Numerical Expressions: Grade 5 Math Worksheet Answer Key – PDF Download

Grade 5 Expressions Worksheet Answer Key: problems 1–5

Problem 1: Add, then multiply

1. Inside the parentheses, add: \(8 + 4 = 12\). The expression is now \(12 \times 3\).
2. Now multiply: \(12 \times 3 = 36\). The expression is now \(36\).

The value is \(36\).

Problem 2: Subtract a sum

1. Inside the parentheses, add: \(12 + 6 = 18\). The expression is now \(30 – 18\).
2. Now subtract: \(30 – 18 = 12\). The expression is now \(12\).

The value is \(12\).

Problem 3: Subtract, then multiply

1. Inside the parentheses, subtract: \(9 – 4 = 5\). The expression is now \(5 \times 5\).
2. Now multiply: \(5 \times 5 = 25\). The expression is now \(25\).

The value is \(25\).

Problem 4: Divide by a sum

1. Inside the parentheses, add: \(2 + 4 = 6\). The expression is now \(48 : 6\).
2. Now divide: \(48 : 6 = 8\). The expression is now \(8\).

The value is \(8\).

Problem 5: Same numbers, different value

First expression:

1. Inside the parentheses, add: \(6 + 3 = 9\). The expression is now \(4 \times 9\).
2. Now multiply: \(4 \times 9 = 36\). The expression is now \(36\).

The value is \(36\).

Second expression:

1. Now multiply: \(4 \times 6 = 24\). The expression is now \(24 + 3\).
2. Now add: \(24 + 3 = 27\). The expression is now \(27\).

The value is \(27\).

The parentheses make the 4 multiply the whole sum \(6 + 3\). Without them, 4 multiplies only the 6. So \(36 \neq 27\).

Grade 5 Expressions Worksheet Answer Key: problems 6–10

Problem 6: Brackets around parentheses

1. Inside the parentheses, add: \(2 + 3 = 5\). The expression is now \(3 \times [10 – 5]\).
2. Inside the brackets, subtract: \(10 – 5 = 5\). The expression is now \(3 \times 5\).
3. Now multiply: \(3 \times 5 = 15\). The expression is now \(15\).

The value is \(15\).

Problem 7: Brackets, then divide

1. Inside the parentheses, multiply: \(6 \times 4 = 24\). The expression is now \([18 + 24] : 7\).
2. Inside the brackets, add: \(18 + 24 = 42\). The expression is now \(42 : 7\).
3. Now divide: \(42 : 7 = 6\). The expression is now \(6\).

The value is \(6\).

Problem 8: Subtract a bracket

1. Inside the parentheses, add: \(2 + 3 = 5\). The expression is now \(50 – [4 \times 5]\).
2. Inside the brackets, multiply: \(4 \times 5 = 20\). The expression is now \(50 – 20\).
3. Now subtract: \(50 – 20 = 30\). The expression is now \(30\).

The value is \(30\).

Problem 9: Braces, brackets, and parentheses

1. Inside the parentheses, add: \(3 + 2 = 5\). The expression is now \(\{40 – [5 \times 5]\} : 3\).
2. Inside the brackets, multiply: \(5 \times 5 = 25\). The expression is now \(\{40 – 25\} : 3\).
3. Inside the braces, subtract: \(40 – 25 = 15\). The expression is now \(15 : 3\).
4. Now divide: \(15 : 3 = 5\). The expression is now \(5\).

The value is \(5\).

Problem 10: Multiply a braces group

1. Inside the parentheses, add: \(3 + 2 = 5\). The expression is now \(2 \times \{30 – [4 \times 5]\}\).
2. Inside the brackets, multiply: \(4 \times 5 = 20\). The expression is now \(2 \times \{30 – 20\}\).
3. Inside the braces, subtract: \(30 – 20 = 10\). The expression is now \(2 \times 10\).
4. Now multiply: \(2 \times 10 = 20\). The expression is now \(20\).

The value is \(20\).

Grade 5 Expressions Worksheet Answer Key: problems 11–15

Problem 11: Two groups multiplied

1. Inside the parentheses, add: \(7 + 5 = 12\). The expression is now \(12 \times (9 – 6)\).
2. Inside the parentheses, subtract: \(9 – 6 = 3\). The expression is now \(12 \times 3\).
3. Now multiply: \(12 \times 3 = 36\). The expression is now \(36\).

The value is \(36\).

Problem 12: Two groups subtracted

1. Inside the parentheses, divide: \(36 : 4 = 9\). The expression is now \(9 – (2 \times 3)\).
2. Inside the parentheses, multiply: \(2 \times 3 = 6\). The expression is now \(9 – 6\).
3. Now subtract: \(9 – 6 = 3\). The expression is now \(3\).

