Numerical Expressions — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. Without calculating, 6 × (15 + 4) > 5 × (15 + 4). Use >, <, or =.
Both expressions multiply the same value (15 + 4) by different factors. Since 6 > 5, the first expression produces a larger result.
2. Without calculating, (30 − 7) ÷ 2 < (30 − 7) × 2. Use >, <, or =.
Both operate on the same value (30 − 7). Dividing by 2 gives half the value; multiplying by 2 doubles it. Half < double, so ÷2 < ×2.
3. Without calculating, 4 × (9 + 3) < 4 × (9 + 5). Use >, <, or =.
Both multiply by 4, but (9 + 5) = 14 > (9 + 3) = 12. Since the second expression multiplies a larger value by the same factor, it is larger.
4. Without calculating, (8 + 12) × 3 = 3 × (12 + 8). Use >, <, or =.
Both expressions multiply the same sum (8 + 12 = 12 + 8 by commutative property) by 3. They are equal.
5. Without calculating, (40 ÷ 5) + 10 > (40 ÷ 5) + 7. Use >, <, or =.
Both expressions start with (40 ÷ 5), then add different numbers. Adding 10 gives a larger result than adding 7.
6. Without calculating, 2 × (16 + 9) > (16 + 9). Use >, <, or =.
Multiplying (16 + 9) by 2 doubles its value. 2 × any positive number > the number itself.
7. Without calculating, (50 − 20) ÷ 6 < (50 − 20) ÷ 3. Use >, <, or =.
Both divide (50 − 20) by different numbers. Dividing by a larger number (6) produces a smaller result than dividing by a smaller number (3).
8. Without calculating, 7 × (11 − 4) = 7 × (11 − 4). Use >, <, or =.
These are identical expressions. Any expression compared to itself is equal.
9. Without calculating, 10 × (5 + 3) > 9 × (5 + 3). Use >, <, or =.
Both multiply the same value (5 + 3) by different factors. Since 10 > 9, the first expression is larger.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
3 × (20 + 5) compared to (20 + 5)
→ first is 3 times as large
equal — same expression
(48 ÷ 6) compared to (48 ÷ 2)
→ second is larger — dividing by smaller gives more
second is larger — dividing by smaller gives more
(14 + 6) × 4 compared to (14 + 6) × 4
→ equal — same expression
first is 3 times as large
2 × (9 + 1) compared to 8 × (9 + 1)
→ second is larger — 8 times vs. 2 times
second is larger — 8 times vs. 2 times
3×(20+5) is 3× larger than (20+5); 48÷2>48÷6 (smaller divisor=larger result); identical expressions are equal; 8×(9+1)>2×(9+1).