How to Translate Phrases into an Algebraic Statement? (+FREE Worksheet!)

To solve some algebra problems, sometimes you need to translate phrases into algebraic statements then solve the problem.

Step by step guide to translating phrases into an algebraic Statement

Translating key words and phrases into algebraic expressions:

• Addition: plus, more than, the sum of, etc.
• Subtraction: minus, less than, decreased, etc.
• Multiplication: times, product, multiplied, etc.
• Division: quotient, divided, ratio, etc.

Translate Phrases into an Algebraic Statement – Example 1:

Write an algebraic expression for this phrase “$$12$$ times the sum of $$5$$ and $$x$$”.

Solution:

Sum of $$5$$ and $$x: 5 \ + \ x$$. Times means multiplication. Then: $$12 \ × \ (5 \ + \ x)$$

Translate Phrases into an Algebraic Statement – Example 2:

Write an algebraic expression for this phrase. “Nine more than a number is $$18$$”

Solution:

More than mean plus, a number $$=x$$
Then: $$9 \ + \ x=18$$

Translate Phrases into an Algebraic Statement – Example 3:

Write an algebraic expression for this phrase. “Eight more than a number is $$20$$”

Solution:

More than mean plus, a number $$=x$$
Then: $$8+x=20$$

Translate Phrases into an Algebraic Statement – Example 4:

Write an algebraic expression for this phrase. “$$5$$ times the sum of $$8$$ and $$x$$”

Solution:

Sum of $$8$$ and $$x: 8+x$$. Times means multiplication. Then: $$5×(8 +x)$$

Exercises for Translating Phrases into an Algebraic Statement

Write an algebraic expression for each phrase.

• A number increased by forty–two.
• The sum of fifteen and a number
• The difference between fifty–six and a number.
• The quotient of thirty and a number.
• Twice a number decreased by $$25$$.
• Four times the sum of a number and $$– 12$$.

• $$\color{blue}{x + 42}$$
• $$\color{blue}{15 + x}$$
• $$\color{blue}{56 – x}$$
• $$\color{blue}{\frac {30} {x}}$$
• $$\color{blue}{2x – 25}$$
• $$\color{blue}{4(x + (–12))}$$

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