The value is \(3\).

Problem 13: Insert parentheses, sum first

Without parentheses, \(4 + 6 \times 3\) equals \(22\), which is not 30. Try grouping the first operation: \((4 + 6) \times 3\).

1. Inside the parentheses, add: \(4 + 6 = 10\). The expression is now \(10 \times 3\).
2. Now multiply: \(10 \times 3 = 30\). The expression is now \(30\).

The value is \(30\).

Problem 14: Insert parentheses, difference first

Without parentheses, \(20 – 8 : 4\) equals \(18\), which is not 3. Try grouping the first operation: \((20 – 8) : 4\).

1. Inside the parentheses, subtract: \(20 – 8 = 12\). The expression is now \(12 : 4\).
2. Now divide: \(12 : 4 = 3\). The expression is now \(3\).

The value is \(3\).

Problem 15: Add, then double

The sum of 8 and 7 is one chunk, so it goes in parentheses: \(2 \times (8 + 7)\).

Check: \(2 \times (8 + 7)\) \(= 30\), because \(8 + 7 = 15\) and \(2 \times 15 = 30\).

Grade 5 Expressions Worksheet Answer Key: problems 16–20

Problem 16: Subtract, then divide

Subtract first, so \(20 – 6\) goes in parentheses. Then divide that result by 7: \((20 – 6) : 7\).

Check: \(20 – 6 = 14\) and \(14 : 7 = 2\).

Problem 17: Triple a sum

“Triple” means multiply by 3. The sum of 12 and 9 is one chunk: \(3 \times (12 + 9)\).

Check: \(12 + 9 = 21\) and \(3 \times 21 = 63\).

Problem 18: Divide by a difference

The difference of 11 and 6 is one chunk, and 45 is divided by it: \(45 : (11 – 6)\).

Check: \(11 – 6 = 5\) and \(45 : 5 = 9\).

Problem 19: Compare without calculating

The sum \(18 + 5\) is multiplied by 3, so \(3 \times (18 + 5)\) is 3 times as large as \(18 + 5\).

Check: \(18 + 5 = 23\) and \(3 \times 23 = 69\).

Problem 20: Half of a sum

The sum \(36 + 18\) is multiplied by \(\frac{1}{2}\), so the expression is half as large as \(36 + 18\).

Check: \(36 + 18 = 54\) and half of 54 is 27.

Grade 5 Expressions Worksheet Answer Key: problems 21–24

Problem 21: Little League roster

Each team has \(12 + 2\) people, and there are 6 teams: \(6 \times (12 + 2)\).

1. Inside the parentheses, add: \(12 + 2 = 14\). The expression is now \(6 \times 14\).
2. Now multiply: \(6 \times 14 = 84\). The expression is now \(84\).

The value is \(84\).

The league has 84 people.

Problem 22: School store stickers

Packs cost \(4 \times 3\), the card adds \(5\), and the coupon subtracts \(2\): \(4 \times 3 + 5 – 2\).

1. Now multiply: \(4 \times 3 = 12\). The expression is now \(12 + 5 – 2\).
2. Now add: \(12 + 5 = 17\). The expression is now \(17 – 2\).
3. Now subtract: \(17 – 2 = 15\). The expression is now \(15\).

The value is \(15\).

Maya pays $15.

Problem 23: Spending from $50

The total spent is \(3 \times 9 + 2 \times 6\). Subtract that whole amount from 50, so it goes in parentheses: \(50 – (3 \times 9 + 2 \times 6)\).

1. Inside the parentheses, multiply: \(3 \times 9 = 27\). The expression is now \(50 – (27 + 2 \times 6)\).
2. Inside the parentheses, multiply: \(2 \times 6 = 12\). The expression is now \(50 – (27 + 12)\).
3. Inside the parentheses, add: \(27 + 12 = 39\). The expression is now \(50 – 39\).
4. Now subtract: \(50 – 39 = 11\). The expression is now \(11\).

The value is \(11\).

Ethan has $11 left.

Problem 24: Find the mistake

Diego got 37 by doing \(5 \times 8 = 40\) and then \(40 – 3 = 37\). He ignored the parentheses and multiplied only the 8.

1. Inside the parentheses, subtract: \(8 – 3 = 5\). The expression is now \(5 \times 5\).
2. Now multiply: \(5 \times 5 = 25\). The expression is now \(25\).

The value is \(25\).

The correct value is 25.

How to use this grade 5 expressions worksheet answer key

Read this grade 5 expressions worksheet answer key after trying each problem yourself, and redo any problem you missed.

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