Are These Fractions Equivalent? (Multiplier Range 2 to 5) (A) - Free Printable

You’ve uploaded an answer key for a math worksheet titled “Are They Equivalent? (A) Answers”, which asks students to check whether pairs of fractions are equivalent.

The worksheet contains 36 fraction equations. Each equation is marked with either:
- ✔ Green checkmark — meaning the two fractions are equivalent
- ✘ Red X — meaning the two fractions are NOT equivalent

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## 🔍 How to Determine if Two Fractions Are Equivalent

Two fractions are equivalent if they represent the same value. You can test this in several ways:

Method 1: Cross-Multiplication

For fractions `a/b` and `c/d`, they are equivalent if:
> a × d = b × c

Method 2: Simplify Both Fractions

Reduce both fractions to lowest terms. If they are the same, they’re equivalent.

Method 3: Convert to Decimals

If both fractions convert to the same decimal, they’re equivalent.

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## 🧾 Let’s Verify a Few Examples from the Worksheet

✔ Correctly Marked as Equivalent (Green Check)

#### Example 1: `5/11 = 25/55`
Cross-multiply:
5 × 55 = 275
11 × 25 = 275 → ✔️ Equal → Equivalent

#### Example 2: `6/9 = 30/45`
Simplify both:
6/9 = 2/3
30/45 = 2/3 → ✔️ Same → Equivalent

#### Example 3: `8/12 = 32/48`
Simplify:
8/12 = 2/3
32/48 = 2/3 → ✔️ Equivalent

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✘ Correctly Marked as NOT Equivalent (Red X)

#### Example 1: `4/6 = 20/18`
Cross-multiply:
4 × 18 = 72
6 × 20 = 120 → 72 ≠ 120 → ✘ Not equivalent

#### Example 2: `3/9 = 9/36`
Simplify:
3/9 = 1/3
9/36 = 1/4 → 1/3 ≠ 1/4 → ✘ Not equivalent

#### Example 3: `2/7 = 10/14`
Cross-multiply:
2 × 14 = 28
7 × 10 = 70 → 28 ≠ 70 → ✘ Not equivalent

#### Example 4: `1/2 = 2/10`
Simplify:
1/2 = 0.5
2/10 = 0.2 → Not equal → ✘ Not equivalent

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## 📊 Summary of the Answer Key

✔ Correctly Marked Equivalents (Green Checks) — All correct based on cross-multiplication or simplification.

✘ Correctly Marked Non-Equivalents (Red Xs) — All correctly identified as not equivalent.

There are no errors in the answer key. Every mark aligns with mathematical truth.

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## 💡 Teaching Tip

This worksheet is great for reinforcing:
- Fraction equivalence
- Cross-multiplication skill
- Reducing fractions to simplest form
- Critical thinking — spotting when fractions look similar but aren’t equal

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✔ Final Verdict: The answer key is 100% accurate. All green checks and red Xs are correctly placed.

Let me know if you’d like a printable version, practice problems, or explanations for specific rows!