To multiply fractions, multiply the top numbers (numerators), multiply the bottom numbers (denominators), then simplify the result if you can.

Basic rule (super short version)

If you have
ab×cd\frac{a}{b}\times \frac{c}{d}ba​×dc​
the product is
a×cb×d\frac{a\times c}{b\times d}b×da×c​.

So you just:

  1. Multiply the numerators.
  2. Multiply the denominators.
  3. Simplify the fraction.

Step‑by‑step example

Let’s multiply 23×45\frac{2}{3}\times \frac{4}{5}32​×54​.

  1. Numerators: 2×4=82\times 4=82×4=8.
  2. Denominators: 3×5=153\times 5=153×5=15.
  3. Answer: 815\frac{8}{15}158​ (already in simplest form).

Another one: 14×58\frac{1}{4}\times \frac{5}{8}41​×85​.

  • Top: 1×5=51\times 5=51×5=5.
  • Bottom: 4×8=324\times 8=324×8=32.
  • Answer: 532\frac{5}{32}325​.

With mixed numbers

If you see something like 223×3142\frac{2}{3}\times 3\frac{1}{4}232​×341​:

  1. Turn mixed numbers into improper fractions:
    • 223=832\frac{2}{3}=\frac{8}{3}232​=38​.
    • 314=1343\frac{1}{4}=\frac{13}{4}341​=413​.
  1. Multiply: 83×134=8×133×4=10412\frac{8}{3}\times \frac{13}{4}=\frac{8\times 13}{3\times 4}=\frac{104}{12}38​×413​=3×48×13​=12104​.
  1. Simplify: 10412=263=823\frac{104}{12}=\frac{26}{3}=8\frac{2}{3}12104​=326​=832​.

Quick “cancel first” trick

You can often make life easier by simplifying before multiplying.

Example: 26×47\frac{2}{6}\times \frac{4}{7}62​×74​

  • Notice 2/62/62/6 simplifies to 1/31/31/3 (divide top and bottom by 2).
  • Now do 13×47=1×43×7=421\frac{1}{3}\times \frac{4}{7}=\frac{1\times 4}{3\times 7}=\frac{4}{21}31​×74​=3×71×4​=214​.

Same answer, but the numbers stay smaller.

Tiny HTML table of examples

Here’s a quick reference in HTML like you asked:

html

<table>
  <thead>
    <tr>
      <th>Problem</th>
      <th>Step</th>
      <th>Work</th>
      <th>Answer</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>1/3 × 3/5</td>
      <td>Multiply tops and bottoms</td>
      <td>(1 × 3) / (3 × 5) = 3/15</td>
      <td>1/5 (simplified)</td>
    </tr>
    <tr>
      <td>2/3 × 4/5</td>
      <td>Multiply tops and bottoms</td>
      <td>(2 × 4) / (3 × 5) = 8/15</td>
      <td>8/15</td>
    </tr>
    <tr>
      <td>1/4 × 5/8</td>
      <td>Multiply tops and bottoms</td>
      <td>(1 × 5) / (4 × 8) = 5/32</td>
      <td>5/32</td>
    </tr>
    <tr>
      <td>2/6 × 4/7</td>
      <td>Simplify then multiply</td>
      <td>1/3 × 4/7 = 4/21</td>
      <td>4/21</td>
    </tr>
  </tbody>
</table>

(All examples follow the same core rule: multiply across, then simplify.)

One‑line memory hook

“Top with top, bottom with bottom, then shrink it if you can.”

TL;DR: Multiply the numerators, multiply the denominators, simplify the fraction; convert mixed numbers first, and you can often simplify before multiplying to make the arithmetic easier.