Which Of The Following Is Equal To The Fraction Below

Finding an equivalent fraction sounds like a basic skill — something you mastered in fourth grade and never thought about again. Then you're helping a kid with homework, or staring at a recipe that calls for 3/4 cup when you only have a 1/3 measure, or trying to compare two mortgage rates expressed differently, and suddenly it matters.

The question "which of the following is equal to the fraction below" shows up everywhere. But the reasoning* behind the answer? Code that handles ratios. Standardized tests. Because of that, kitchen math. Consider this: job aptitude screens. The format is always the same: one fraction, four or five options, only one correct answer. That's where people get tripped up.

What Is an Equivalent Fraction

Two fractions are equivalent when they represent the exact same quantity. Which means different numbers, same value. Which means 1/2 equals 2/4 equals 3/6 equals 50/100. The numerator and denominator change, but the proportion doesn't.

Think of it like currency. Here's the thing — the count* of coins differs. And four quarters, ten dimes, twenty nickels, a hundred pennies — all equal one dollar. The value* doesn't.

Mathematically, fraction a/b equals fraction c/d when a × d = b × c. It's the definitive test. Cross-multiplication. Plus, if the cross-products match, the fractions are equivalent. If they don't, they're not.

The Multiplication Rule

You create equivalent fractions by multiplying (or dividing) both the numerator and denominator by the same non-zero number. Which means multiply by 7: 21/35. Multiply top and bottom by 2: 3/5 becomes 6/10. The value stays identical because you're essentially multiplying by 1 — just written as 2/2, 7/7, 100/100.

This works in reverse too. 18/24 divided by 6 gives 3/4. Which means divide top and bottom by a common factor and you simplify. Same value, smaller numbers.

Why "Same Number" Matters

Here's where mistakes happen. 0.Day to day, 5 versus 0. 1/2 becomes 2/3 if you add 1 to both. Adding the same number to top and bottom does not* preserve equivalence. Think about it: that's not the same fraction. But 666... — clearly different.

Multiplying numerator and denominator by different numbers also breaks equivalence. That said, 2/3 × 2/5 = 4/15. Not equivalent to 2/3. The multiplier must be identical.

Why It Matters / Why People Care

Equivalent fractions aren't just a test-taking trick. They're the gateway to every fraction operation that follows.

Adding and Subtracting Requires Common Denominators

You can't add 1/3 + 1/4 directly. Still, the pieces are different sizes. But convert both to twelfths — 4/12 + 3/12 — and suddenly it's just 7/12. Finding equivalent fractions with a shared denominator is the only* way to add or subtract fractions with unlike denominators.

Comparing Fractions

Which is larger: 5/8 or 3/5? Not obvious at a glance. Day to day, convert both to fortieths: 25/40 versus 24/40. Now it's clear. 5/8 wins. Cross-multiplication works too (5×5=25, 8×3=24), but the equivalent-fraction approach builds the same intuition.

Real-World Scaling

Recipes. Construction plans. That said, map scales. Practically speaking, medication dosages. So any time you scale a ratio up or down, you're working with equivalent fractions. So a blueprint at 1/4" = 1' means every quarter inch on paper equals a foot in reality. In real terms, that's 1/48 scale. If you print the drawing at 50% size, the scale becomes 1/96. You just found an equivalent fraction.

Standardized Tests Love This Format

The "which of the following" question appears on the SAT, ACT, GRE, GMAT, ASVAB, Praxis, state certification exams, civil service tests — anywhere quantitative reasoning is measured. It's a reliable discriminator. Students who understand the concept answer in seconds. Students who memorized rules without understanding get stuck or guess.

How It Works: Finding the Match

Let's walk through the actual process. You're given a target fraction and a list of candidates. One matches. The rest don't.

Step 1: Simplify the Target (If Possible)

Start by reducing the given fraction to lowest terms. It's easier to recognize equivalents when the numbers are small.

Given: 24/36

Both divisible by 2: 12/18
Still divisible by 2: 6/9
Divisible by 3: 2/3

Lowest terms: 2/3. Any equivalent fraction must also simplify to 2/3.

Step 2: Test Each Option

Two reliable methods. Pick one and stick with it.

Continue exploring with our guides on hope is the thing with feathers meaning and replace with an expression that will make the equation valid.

Method A: Cross-Multiplication

For each option, cross-multiply with the target (or its simplified form).

Target: 2/3
Option: 14/21

2 × 21 = 42
3 × 14 = 42

Match. It's equivalent.

Option: 10/16

2 × 16 = 32
3 × 10 = 30

No match. Not equivalent.

Cross-multiplication is fast, works with any size numbers, and never lies.

Method B: Simplify Each Option

Reduce every candidate to lowest terms. See which one matches your simplified target.

Option: 14/21 → divide by 7 → 2/3 ✓
Option: 10/16 → divide by 2 → 5/8 ✗
Option: 8/12 → divide by 4 → 2/3 ✓ (wait, two matches?)

If two options simplify to the same fraction, check the original problem. Sometimes tests include multiple* correct answers and ask "select all that apply." Sometimes you mis-simplified. Double-check.

Step 3: Verify the Multiplier Relationship

When you spot the equivalent fraction, you should be able to name the multiplier.

2/3 → 14/21. Multiply top and bottom by 7.That said, 2/3 → 200/300. 2/3 → 8/12. Here's the thing — multiply by 4. Multiply by 100.

If you can't find a clean integer multiplier, something's off. Equivalent fractions always* share an integer multiplier relationship (assuming both are in integer form).

Worked Example

Question: Which of the following is equal to 18/24?

A) 3/4
B) 6/8
C) 9/12
D) 15/2

Worked Example (continued)

Question: Which of the following is equal to 18⁄24?

A) 3⁄4  B) 6⁄8  C) 9⁄12  D) 15⁄2

Step 1 – Simplify the target.
Both numerator and denominator are divisible by 6:

[ \frac{18}{24};=;\frac{18\div6}{24\div6};=;\frac{3}{4}. ]

So any equivalent fraction must also reduce to 3⁄4.

Step 2 – Test each option.

Options A, B, and C all simplify to 3⁄4, so each is equivalent to 18⁄24. Option D is not.

Step 3 – Identify the multiplier.
Starting from the reduced target 3⁄4:

• To get 3⁄4 → 3⁄4 (A) multiply by 1.
• To get 3⁄4 → 6⁄8 (B) multiply numerator and denominator by 2.
• To get 3⁄4 → 9⁄12 (C) multiply by 3.

Each equivalent fraction is produced by an integer multiplier, confirming the relationship.

What if the test expects a single answer?
If the item is phrased “Which one of the following …?” the test‑maker likely intends the simplest form, 3⁄4 (choice A). In that case, the other options are considered “distractors” that are technically equivalent but not in lowest terms. Always read the stem carefully: “select all that apply” versus “choose the best answer.”

Conclusion

Mastering equivalent fractions hinges on two habits: (1) reduce the given fraction to lowest terms first, and (2) verify each candidate by either cross‑multiplication or by reducing it to the same simplest form. When you can name the integer multiplier that links the target to a choice, you have certainty—no guessing required. Apply this routine on any standardized‑test item, and you’ll turn a seemingly tricky “which of the following” question into a quick, confident answer.