Here’s a ready-to-use “Quick Scoop” style explainer post tailored to the query “which fraction is equivalent to…”.

Which Fraction Is Equivalent To…?

Ever get stuck on a worksheet that says “Which fraction is equivalent to …?” and shows a list of choices underneath? This is a classic fractions question, and the trick to solving it is always the same: look for fractions that represent the same value , even if they look different on paper.

What “Equivalent Fractions” Really Mean

Two fractions are equivalent if they have the same value when simplified or written as a decimal.

  • Example:
    • 12\frac{1}{2}21​ and 24\frac{2}{4}42​ are equivalent because both represent “one half” of something.
* If you simplify 24\frac{2}{4}42​ by dividing top and bottom by 2, you get 12\frac{1}{2}21​.

Think of it like different names for the same amount—“0.5”, “one-half”, and “2/4” all describe the same portion.

The Two Main Tricks

Whenever you see a question like “Which fraction is equivalent to 3/4?” , your brain should go straight to these two strategies.

1. Multiply Top and Bottom by the Same Number

If you multiply the numerator (top) and denominator (bottom) by the same whole number , you get an equivalent fraction.

  • Starting fraction: 34\frac{3}{4}43​
  • Multiply by 2:
    • Numerator: 3×2=63\times 2=63×2=6
    • Denominator: 4×2=84\times 2=84×2=8
    • New fraction: 68\frac{6}{8}86​ → equivalent to 34\frac{3}{4}43​.

More examples:

  • 14\frac{1}{4}41​:
    • Multiply both by 2 → 28\frac{2}{8}82​
* Multiply both by 3 → 312\frac{3}{12}123​
  • 23\frac{2}{3}32​:
    • Multiply both by 5 → 1015\frac{10}{15}1510​
* Multiply both by 6 → 1218\frac{12}{18}1812​

So if your problem is:

Which fraction is equivalent to 2/3?
and the choices include 10/15 and 5/6 , you can spot that 10/15 is equivalent (both top and bottom are 2×5 and 3×5).

2. Divide Top and Bottom by the Same Number (Simplifying)

You can also go the other way: divide both numerator and denominator by the same number to see what a fraction simplifies to.

  • Example: 72108\frac{72}{108}10872​
* Both 72 and 108 are divisible by 2:
  * 72÷2=3672\div 2=3672÷2=36
  * 108÷2=54108\div 2=54108÷2=54
  * So 72108=3654\frac{72}{108}=\frac{36}{54}10872​=5436​.

* You can keep simplifying until you can’t go further.

This helps when the question is reversed, like:

Are 2/12 and 3/18 equivalent?

You can simplify both or use a quick method like cross-multiplication:

  • 2×18=362\times 18=362×18=36
  • 3×12=363\times 12=363×12=36
    The products match, so the fractions are equivalent.

Quick Methods to Check Equivalence

If your question provides several options and asks “Which fraction is equivalent to…” , here’s a simple mental checklist.

  1. Simplify each option
    • Reduce each choice to lowest terms and see which one matches the original fraction.
 * Example: Original: 34\frac{3}{4}43​
   * Option A: 68\frac{6}{8}86​ → divide by 2 → 34\frac{3}{4}43​ ✅

   * Option B: 612\frac{6}{12}126​ → divide by 6 → 12\frac{1}{2}21​ ❌
  1. Cross-multiply two fractions
    • For fractions ab\frac{a}{b}ba​ and cd\frac{c}{d}dc​:
      • Compute a×da\times da×d and b×cb\times cb×c.
      • If the products are equal, the fractions are equivalent.
 * Example: Are 212\frac{2}{12}122​ and 318\frac{3}{18}183​ equivalent?
   * 2×18=362\times 18=362×18=36
   * 3×12=363\times 12=363×12=36 → products match → they are equivalent.
  1. Compare decimal forms (when easy)
    • Convert both fractions to decimals.
    • If the decimals match, the fractions are equivalent.
 * Example:
   * 12=0.5\frac{1}{2}=0.521​=0.5
   * 24=0.5\frac{2}{4}=0.542​=0.5 → equivalent.

Example Question Types (Like on Worksheets)

Here are some typical prompts you might see under the heading “Which fraction is equivalent to…” and how you’d think them through.

Type 1: Single Correct Choice

Which fraction is equivalent to 3/4?
A) 6/8
B) 3/8
C) 4/6

  • Check A: 6/86/86/8 → divide by 2 → 3/43/43/4 ✅
  • Check B: 3/83/83/8 → already simplified → not 3/4 ❌
  • Check C: 4/64/64/6 → divide by 2 → 2/32/32/3 ❌

Answer: A) 6/8.

Type 2: Fill in the Blank

14=__8\frac{1}{4}=\frac{\\}{8}41​=8__​

You ask: “What did we multiply 4 by to get 8?”

  • 4 × 2 = 8 → so multiply the numerator 1 by 2 as well → 1 × 2 = 2.

Answer: 14=28\frac{1}{4}=\frac{2}{8}41​=82​.

Type 3: Multiple Equivalent Fractions

Write two fractions equivalent to 2/3.

You pick any whole numbers to multiply:

  • Multiply by 2: 2×23×2=46\frac{2\times 2}{3\times 2}=\frac{4}{6}3×22×2​=64​
  • Multiply by 5: 2×53×5=1015\frac{2\times 5}{3\times 5}=\frac{10}{15}3×52×5​=1510​

Possible answers: 4/6 and 10/15.

Handy Mini-Table of Common Equivalent Fractions

Here’s an HTML table you can reuse in a worksheet or blog post, showing popular fractions and some equivalents.

html

<table>
  <thead>
    <tr>
      <th>Base Fraction</th>
      <th>Equivalent Fraction #1</th>
      <th>Equivalent Fraction #2</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>1/2</td>
      <td>2/4</td>
      <td>3/6</td>
    </tr>
    <tr>
      <td>1/3</td>
      <td>2/6</td>
      <td>3/9</td>
    </tr>
    <tr>
      <td>1/4</td>
      <td>2/8</td>
      <td>3/12</td>
    </tr>
    <tr>
      <td>2/3</td>
      <td>4/6</td>
      <td>10/15</td>
    </tr>
    <tr>
      <td>3/4</td>
      <td>6/8</td>
      <td>9/12</td>
    </tr>
  </tbody>
</table>

All of these pairs come from multiplying numerator and denominator by the same whole number (like 2, 3, 5, etc.).

Quick “Story” to Remember the Rule

Imagine you and a friend are sharing pizzas:

  • You cut one pizza into 2 slices and eat 1 slice → that’s 1/21/21/2.
  • Your friend cuts the same-size pizza into 4 slices and eats 2 slices → that’s 2/42/42/4.

You both ate the same amount of pizza , even though the fractions (1/2 and 2/4) look different. That’s exactly what equivalent fractions are.

TL;DR – The Core Rule

When you see a question like “Which fraction is equivalent to…” :

  • Multiply or divide the numerator and denominator of the original fraction by the same number.
  • Or simplify each answer choice and see which one matches the original.
  • If both fractions simplify to the same basic form, they are equivalent.

If you send me the exact fraction and answer choices you’re working with, I can walk through that specific problem step by step.