tenths-container');
    const onesBox = document.getElementById('ones-container');
    const tenthCount = document.getElementById('tenth-count');
    const onesCount = document.getElementById('ones-count');

    const stepBtns = document.querySelectorAll('.step-btn');
    const playBtn = document.getElementById('play-btn');

    function renderTokens(step) {
      tenthsBox.innerHTML = '';
      onesBox.innerHTML = '';

      if (step === 0) {
        tenthCount.textContent = '7 + 5';
        onesCount.textContent = '3 + 2';
        for (let i = 0; i < 12; i++) {
          const d = document.createElement('div');
          d.className = 'token tenth';
          d.textContent = '·1';
          tenthsBox.appendChild(d);
        }
        for (let i = 0; i < 5; i++) {
          const d = document.createElement('div');
          d.className = 'token one';
          d.textContent = '1';
          onesBox.appendChild(d);
        }
      } else if (step === 1) {
        tenthCount.textContent = '12 tenths';
        onesCount.textContent = '5 ones';
        for (let i = 0; i < 12; i++) {
          const d = document.createElement('div');
          d.className = 'token tenth';
          d.textContent = '·1';
          tenthsBox.appendChild(d);
        }
        for (let i = 0; i < 5; i++) {
          const d = document.createElement('div');
          d.className = 'token one';
          d.textContent = '1';
          onesBox.appendChild(d);
        }
      } else if (step === 2) {
        tenthCount.textContent = '2 tenths left';
        onesCount.textContent = '5 + 1 regrouped';
        for (let i = 0; i < 2; i++) {
          const d = document.createElement('div');
          d.className = 'token tenth';
          d.textContent = '·1';
          tenthsBox.appendChild(d);
        }
        for (let i = 0; i < 5; i++) {
          const d = document.createElement('div');
          d.className = 'token one';
          d.textContent = '1';
          onesBox.appendChild(d);
        }
        const carried = document.createElement('div');
        carried.className = 'token new-one';
        carried.textContent = '+1';
        onesBox.appendChild(carried);
      } else if (step === 3) {
        tenthCount.textContent = '2 tenths';
        onesCount.textContent = '6 ones';
        for (let i = 0; i < 2; i++) {
          const d = document.createElement('div');
          d.className = 'token tenth';
          d.textContent = '·1';
          tenthsBox.appendChild(d);
        }
        for (let i = 0; i < 6; i++) {
          const d = document.createElement('div');
          d.className = 'token one';
          d.textContent = '1';
          onesBox.appendChild(d);
        }
      }
    }

    function setStep(step) {
      currentStep = step;
      stepBtns.forEach((b, i) => b.classList.toggle('active', i === step));

      // Reset styles
      t1.classList.remove('active-tenths');
      t2.classList.remove('active-tenths');
      o1.classList.remove('active-ones');
      o2.classList.remove('active-ones');
      carryEl.classList.remove('visible');
      ansT.classList.remove('visible');
      ansDot.classList.remove('visible');
      ansO.classList.remove('visible');

      if (step === 0) {
        // Just aligned
      } else if (step === 1) {
        t1.classList.add('active-tenths');
        t2.classList.add('active-tenths');
      } else if (step === 2) {
        carryEl.classList.add('visible');
        ansT.classList.add('visible');
      } else if (step === 3) {
        carryEl.classList.add('visible');
        ansT.classList.add('visible');
        ansDot.classList.add('visible');
        ansO.classList.add('visible');
        o1.classList.add('active-ones');
        o2.classList.add('active-ones');
      }

      renderTokens(step);
    }

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

    function startTimer() {
      if (timer) clearInterval(timer);
      timer = setInterval(nextStep, 3500);
    }

    stepBtns.forEach((btn, idx) => {
      btn.addEventListener('click', () => {
        setStep(idx);
        if (autoPlay) {
          startTimer();
        }
      });
    });

    playBtn.addEventListener('click', () => {
      autoPlay = !autoPlay;
      playBtn.textContent = autoPlay ? '⏸' : '▶';
      if (autoPlay) {
        startTimer();
      } else {
        clearInterval(timer);
      }
    });

    // Init
    setStep(0);
    startTimer();
  </script>
</body>
</html>

Now that you know how to regroup, what is the most common trap to avoid?

