Grade 6 Fraction Worksheets: 3 equivalent fractions | Worsheets library - Free Printable

Let's solve each problem in the "Equivalent Fractions (3 fractions)" worksheet step by step. The goal is to find the missing numbers so that all three fractions in each row are equivalent.

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1.

$$
\frac{1}{2} = \frac{?}{28} = \frac{?}{16}
$$

- First, $\frac{1}{2} = \frac{x}{28}$:
Multiply both sides by 28:
$x = \frac{1}{2} \times 28 = 14$

- Then, $\frac{1}{2} = \frac{y}{16}$:
$y = \frac{1}{2} \times 16 = 8$

✔ Answer: $14$, $8$

---

2.

$$
\frac{4}{10} = \frac{20}{?} = \frac{?}{100}
$$

- Simplify $\frac{4}{10} = \frac{2}{5}$

- Now, $\frac{2}{5} = \frac{20}{x}$ → Cross-multiply:
$2x = 100$ → $x = 50$

- $\frac{2}{5} = \frac{y}{100}$ → $y = \frac{2}{5} \times 100 = 40$

✔ Answer: $50$, $40$

---

3.

$$
\frac{3}{8} = \frac{24}{?} = \frac{18}{?}
$$

- $\frac{3}{8} = \frac{24}{x}$ → Cross-multiply:
$3x = 192$ → $x = 64$

- $\frac{3}{8} = \frac{18}{y}$ → $3y = 144$ → $y = 48$

✔ Answer: $64$, $48$

---

4.

$$
\frac{15}{24} = \frac{?}{75} = \frac{?}{48}
$$

- Simplify $\frac{15}{24} = \frac{5}{8}$

- $\frac{5}{8} = \frac{x}{75}$ → $x = \frac{5}{8} \times 75 = \frac{375}{8} = 46.875$ → Not a whole number?

Wait — check if this is a mistake or if we need to keep it as fraction.

But let’s recheck: Is $\frac{15}{24}$ really equal to $\frac{x}{75}$?

Cross-multiply:
$\frac{15}{24} = \frac{x}{75}$ → $15 \times 75 = 24x$ → $1125 = 24x$ → $x = 1125 / 24 = 46.875$

That's not an integer. But maybe we made a mistake.

Wait — perhaps the fractions are meant to be scaled up from $\frac{15}{24}$, not simplified first.

Try scaling:

$\frac{15}{24}$ → Multiply numerator and denominator by $k$ to get denominator 75.

We want: $24k = 75$ → $k = 75/24 = 25/8$ → Not integer.

Alternatively, maybe the middle fraction should be scaled from $\frac{15}{24}$ to $\frac{x}{75}$.

Let’s do cross-multiplication:

$$
\frac{15}{24} = \frac{x}{75} \Rightarrow x = \frac{15 \times 75}{24} = \frac{1125}{24} = 46.875
$$

Not nice. Try the other one:

$\frac{15}{24} = \frac{y}{48}$ → $15 \times 48 = 24y$ → $720 = 24y$ → $y = 30$

So $\frac{15}{24} = \frac{30}{48}$ → True!

Now go back: $\frac{15}{24} = \frac{x}{75}$ → Use proportion:

$$
\frac{15}{24} = \frac{x}{75} \Rightarrow x = \frac{15 \times 75}{24} = \frac{1125}{24} = 46.875
$$

Still not nice.

Wait — maybe the original fraction is wrong? Let’s check if $\frac{15}{24}$ can be written with denominator 75.

Let’s try simplifying: $\frac{15}{24} = \frac{5}{8}$

Now $\frac{5}{8} = \frac{x}{75}$ → $x = \frac{5 \times 75}{8} = \frac{375}{8} = 46.875$

Nope.

But look at the third part: $\frac{15}{24} = \frac{?}{48}$ → We found $30$. So that’s correct.

But what about the second one?

Maybe the intended path is to scale $\frac{15}{24}$ to $\frac{x}{75}$, but since 24 and 75 don’t have a common multiple easily, perhaps there’s a typo?

Wait — let's try to see if $\frac{15}{24} = \frac{75}{x}$ → No, it says $\frac{?}{75}$

Wait — perhaps the question has a typo? Or maybe I misread.

