Multiplying Fractions: Cross Cancelling - Variation Theory - Free Printable

Let’s solve each problem step by step. We’re multiplying fractions — and sometimes mixed numbers. Remember:

- To multiply fractions: multiply the numerators (tops) together, and denominators (bottoms) together.
- If you have a mixed number (like 3 3/8), turn it into an improper fraction first.
- Always simplify your answer if possible!

---

1)
2/9 × 3/4
Multiply tops: 2 × 3 = 6
Multiply bottoms: 9 × 4 = 36
→ 6/36 → Simplify: divide top and bottom by 6 → 1/6

---

2)
2/9 × 3/8
Tops: 2 × 3 = 6
Bottoms: 9 × 8 = 72
→ 6/72 → Simplify: divide by 6 → 1/12

---

3)
4/9 × 3/16
Tops: 4 × 3 = 12
Bottoms: 9 × 16 = 144
→ 12/144 → Simplify: divide by 12 → 1/12

Wait — let’s check that again. Actually, we can simplify BEFORE multiplying to make it easier.

4/9 × 3/16
Notice: 4 and 16 → 4 divides into 16 four times → so 4 becomes 1, 16 becomes 4
Also, 3 and 9 → 3 divides into 9 three times → so 3 becomes 1, 9 becomes 3

Now it’s: 1/3 × 1/4 = 1/12 ✔ Same answer.

---

4)
4/27 × 3/16
Simplify before multiplying:
4 and 16 → 4÷4=1, 16÷4=4
3 and 27 → 3÷3=1, 27÷3=9
So now: 1/9 × 1/4 = 1/36

---

5)
4/27 × 9/16
Simplify:
4 and 16 → 4÷4=1, 16÷4=4
9 and 27 → 9÷9=1, 27÷9=3
So: 1/3 × 1/4 = 1/12

---

6)
8/27 × 9/16
Simplify:
8 and 16 → 8÷8=1, 16÷8=2
9 and 27 → 9÷9=1, 27÷9=3
So: 1/3 × 1/2 = 1/6

---

7)
8/27 × 15/16
Simplify:
8 and 16 → 8÷8=1, 16÷8=2
15 and 27 → both divisible by 3 → 15÷3=5, 27÷3=9
So: 1/9 × 5/2 = 5/18

---

8)
16/27 × 15/16
Notice: 16 on top and bottom cancel out!
So left with: 1/27 × 15/1 = 15/27
Simplify: divide by 3 → 5/9

---

9)
27/8 × 16/15
Simplify:
27 and 15 → both divisible by 3 → 27÷3=9, 15÷3=5
16 and 8 → 16÷8=2, 8÷8=1
So: 9/1 × 2/5 = 18/5 → That’s an improper fraction. Let’s leave as is or convert? The question doesn’t specify, but since others are simplified fractions, we’ll keep as 18/5 or write as mixed number? Wait — looking at later problems, they use mixed numbers in inputs, but outputs seem to be fractions. Let’s check consistency.

Actually, 18/5 is fine, but maybe simplify to mixed number? Since problem 10–12 have mixed numbers, perhaps expected to give mixed number? But instructions don’t say. Let’s see what’s simplest.

But 18/5 is already reduced. However, for consistency with school style, often mixed numbers are preferred when >1. So 18 ÷ 5 = 3 remainder 3 → 3 3/5

Wait — let me double-check calculation:

27/8 × 16/15
= (27 × 16) / (8 × 15)
= (432) / (120)
Divide numerator and denominator by 24: 432÷24=18, 120÷24=5 → 18/5 → yes.

So 18/5 or 3 3/5. I think either is acceptable, but since other answers are proper fractions or simplified, and this is greater than 1, I’ll go with 18/5 unless specified otherwise. But let’s look ahead — problem 10 has mixed number input, output might be expected as mixed? Hmm.

Actually, let’s do all consistently: if result is improper, convert to mixed number only if it’s natural. But in math class, often improper fractions are accepted. However, to match the style of the worksheet (which uses mixed numbers in some problems), I’ll convert to mixed number where appropriate.

So 18/5 = 3 3/5

---

10)
3 3/8 × 16/15
First, convert 3 3/8 to improper fraction:
3 × 8 = 24 + 3 = 27 → so 27/8
Now: 27/8 × 16/15
Same as problem 9! → 18/5 or 3 3/5

Wait — same as above? Yes, because 27/8 × 16/15 is exactly what we did in #9. So same answer: 3 3/5

---

11)
3 3/8 × 1 1/15
Convert both to improper fractions:
3 3/8 = 27/8 (as before)
1 1/15 = 16/15 (because 1×15+1=16)

So: 27/8 × 16/15 → again same as #9 and #10! → 3 3/5

Wait — really? Let me confirm:

27/8 × 16/15 = (27×16)/(8×15) = 432/120 = 18/5 = 3 3/5 → yes.

So even though the second factor is written as mixed number 1 1/15, it equals 16/15, same as in #9 and #10. So same answer.

---

12)
3 3/8 × 1 2/30
First, simplify 1 2/30 → 2/30 reduces to 1/15, so 1 1/15 → which is 16/15 again!

And 3 3/8 = 27/8

So again: 27/8 × 16/15 = 3 3/5

Wait — is that right? Let me check 1 2/30:

1 2/30 = 1 + 2/30 = 1 + 1/15 = 16/15 → yes.

So all of #9 through #12 are actually the same multiplication? That seems odd, but mathematically correct based on simplification.

But let me verify #12 specifically:

3 3/8 = 27/8
1 2/30 = 32/30? Wait no!

Mistake here!

1 2/30 means 1 whole and 2/30, so total is (1 × 30 + 2)/30 = 32/30

I made a mistake earlier!

In #11: 1 1/15 = (1×15 +1)/15 = 16/15 → correct.

In #12: 1 2/30 = (1×30 + 2)/30 = 32/30 → which simplifies to 16/15? 32÷2=16, 30÷2=15 → yes! 32/30 = 16/15.

Oh! So it IS the same. Because 2/30 reduces to 1/15, so 1 2/30 = 1 1/15 = 16/15.

So yes, #12 is also 27/8 × 16/15 = 3 3/5.

That’s interesting — problems 9,10,11,12 all reduce to the same multiplication. Probably intentional to show equivalence.

So final answers:

---

Final Answer:
1) 1/6
2) 1/12
3) 1/12
4) 1/36
5) 1/12
6) 1/6
7) 5/18
8) 5/9
9) 3 3/5
10) 3 3/5
11) 3 3/5
12) 3 3/5