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

How to Multiply Fractions (Quick Scoop)

1. The core rule

When you see something like ab×cd\frac{a}{b}\times \frac{c}{d}ba​×dc​:

  • Multiply the numerators: a×ca\times ca×c.
  • Multiply the denominators: b×db\times db×d.
  • Write the answer as one fraction and simplify.

For example:
13×53=1×53×3=59\frac{1}{3}\times \frac{5}{3}=\frac{1\times 5}{3\times 3}=\frac{5}{9}31​×35​=3×31×5​=95​.

Another example:
23×45=2×43×5=815\frac{2}{3}\times \frac{4}{5}=\frac{2\times 4}{3\times 5}=\frac{8}{15}32​×54​=3×52×4​=158​.

2. Step‑by‑step recipe

  1. Make sure each number is a proper or improper fraction (no mixed numbers yet).
  2. Multiply the numerators.
  3. Multiply the denominators.
  4. Simplify the fraction (divide top and bottom by any common factor).

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

  • Multiply tops: 2×4=82\times 4=82×4=8.
  • Multiply bottoms: 6×7=426\times 7=426×7=42.
  • Fraction: 842\frac{8}{42}428​.
  • Simplify by dividing by 2 → 421\frac{4}{21}214​.

3. A quicker trick: simplify first

You can often make life easier by simplifying before you multiply.

  • Look for common factors “across” a fraction: a numerator from one and a denominator from the other.
  • Divide them by the same number first, then multiply.

Example (same problem as above):
26×47\frac{2}{6}\times \frac{4}{7}62​×74​

  • Notice 2 and 6 share a factor of 2 → 26=13\frac{2}{6}=\frac{1}{3}62​=31​.
  • Now you have 13×47\frac{1}{3}\times \frac{4}{7}31​×74​.
  • Multiply tops: 1×4=41\times 4=41×4=4.
  • Multiply bottoms: 3×7=213\times 7=213×7=21.
  • Answer: 421\frac{4}{21}214​ (no extra simplification needed).

Same answer, less work.

4. Mixed numbers and whole numbers

Mixed numbers

If you have mixed numbers (like 1231\frac{2}{3}132​):

  1. Convert to improper fractions.
  2. Then use the normal fraction‑multiplication steps.
  3. Simplify and optionally convert back to a mixed number.

Example: 123×3141\frac{2}{3}\times 3\frac{1}{4}132​×341​

  • Convert:
    • 123=531\frac{2}{3}=\frac{5}{3}132​=35​.
    • 314=1343\frac{1}{4}=\frac{13}{4}341​=413​.
  • Multiply: 53×134=6512\frac{5}{3}\times \frac{13}{4}=\frac{65}{12}35​×413​=1265​.
  • Simplify if possible (here it’s already simplified); convert to mixed number if desired.

Whole numbers

Any whole number nnn is n1\frac{n}{1}1n​.

Example: 53×4\frac{5}{3}\times 435​×4

  • Rewrite 4 as 41\frac{4}{1}14​.
  • 53×41=5×43×1=203\frac{5}{3}\times \frac{4}{1}=\frac{5\times 4}{3\times 1}=\frac{20}{3}35​×14​=3×15×4​=320​.

5. Tiny FAQ (today‑style)

  • Does order matter?
    No. 23×45=45×23\frac{2}{3}\times \frac{4}{5}=\frac{4}{5}\times \frac{2}{3}32​×54​=54​×32​.
  • What if the answer is an improper fraction?
    It’s perfectly fine, but teachers often want a mixed number, so convert if needed.
  • Is multiplying fractions harder than adding them?
    Not really: multiplying is usually easier because you don’t need common denominators; you just multiply straight across.

6. Simple HTML table version

Here’s a small HTML table of examples you can reuse:

html

<table>
  <tr>
    <th>Problem</th>
    <th>Step Work</th>
    <th>Answer</th>
  </tr>
  <tr>
    <td>1/3 × 5/3</td>
    <td>(1 × 5) / (3 × 3)</td>
    <td>5/9</td>
  </tr>
  <tr>
    <td>2/3 × 4/5</td>
    <td>(2 × 4) / (3 × 5)</td>
    <td>8/15</td>
  </tr>
  <tr>
    <td>2/6 × 4/7</td>
    <td>Simplify first → 1/3 × 4/7</td>
    <td>4/21</td>
  </tr>
  <tr>
    <td>5/3 × 4</td>
    <td>4 = 4/1 → (5 × 4) / (3 × 1)</td>
    <td>20/3</td>
  </tr>
</table>

All information gathered from public forums or data available on the internet and portrayed here.