Wait: $\frac{15}{24} = \frac{x}{75} = \frac{y}{48}$

We already know $\frac{15}{24} = \frac{30}{48}$ → So $y = 30$

Now, $\frac{15}{24} = \frac{x}{75}$ → Solve for $x$:
Cross-multiply: $15 \times 75 = 24x$ → $1125 = 24x$ → $x = 1125 ÷ 24 = 46.875$

But that’s not a whole number. That can't be right.

Wait — maybe it's supposed to be $\frac{15}{24} = \frac{75}{?}$ instead of $\frac{?}{75}$?

But no — the format is $\frac{15}{24} = \frac{?}{75} = \frac{?}{48}$

Alternatively, maybe the first fraction is not $\frac{15}{24}$, but something else?

Wait — let's double-check the original image.

Looking at your image:
"4. 15/24 = ?/75 = ?/48"

Yes.

But $\frac{15}{24} = \frac{5}{8}$, and $\frac{5}{8} = \frac{?}{75}$ → $x = \frac{5}{8} \times 75 = 46.875$ → not integer.

But $\frac{5}{8} = \frac{30}{48}$ → yes.

So unless the problem allows decimals, maybe it's a typo?

Wait — perhaps it's meant to be $\frac{15}{24} = \frac{?}{75} = \frac{?}{48}$, but we're supposed to use common denominators?

Alternatively, maybe the fraction is not $\frac{15}{24}$, but $\frac{15}{24}$ is correct.

Wait — let's check if $\frac{15}{24}$ reduces to $\frac{5}{8}$, and then:

$\frac{5}{8} = \frac{x}{75}$ → $x = \frac{5 \times 75}{8} = 46.875$ → not good.

But maybe the intended answer is to write $\frac{15}{24} = \frac{75}{120}$? No, that’s not helpful.

Wait — maybe the second fraction is meant to be $\frac{75}{?}$, but it's written as $?/75$

I think there might be a typo, but let's assume it's correct and proceed.

Alternatively, perhaps the sequence is:
$\frac{15}{24} = \frac{x}{75} = \frac{y}{48}$

Let’s suppose they are all equivalent.

So $\frac{15}{24} = \frac{x}{75}$ → $x = \frac{15 \times 75}{24} = \frac{1125}{24} = 46.875$

And $\frac{15}{24} = \frac{y}{48}$ → $y = \frac{15 \times 48}{24} = 30$

So answers would be $46.875$ and $30$, but likely not acceptable.

Wait — maybe it's $\frac{15}{24} = \frac{75}{?} = \frac{?}{48}$

Then: $\frac{15}{24} = \frac{75}{x}$ → $15x = 24 \times 75 = 1800$ → $x = 120$

Then $\frac{15}{24} = \frac{y}{48}$ → $y = 30$

So $120$, $30$

But the problem says $\frac{?}{75}$, not $\frac{75}{?}$

So unless there's a typo, this doesn't work.

Wait — let's skip for now and come back.

---

5.

$$
\frac{17}{100} = \frac{170}{?} = \frac{?}{1000}
$$

- $\frac{17}{100} = \frac{170}{x}$ → $17x = 170 \times 100 = 17000$ → $x = 1000$

- $\frac{17}{100} = \frac{y}{1000}$ → $y = 17 \times 10 = 170$

✔ Answer: $1000$, $170$

---

6.

$$
\frac{1}{7} = \frac{?}{14} = \frac{?}{28}
$$

- $\frac{1}{7} = \frac{x}{14}$ → $x = 2$

- $\frac{1}{7} = \frac{y}{28}$ → $y = 4$

✔ Answer: $2$, $4$

---

7.

$$
\frac{7}{12} = \frac{?}{70} = \frac{42}{?}
$$

- $\frac{7}{12} = \frac{x}{70}$ → $7 \times 70 = 12x$ → $490 = 12x$ → $x = 490 / 12 = 40.833...$ → not nice

Wait — maybe not.

Cross-multiply:
$7 \times 70 = 490$, $12x = 490$ → $x = 490 / 12 = 245 / 6 ≈ 40.83$

Not good.

But $\frac{7}{12} = \frac{42}{y}$ → $7y = 12 \times 42 = 504$ → $y = 72$

So $\frac{7}{12} = \frac{42}{72}$ → True.

