US Trends

how do you multiply fractions

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.