To multiply fractions with whole numbers, turn the whole number into a fraction, multiply straight across (top with top, bottom with bottom), then simplify if you can.

What’s going on when you multiply?

Think of multiplying a fraction by a whole number as repeated addition.

For example, 14×3\frac{1}{4}\times 341​×3 means “three groups of one-quarter,” the same as 14+14+14\frac{1}{4}+\frac{1}{4}+\frac{1}{4}41​+41​+41​.

Step‑by‑step method

Use these steps every time:

  1. Write the whole number as a fraction.
    • Example: 5 becomes 51\frac{5}{1}15​.
  1. Multiply the numerators (top numbers).
    • Example: 23×4=23×41⇒2×4=8\frac{2}{3}\times 4=\frac{2}{3}\times \frac{4}{1}\Rightarrow 2\times 4=832​×4=32​×14​⇒2×4=8.
  1. Multiply the denominators (bottom numbers).
    • Continuing: 3×1=33\times 1=33×1=3, so you get 83\frac{8}{3}38​.
  1. Simplify or turn into a mixed number if needed.
    • 83=223\frac{8}{3}=2\frac{2}{3}38​=232​ because 8 ÷ 3 = 2 remainder 2.

A few quick examples

Think of each one as “that fraction, this many times in a row.”

  1. 18×5\frac{1}{8}\times 581​×5
    • Turn 5 into a fraction: 51\frac{5}{1}15​.
    • Multiply: 18×51=1×58×1=58\frac{1}{8}\times \frac{5}{1}=\frac{1\times 5}{8\times 1}=\frac{5}{8}81​×15​=8×11×5​=85​.
  1. 34×4\frac{3}{4}\times 443​×4
    • 4=414=\frac{4}{1}4=14​.
    • 34×41=3×44×1=124=3\frac{3}{4}\times \frac{4}{1}=\frac{3\times 4}{4\times 1}=\frac{12}{4}=343​×14​=4×13×4​=412​=3.
  1. 13×15\frac{1}{3}\times 1531​×15
    • 15=15115=\frac{15}{1}15=115​.
    • 1×153×1=153=5\frac{1\times 15}{3\times 1}=\frac{15}{3}=53×11×15​=315​=5.

What about mixed numbers?

If you have a mixed number (like 1251\frac{2}{5}152​) and a whole number, there’s just one extra step.

  1. Turn the mixed number into an improper fraction.
    • 125=751\frac{2}{5}=\frac{7}{5}152​=57​ (because 1×5+2=71\times 5+2=71×5+2=7).
  1. Turn the whole number into a fraction.
    • 10 becomes 101\frac{10}{1}110​.
  1. Multiply numerators and denominators.
    • 75×101=7×105×1=705\frac{7}{5}\times \frac{10}{1}=\frac{7\times 10}{5\times 1}=\frac{70}{5}57​×110​=5×17×10​=570​.
  1. Simplify.
    • 705=14\frac{70}{5}=14570​=14.

Handy mental shortcut

Sometimes you can simplify early:

  • Example: 45×25\frac{4}{5}\times 2554​×25
    • Write as fractions: 45×251\frac{4}{5}\times \frac{25}{1}54​×125​.
    • Notice 25 ÷ 5 = 5, so cancel: 45×251=4×5=20\frac{4}{\cancel{5}}\times \frac{\cancel{25}}{1}=4\times 5=205​4​×125​=4×5=20.

This “simplify before multiplying” trick keeps numbers smaller and easier to work with.

Mini practice (with answers)

Try these in your head or on paper:

  1. 25×3=?\frac{2}{5}\times 3=?52​×3=?
  2. 56×4=?\frac{5}{6}\times 4=?65​×4=?
  3. 213×3=?2\frac{1}{3}\times 3=?231​×3=?

Answers:

  1. 25×3=65=115\frac{2}{5}\times 3=\frac{6}{5}=1\frac{1}{5}52​×3=56​=151​.
  2. 56×4=206=103=313\frac{5}{6}\times 4=\frac{20}{6}=\frac{10}{3}=3\frac{1}{3}65​×4=620​=310​=331​.
  3. 213=732\frac{1}{3}=\frac{7}{3}231​=37​, so 73×3=213=7\frac{7}{3}\times 3=\frac{21}{3}=737​×3=321​=7.

Simple HTML table of examples

Since you asked for tables as HTML, here’s a quick reference:

html

<table>
  <tr>
    <th>Expression</th>
    <th>Step as Fractions</th>
    <th>Product</th>
    <th>Mixed Number</th>
  </tr>
  <tr>
    <td>1/8 × 5</td>
    <td>(1/8) × (5/1)</td>
    <td>5/8</td>
    <td>5/8</td>
  </tr>
  <tr>
    <td>3/4 × 4</td>
    <td>(3/4) × (4/1)</td>
    <td>12/4</td>
    <td>3</td>
  </tr>
  <tr>
    <td>1/3 × 15</td>
    <td>(1/3) × (15/1)</td>
    <td>15/3</td>
    <td>5</td>
  </tr>
  <tr>
    <td>1 2/5 × 10</td>
    <td>(7/5) × (10/1)</td>
    <td>70/5</td>
    <td>14</td>
  </tr>
</table>

TL;DR:

  • Turn the whole number into a fraction with 1 on the bottom.
  • Multiply tops, multiply bottoms, then simplify or turn into a mixed number.

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