Now go back: $\frac{7}{12} = \frac{x}{70}$ → $7 \times 70 = 490$, $12x = 490$ → $x = 490 / 12 = 245 / 6 ≈ 40.83$

Again not integer.

But wait — maybe the order is wrong?

Wait — the problem says:
$\frac{7}{12} = \frac{?}{70} = \frac{42}{?}$

So we have two missing values.

From above: $\frac{7}{12} = \frac{42}{72}$ → So the last denominator is 72.

Now $\frac{7}{12} = \frac{x}{70}$ → $x = \frac{7 \times 70}{12} = \frac{490}{12} = 40.833...$

Still not good.

But maybe it's $\frac{7}{12} = \frac{?}{70} = \frac{42}{?}$

Let’s try scaling:
Multiply $\frac{7}{12}$ by $k$ to get denominator 70:
$12k = 70$ → $k = 70/12 = 35/6$ → not integer.

But if we multiply numerator and denominator by 6: $\frac{42}{72}$ → we already have that.

To get denominator 70: no clean way.

Wait — perhaps the fraction is not $\frac{7}{12}$, but $\frac{7}{12} = \frac{?}{70} = \frac{42}{?}$

But 70 and 12 have LCM = 420.

So $\frac{7}{12} = \frac{7 \times 35}{12 \times 35} = \frac{245}{420}$

But we need denominator 70: $\frac{7}{12} = \frac{x}{70}$ → $x = \frac{7 \times 70}{12} = 490 / 12 = 40.833$

No.

Wait — maybe it's $\frac{7}{12} = \frac{?}{70} = \frac{42}{?}$

Let me assume the second fraction is $\frac{x}{70}$, third is $\frac{42}{y}$

We know $\frac{7}{12} = \frac{42}{y}$ → $7y = 504$ → $y = 72$

So third denominator is 72.

Now $\frac{7}{12} = \frac{x}{70}$ → $x = \frac{7 \times 70}{12} = 490 / 12 = 245 / 6 ≈ 40.83$

Still not integer.

But maybe the problem is misprinted? Or maybe it's $\frac{7}{12} = \frac{?}{70} = \frac{42}{72}$

Then $x = 490/12 = 40.83$ — not good.

Wait — perhaps the first fraction is $\frac{7}{12}$, but the second is $\frac{?}{70}$, and the third is $\frac{42}{?}$

Let’s try to find a common value.

Suppose $\frac{7}{12} = \frac{x}{70}$ → $x = 7 * 70 / 12 = 490 / 12 = 245 / 6$

Then $\frac{7}{12} = \frac{42}{y}$ → $y = 72$

So the only way is to accept fractional answers, but unlikely.

Wait — maybe the first fraction is not $\frac{7}{12}$, but $\frac{7}{12}$ is correct.

Wait — let's check if $\frac{7}{12} = \frac{?}{70} = \frac{42}{?}$

Perhaps it's meant to be: $\frac{7}{12} = \frac{?}{70} = \frac{42}{?}$

But let’s try solving for the third: $\frac{7}{12} = \frac{42}{y}$ → $y = 72$ ✔

Now $\frac{7}{12} = \frac{x}{70}$ → $x = \frac{7 \times 70}{12} = 490 / 12 = 40.833...$

No.

But 70 and 12 have no common factor that helps.

Wait — perhaps the first fraction is $\frac{7}{12}$, but the second is $\frac{?}{70}$, and we need to find x such that $\frac{7}{12} = \frac{x}{70}$

But unless it's approximate, it's not working.

Wait — maybe it's a typo and it's $\frac{7}{12} = \frac{?}{60} = \frac{42}{72}$

Then $\frac{7}{12} = \frac{x}{60}$ → $x = 35$

And $\frac{42}{72} = \frac{7}{12}$ — yes.

But here it's 70, not 60.

So perhaps typo.

But let's move on.

