Let’s go through each problem one by one, step by step. I’ll solve them carefully and check my work as we go.
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Problem 1: Write 0.7% in expanded notation.
Expanded notation means writing the number as a sum of its place values.
0.7% = 0.7 per hundred = 0.7 / 100 = 0.007
Now write 0.007 in expanded form:
0.007 = 0 + 0/10 + 0/100 + 7/1000
= 0 + 0×(1/10) + 0×(1/100) + 7×(1/1000)
Looking at the options:
[A] 0 + (7 × 1/100) → that’s 0.07 — too big
[B] 0 + (7 × 1/1000) → that’s 0.007 — correct!
[C] 0 + (7 × 1/10) → 0.7 — way too big
[D] 0 + (7 × 1/10000) → 0.0007 — too small
✔ So answer is
[B]
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Problem 2: Solve for x: 3x - 5 = 16
Add 5 to both sides:
3x = 16 + 5 = 21
Divide both sides by 3:
x = 21 ÷ 3 = 7
Check: 3×7 - 5 = 21 - 5 = 16 ✔️
Options: [A] 4 [B] 5 [C] 6 [D] 7
✔ Answer is
[D]
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Problem 3: Subtract: 1298 - 438
Do it step by step:
1298
-438
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Start from right:
8 - 8 = 0
9 - 3 = 6
2 - 4 → can’t do, borrow from 1 → 12 - 4 = 8, and the 1 becomes 0
So: 860
Wait — let me double-check:
1298 - 400 = 898
898 - 38 = 860 ✔️
Options: [A] 860 [B] 846 [C] 850 [D] 870
✔ Answer is
[A]
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Problem 4: Divide 72 ÷ 8
Basic fact: 8 × 9 = 72 → so 72 ÷ 8 = 9
Options: [A] 6 [B] 7 [C] 8 [D] 9
✔ Answer is
[D]
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Problem 5: Simplify: 4 + 3 × 2 - 1
Order of operations: multiplication first!
3 × 2 = 6
Then: 4 + 6 - 1 = 10 - 1 = 9
Options: [A] 7 [B] 8 [C] 9 [D] 10
✔ Answer is
[C]
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Problem 6: Evaluate (3a + 2b) if a = 4 and b = 3
Plug in:
3×4 + 2×3 = 12 + 6 = 18
Options: [A] 15 [B] 16 [C] 17 [D] 18
✔ Answer is
[D]
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Problem 7: Which fraction is equivalent to 3/4?
We need to find which option equals 3/4 when simplified.
[A] 6/8 → divide numerator and denominator by 2 → 3/4 ✔️
[B] 9/12 → divide by 3 → 3/4 ✔️
[C] 12/16 → divide by 4 → 3/4 ✔️
[D] All of these → since A, B, C all equal 3/4
✔ Answer is
[D]
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Problem 8: What percent represents the shaded circles?
There are 10 circles total. 4 are shaded.
So percent = (shaded / total) × 100 = (4/10) × 100 = 40%
Options: [A] 20% [B] 30% [C] 40% [D] 50%
✔ Answer is
[C]
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Problem 9: Write 0.25 as a fraction.
0.25 = 25/100 = simplify by dividing numerator and denominator by 25 → 1/4
Options: [A] 1/2 [B] 1/4 [C] 1/5 [D] 1/10
✔ Answer is
[B]
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Problem 10: Write 0.25 as a percent.
To convert decimal to percent, multiply by 100:
0.25 × 100 = 25%
Options: [A] 2.5% [B] 25% [C] 250% [D] 0.25%
✔ Answer is
[B]
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Final Answer:
1. [B]
2. [D]
3. [A]
4. [D]
5. [C]
6. [D]
7. [D]
8. [C]
9. [B]
10. [B]
Parent Tip: Review the logic above to help your child master the concept of number sense and operations worksheet.
