Writing Numerical Expressions - SmartMathz - Free Printable

Let’s go step by step to solve each part of the worksheet.

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Part 1: Write the numerical expressions.

We need to turn word phrases into math expressions using numbers and operations like +, −, ×, ÷, and parentheses when needed.

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a. The sum of 21 and 4, doubled.

- “Sum” means add → 21 + 4
- “Doubled” means multiply by 2 → (21 + 4) × 2

✔ Expression: (21 + 4) × 2

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b. 5 times the sum of 7 and 23.

- “Sum of 7 and 23” → 7 + 23
- “5 times” that → 5 × (7 + 23)

✔ Expression: 5 × (7 + 23)

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c. Triple the sum of 45 and 55.

- “Triple” means multiply by 3
- “Sum of 45 and 55” → 45 + 55
- So: 3 × (45 + 55)

✔ Expression: 3 × (45 + 55)

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d. The sum of 3 fifteens and 4 twos.

- “3 fifteens” = 3 × 15
- “4 twos” = 4 × 2
- “Sum” means add them → (3 × 15) + (4 × 2)

✔ Expression: (3 × 15) + (4 × 2)

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e. 2 times the difference between 49.5 – 37.5.

Wait — this is written as “the difference between 49.5 – 37.5”, which already gives us the subtraction. But let’s read carefully:

It says: “2 times the difference between 49.5 – 37.5”

Actually, “difference between A and B” usually means |A - B|, but here it’s written as “between 49.5 – 37.5”, which is confusing. Looking at the phrasing, it probably means:

“2 times the result of (49.5 minus 37.5)”

So: 2 × (49.5 – 37.5)

✔ Expression: 2 × (49.5 – 37.5)

*(Note: In part f, they use “difference between X and Y”, so maybe e was meant to be “difference between 49.5 and 37.5”. But since it says “between 49.5 – 37.5”, we’ll take it literally as written — meaning the expression inside is already given as a subtraction.)*

But to match standard wording, perhaps it’s a typo and should be “difference between 49.5 and 37.5”. Let’s assume that for consistency with part f.

So better interpretation:
“2 times the difference between 49.5 and 37.5” → 2 × (49.5 – 37.5)

Same answer either way.

✔ Final for e: 2 × (49.5 – 37.5)

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f. The difference between 9 thirty-sevens and 8 thirty-sevens.

- “9 thirty-sevens” = 9 × 37
- “8 thirty-sevens” = 8 × 37
- “Difference between” → subtract: (9 × 37) – (8 × 37)

You could also factor: (9 – 8) × 37 = 1 × 37, but the question asks for the expression, not simplified.

✔ Expression: (9 × 37) – (8 × 37)

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Part 2: Write the numerical expressions in words, then solve.

We have to write what the expression means in words, then calculate the answer.

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a. 10 × (3.5 + 12.5)

Words:
→ Ten times the sum of three point five and twelve point five.

Solve:
First, inside parentheses: 3.5 + 12.5 = 16
Then: 10 × 16 = 160

✔ Words: Ten times the sum of 3.5 and 12.5
✔ Solution: 160

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b. (88 – 78) × 11

Words:
→ The difference between eighty-eight and seventy-eight, multiplied by eleven.

Solve:
88 – 78 = 10
10 × 11 = 110

✔ Words: The difference between 88 and 78, multiplied by 11
✔ Solution: 110

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c. (51 + 49) × 26

Words:
→ The sum of fifty-one and forty-nine, multiplied by twenty-six.

Solve:
51 + 49 = 100
100 × 26 = 2600

✔ Words: The sum of 51 and 49, multiplied by 26
✔ Solution: 2600

*(Note: There are two rows labeled “c.” — probably a typo. We’ll treat both as same or ignore duplicate. Since second one is identical, we’ll just do once.)*

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Now, compiling all answers clearly.

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Final Answer:

Part 1: Numerical Expressions

a. (21 + 4) × 2
b. 5 × (7 + 23)
c. 3 × (45 + 55)
d. (3 × 15) + (4 × 2)
e. 2 × (49.5 – 37.5)
f. (9 × 37) – (8 × 37)

Part 2: Words and Solutions

a. Words: Ten times the sum of 3.5 and 12.5 → Solution: 160
b. Words: The difference between 88 and 78, multiplied by 11 → Solution: 110
c. Words: The sum of 51 and 49, multiplied by 26 → Solution: 2600