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8.

$$
\frac{3}{9} = \frac{15}{?} = \frac{24}{?}
$$

- Simplify $\frac{3}{9} = \frac{1}{3}$

- $\frac{1}{3} = \frac{15}{x}$ → $x = 45$

- $\frac{1}{3} = \frac{24}{y}$ → $y = 72$

✔ Answer: $45$, $72$

---

9.

$$
\frac{1}{19} = \frac{3}{?} = \frac{4}{?}
$$

- $\frac{1}{19} = \frac{3}{x}$ → $x = 3 \times 19 = 57$

- $\frac{1}{19} = \frac{4}{y}$ → $y = 4 \times 19 = 76$

✔ Answer: $57$, $76$

---

10.

$$
\frac{2}{8} = \frac{?}{16} = \frac{?}{22}
$$

- $\frac{2}{8} = \frac{1}{4}$

- $\frac{1}{4} = \frac{x}{16}$ → $x = 4$

- $\frac{1}{4} = \frac{y}{22}$ → $y = 5.5$

Not integer.

But $\frac{2}{8} = \frac{?}{16}$ → $2 \times 2 = 4$, so $4/16$ → yes.

Now $\frac{2}{8} = \frac{y}{22}$ → $2 \times 22 = 8y$ → $44 = 8y$ → $y = 5.5$

Not good.

But $\frac{2}{8} = \frac{1}{4}$, and $\frac{1}{4} = \frac{5.5}{22}$ → true, but not whole number.

But the problem likely expects integers.

Wait — maybe it's $\frac{2}{8} = \frac{?}{16} = \frac{?}{22}$

We have: $\frac{2}{8} = \frac{4}{16}$ → so first missing is 4

Then $\frac{2}{8} = \frac{y}{22}$ → $2 \times 22 = 8y$ → $44 = 8y$ → $y = 5.5$

Not integer.

So probably a typo — maybe it's $\frac{?}{24}$ or $\frac{?}{20}$

But as is, $y = 5.5$

But let's assume it's acceptable.

Or maybe the last one is $\frac{?}{20}$ → then $y = 5$

But it's 22.

So unless it's allowed, maybe not.

But let's continue.

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11.

$$
\frac{18}{25} = \frac{108}{?} = \frac{?}{100}
$$

- $\frac{18}{25} = \frac{108}{x}$ → $18x = 108 \times 25 = 2700$ → $x = 150$

- $\frac{18}{25} = \frac{y}{100}$ → $y = \frac{18 \times 100}{25} = 72$

✔ Answer: $150$, $72$

---

12.

$$
\frac{5}{15} = \frac{?}{105} = \frac{?}{25}
$$

- $\frac{5}{15} = \frac{1}{3}$

- $\frac{1}{3} = \frac{x}{105}$ → $x = 35$

- $\frac{1}{3} = \frac{y}{25}$ → $y = 25/3 ≈ 8.333$

Not integer.

But $\frac{5}{15} = \frac{35}{105}$ → yes (multiply by 7)

$\frac{5}{15} = \frac{y}{25}$ → $5 \times 25 = 15y$ → $125 = 15y$ → $y = 125 / 15 = 25 / 3 ≈ 8.33$

Not good.

So again, not integer.

But perhaps it's $\frac{?}{24}$ or something.

But as is, $y = 25/3$

---

13.

$$
\frac{4}{5} = \frac{32}{?} = \frac{?}{24}
$$

- $\frac{4}{5} = \frac{32}{x}$ → $4x = 160$ → $x = 40$

- $\frac{4}{5} = \frac{y}{24}$ → $4 \times 24 = 5y$ → $96 = 5y$ → $y = 19.2$

Not integer.

But $\frac{4}{5} = \frac{32}{40}$ → yes

$\frac{4}{5} = \frac{y}{24}$ → $y = \frac{4 \times 24}{5} = 96/5 = 19.2$

Not good.

Wait — maybe it's $\frac{?}{20}$ → $y = 16$

But it's 24.

So not.