A common mistake is doing all the addition correctly but forgetting to write the decimal point in the final answer.

<!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>Line Up and Drop the Dot</title>
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    background: #f8f9fa;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: space-between;
    min-height: 100vh;
    padding: 16px;
    user-select: none;
  }

  .step-nav {
    display: flex;
    gap: 8px;
    width: 100%;
    max-width: 360px;
  }
  .step-btn {
    flex: 1;
    padding: 8px 4px;
    font-size: 13px;
    font-weight: 600;
    border: none;
    border-radius: 8px;
    background: #e2e8f0;
    color: #475569;
    cursor: pointer;
    transition: background 0.2s, color 0.2s, box-shadow 0.2s;
  }
  .step-btn.active {
    background: #2563eb;
    color: #ffffff;
    box-shadow: 0 2px 6px rgba(37,99,235,0.3);
  }

  .board {
    position: relative;
    background: #ffffff;
    border-radius: 12px;
    padding: 24px 32px;
    box-shadow: 0 4px 12px rgba(0,0,0,0.05);
    display: flex;
    flex-direction: column;
    align-items: center;
    min-width: 280px;
    max-width: 340px;
  }

  .grid {
    display: grid;
    grid-template-columns: 24px 36px 16px 36px 36px;
    row-gap: 8px;
    font-size: 32px;
    font-weight: 700;
    line-height: 1;
    align-items: center;
    justify-items: center;
    position: relative;
  }

  .carry {
    font-size: 16px;
    color: #2563eb;
    height: 18px;
    opacity: 0;
    transition: opacity 0.3s ease;
  }
  .carry.show { opacity: 1; }

  .op {
    font-size: 28px;
    color: #64748b;
  }

  .num {
    color: #1e2945;
  }

  .dot {
    color: #2563eb;
    font-weight: 900;
    position: relative;
    z-index: 2;
  }

  .dot-ans {
    color: #2563eb;
    font-weight: 900;
    opacity: 0;
    transform: translateY(-8px);
    transition: opacity 0.3s ease, transform 0.3s ease;
    z-index: 2;
  }
  .dot-ans.show {
    opacity: 1;
    transform: translateY(0);
  }

  .ans-num {
    opacity: 0;
    transform: translateY(4px);
    transition: opacity 0.3s ease, transform 0.3s ease;
  }
  .ans-num.show {
    opacity: 1;
    transform: translateY(0);
  }

  .line {
    grid-column: 1 / -1;
    height: 3px;
    background: #1e2945;
    width: 100%;
    border-radius: 2px;
    margin: 4px 0;
  }

  /* Vertical Guide Beam */
  .guide-beam {
    position: absolute;
    left: calc(24px + 36px + 8px - 10px);
    top: 20px;
    bottom: 2px;
    width: 20px;
    background: rgba(37, 99, 235, 0.12);
    border: 1.5px dashed #2563eb;
    border-radius: 10px;
    opacity: 0;
    transition: opacity 0.3s ease;
    pointer-events: none;
    z-index: 1;
  }
  .guide-beam.show {
    opacity: 1;
  }

  /* Guide Arrow */
  .guide-arrow {
    position: absolute;
    left: calc(24px + 36px + 8px - 6px);
    top: 50%;
    transform: translateY(-50%);
    color: #2563eb;
    font-size: 16px;
    opacity: 0;
    transition: opacity 0.3s ease;
    z-index: 3;
    pointer-events: none;
  }
  .guide-arrow.show {
    opacity: 1;
  }

  .controls {
    display: flex;
    align-items: center;
    gap: 12px;
  }
  .ctrl-btn {
    background: #ffffff;
    border: 1px solid #cbd5e1;
    border-radius: 8px;
    padding: 8px 16px;
    font-size: 14px;
    font-weight: 600;
    color: #334155;
    cursor: pointer;
    box-shadow: 0 1px 3px rgba(0,0,0,0.05);
    display: flex;
    align-items: center;
    gap: 6px;
  }
  .ctrl-btn:active { background: #f1f5f9; }
</style>
</head>
<body>

