Math Buzz worksheet featuring multiplication, subtraction, and coordinate graphing exercises.

Let’s go through each problem one by one. I’ll solve them step by step so you can follow along easily.

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1. Find the rule for Input → Output

We have:

Input | Output
------|-------
15 | 105
12 | 84
20 | 140
14 | 98
18 | 126

Look at the first pair: 15 → 105
What do we multiply 15 by to get 105?
→ 15 × 7 = 105 ✔

Check second: 12 × 7 = 84 ✔
Third: 20 × 7 = 140 ✔
Fourth: 14 × 7 = 98 ✔
Fifth: 18 × 7 = 126 ✔

So the rule is: Multiply the input by 7

Rule: × 7

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2. Multiply and simplify fractions

First problem:
½ × ⁷₁₀ = (1 × 7) / (2 × 10) = ⁷⁄₂₀
Can we simplify ⁷⁄₂₀?
7 and 20 have no common factors besides 1 → already simplified.

Answer: ⁷⁄₂₀

Second problem:
⁵⁄ × ³⁄₅ = (5 × 3) / (6 × 5) = ¹⁵⁄₃₀
Now simplify: divide numerator and denominator by 15 → ¹⁵÷₁₅ / ³⁰÷₁₅ = ¹⁄₂
Or notice: 5 in numerator and denominator cancel, and 3 and 6 → 3/6 = 1/2 → same result.

Answer: ¹⁄₂

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3. Subtract decimals

Problem: ___ = 7.4 – 2.9

Line up decimals:

 7.4
–2.9
_____

Start from right: 4 – 9 → can’t do, borrow 1 from 7 → becomes 6, and 4 becomes 14
14 – 9 = 5
Then 6 – 2 = 4

So: 4.5

Another subtraction:
65.1
– 9.8
______

Again, line up decimals:

 65.1
– 9.8
______

Right column: 1 – 8 → can’t do, borrow from 5 → 5 becomes 4, 1 becomes 11
11 – 8 = 3
Next: 4 – 9 → can’t do, borrow from 6 → 6 becomes 5, 4 becomes 14
14 – 9 = 5
Then 5 – 0 = 5 (since 9.8 has no tens digit)

Wait — let me write it clearly:

 65.1
– 9.8
= ?

Actually, think of it as:

65.1 minus 9.8

You can also think: 65.1 – 10 = 55.1, then add back 0.2 → 55.1 + 0.2 = 55.3

Or do it vertically:

 65.1
– 9.8
______
Borrow: 65.1 → 64 + 1.1 → but better:

Write as:

 65.1
– 9.8
______
Start from tenths: 1 < 8 → borrow from units place.

Units place is 5 → becomes 4, tenths become 11
11 – 8 = 3

Now units: 4 – 9 → can’t → borrow from tens.

Tens: 6 becomes 5, units become 14
14 – 9 = 5

Tens: 5 – 0 = 5

So answer is 55.3

✔ Double-check: 9.8 + 55.3 = 65.1 → yes!

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4. Find difference between 46.3 and 13.5

That means: 46.3 – 13.5

Line up:

 46.3
–13.5
______

Tenths: 3 – 5 → can’t → borrow from 6 → 6 becomes 5, 3 becomes 13
13 – 5 = 8

Units: 5 – 3 = 2

Tens: 4 – 1 = 3

So: 32.8

Check: 13.5 + 32.8 = 46.3 → correct.

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5. Coordinate plane — find point names

Given grid with points labeled A, B, C, D.

Ordered pairs given:

(4, 4) → look at x=4, y=4 → that’s point A

(9, 0) → x=9, y=0 → on x-axis → point B

(7, 10) → x=7, y=10 → point C

(2, 11) → x=2, y=11 → point D

So match:

(4, 4) → A
(9, 0) → B
(7, 10) → C
(2, 11) → D

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Final Answers compiled:

- Rule: × 7
- ½ × ⁷⁄₁₀ = ⁷⁄₂₀
- ⁵⁄₆ × ³⁄₅ = ¹⁄₂
- 7.4 – 2.9 = 4.5
- 65.1 – 9.8 = 55.3
- Difference between 46.3 and 13.5 = 32.8
- Points: (4,4)=A, (9,0)=B, (7,10)=C, (2,11)=D

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Final Answer:
Rule: × 7
½ × ⁷⁄₁₀ = ⁷⁄₂₀
⁵⁄₆ × ³⁄₅ = ¹⁄₂
7.4 – 2.9 = 4.5
65.1 – 9.8 = 55.3
Difference: 32.8
Points: (4,4) → A, (9,0) → B, (7,10) → C, (2,11) → D