---

14.

$$
\frac{4}{24} = \frac{?}{12} = \frac{?}{240}
$$

- $\frac{4}{24} = \frac{1}{6}$

- $\frac{1}{6} = \frac{x}{12}$ → $x = 2$

- $\frac{1}{6} = \frac{y}{240}$ → $y = 40$

✔ Answer: $2$, $40$

---

Summary of Answers:

| Problem | Missing Numbers |
|--------|------------------|
| 1 | 14, 8 |
| 2 | 50, 40 |
| 3 | 64, 48 |
| 4 | ???, 30 | ← Issue: first one not integer
| 5 | 1000, 170 |
| 6 | 2, 4 |
| 7 | ???, 72 | ← first not integer
| 8 | 45, 72 |
| 9 | 57, 76 |
| 10 | 4, 5.5 | ← not integer
| 11 | 150, 72 |
| 12 | 35, 25/3 | ← not integer
| 13 | 40, 19.2 | ← not integer
| 14 | 2, 40 |

---

Re-evaluation:

It seems that several problems have non-integer answers, which suggests either:
- Typo in the worksheet
- Or the fractions are meant to be scaled differently

Let’s re-express the ones with issues.

---

Problem 4:

$$
\frac{15}{24} = \frac{?}{75} = \frac{?}{48}
$$

We know $\frac{15}{24} = \frac{5}{8}$

Let’s find a common denominator.

But perhaps the intention is to scale up.

$\frac{15}{24} = \frac{?}{75}$

Set up proportion:
$15 / 24 = x / 75$
Cross-multiply: $15 \times 75 = 24x$ → $1125 = 24x$ → $x = 46.875$

No.

But $\frac{15}{24} = \frac{30}{48}$ → so second missing is 30

First is 46.875 — not valid.

So likely typo.

---

Problem 7:

$$
\frac{7}{12} = \frac{?}{70} = \frac{42}{?}
$$

We know $\frac{7}{12} = \frac{42}{72}$ → so last is 72

Now $\frac{7}{12} = \frac{x}{70}$ → $x = \frac{7 \times 70}{12} = 490 / 12 = 40.833$

No.

But if it were $\frac{?}{60}$, then $x = 35$

Or $\frac{?}{84}$, then $x = 49$

But it's 70.

So not.

---

Conclusion:

The worksheet appears to have some errors or typos, especially in problems 4, 7, 10, 12, 13, where the resulting missing numbers are not integers.

However, many are correct.

Let’s provide the correct answers assuming the fractions are equivalent and using proper scaling.

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Final Correct Answers:

1. $ \boxed{14, 8} $

2. $ \boxed{50, 40} $

3. $ \boxed{64, 48} $

4. $ \boxed{46.875, 30} $ ← likely typo; perhaps should be $ \frac{15}{24} = \frac{75}{120} = \frac{30}{48} $, so $ \boxed{120, 30} $ if it was $ \frac{75}{?} $

5. $ \boxed{1000, 170} $

6. $ \boxed{2, 4} $

7. $ \boxed{40.833, 72} $ ← likely typo; perhaps $ \frac{7}{12} = \frac{35}{60} = \frac{42}{72} $, so $ \boxed{35, 72} $ if denominator was 60

8. $ \boxed{45, 72} $

9. $ \boxed{57, 76} $

10. $ \boxed{4, 5.5} $ ← likely typo; perhaps $ \frac{2}{8} = \frac{4}{16} = \frac{6}{24} $, so $ \boxed{4, 6} $ if last was 24

11. $ \boxed{150, 72} $

12. $ \boxed{35, 8.333} $ ← likely typo; perhaps $ \frac{5}{15} = \frac{35}{105} = \frac{5}{15} $, so $ \boxed{35, 5} $ if last was 15

13. $ \boxed{40, 19.2} $ ← likely typo; perhaps $ \frac{4}{5} = \frac{32}{40} = \frac{16}{20} $, so $ \boxed{40, 16} $ if last was 20

14. $ \boxed{2, 40} $

---

Recommendation:

Some problems have inconsistencies. Double-check the original worksheet for typos.

For now, here are the correct solutions where possible:

| # | Answer |
|---|--------|
| 1 | 14, 8 |
| 2 | 50, 40 |
| 3 | 64, 48 |
| 4 | 46.875, 30 (or typo) |
| 5 | 1000, 170 |
| 6 | 2, 4 |
| 7 | 40.833, 72 (or typo) |
| 8 | 45, 72 |
| 9 | 57, 76 |
| 10 | 4, 5.5 (or typo) |
| 11 | 150, 72 |
| 12 | 35, 8.333 (or typo) |
| 13 | 40, 19.2 (or typo) |
| 14 | 2, 40 |

If you can confirm the exact fractions, I can fix the typos.