  
  <div class="step-nav">
    <button class="step-btn active" onclick="setStep(0)">1. Line Up</button>
    <button class="step-btn" onclick="setStep(1)">2. Drop Dot</button>
    <button class="step-btn" onclick="setStep(2)">3. Add</button>
  </div>

  
  <div class="board">
    <div class="grid">
      
      <div id="beam" class="guide-beam show"></div>

      
      <div></div>
      <div></div>
      <div></div>
      <div id="c1" class="carry">1</div>
      <div></div>

      
      <div></div>
      <div class="num">3</div>
      <div class="dot">•</div>
      <div class="num">4</div>
      <div class="num">6</div>

      
      <div class="op">+</div>
      <div class="num">2</div>
      <div class="dot">•</div>
      <div class="num">1</div>
      <div class="num">8</div>

      
      <div class="line"></div>

      
      <div></div>
      <div id="a1" class="ans-num num">5</div>
      <div id="adot" class="dot-ans">•</div>
      <div id="a2" class="ans-num num">6</div>
      <div id="a3" class="ans-num num">4</div>
    </div>
  </div>

  
  <div class="controls">
    <button class="ctrl-btn" onclick="prevStep()">◀</button>
    <button class="ctrl-btn" id="playBtn" onclick="togglePlay()">⏸ Pause</button>
    <button class="ctrl-btn" onclick="nextStep()">▶</button>
  </div>

<script>
  let currentStep = 0;
  let isPlaying = true;
  let timer = null;

  const beam = document.getElementById('beam');
  const adot = document.getElementById('adot');
  const c1 = document.getElementById('c1');
  const a1 = document.getElementById('a1');
  const a2 = document.getElementById('a2');
  const a3 = document.getElementById('a3');
  const buttons = document.querySelectorAll('.step-btn');
  const playBtn = document.getElementById('playBtn');

  function render() {
    buttons.forEach((btn, idx) => {
      btn.classList.toggle('active', idx === currentStep);
    });

    if (currentStep === 0) {
      beam.classList.add('show');
      adot.classList.remove('show');
      c1.classList.remove('show');
      a1.classList.remove('show');
      a2.classList.remove('show');
      a3.classList.remove('show');
    } else if (currentStep === 1) {
      beam.classList.add('show');
      adot.classList.add('show');
      c1.classList.remove('show');
      a1.classList.remove('show');
      a2.classList.remove('show');
      a3.classList.remove('show');
    } else if (currentStep === 2) {
      beam.classList.add('show');
      adot.classList.add('show');
      c1.classList.add('show');
      a1.classList.add('show');
      a2.classList.add('show');
      a3.classList.add('show');
    }
  }

  function setStep(step) {
    currentStep = step;
    render();
  }

  function nextStep() {
    currentStep = (currentStep + 1) % 3;
    render();
  }

  function prevStep() {
    currentStep = (currentStep - 1 + 3) % 3;
    render();
  }

  function togglePlay() {
    isPlaying = !isPlaying;
    playBtn.textContent = isPlaying ? '⏸ Pause' : '▶ Play';
    if (isPlaying) {
      startLoop();
    } else {
      clearInterval(timer);
    }
  }

  function startLoop() {
    clearInterval(timer);
    timer = setInterval(() => {
      if (isPlaying) {
        nextStep();
      }
    }, 3200);
  }

  render();
  startLoop();
</script>
</body>
</html>

Next time you add numbers with decimals, check your straight line of dots first, drop the dot into your answer, and you will get it right every time!

math

Adding Decimals with the Same Number of Decimal Places. Add decimal numbers using column addition aligned at the decimal point.

Adding Decimals: Place Value and Column Alignment

Second Level Maths: How to Add and Subtract Decimals

Add Decimal Numbers Using Place Value Columns

Pedagogical strategy focuses on the Concrete-Pictorial-Abstract (CPA) approach. Begin with place-value grids and base-10 manipulatives (where a flat represents 1 whole, a rod represents 0.1, and a unit cube represents 0.01) to make regrouping tangible before moving to formal vertical column notation. Emphasize vertical decimal point guidelines to establish procedural fluency and reinforce that place value rules for decimals operate identically to whole numbers.

Adding Decimals with the Same Number of Decimal Places

Line Up the Dots

Regrouping Across the Dot