6th Grade Writing and Reading Algebraic Expressions Worksheet Solutions (PDF)

6th Grade math worksheet solutions: Writing and Reading Algebraic Expressions – Maths PDF

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This write expressions answers for 6th Grade covers writing and reading algebraic expressions (Common Core 6.EE.A.2a, 6.EE.A.2b), with a free PDF to print.

Check each expression here. The solutions show how key words map to operations, name the terms and coefficients, and give the final expression in bold. Tape diagrams and tables support several answers.

Grade 6 · Common Core State Standards: 6.EE.A.2a, 6.EE.A.2b

Write expressions answers: exercises 1 to 10

Exercise 1 – Sum

“Sum” means add.

$x + 7$

Exercise 2 – Decreased by

“Decreased by” means subtract 5 from y.

$y – 5$

Exercise 3 – Times a number

Write the coefficient 6 next to the variable.

$6n$

Exercise 4 – Quotient

The first quantity named is the dividend.

$\frac{m}{4}$ (or $m \div 4$)

Exercise 5 – Less than

“8 less than k” means k with 8 taken away. The order is reversed from the words.

$k – 8$

Exercise 6 – Twice a sum

The sum is $n + 3$. Twice it means multiply by 2, so use parentheses.

$2(n + 3)$

Two groups of n + 3.

Exercise 7 – Product with a difference

The difference of x and 2 is $x – 2$. The product of 5 and that is $5(x – 2)$.

$5(x – 2)$

Exercise 8 – Terms and coefficient

Terms are the parts added: $7x$ and $3$.

The coefficient of $x$ is 7, and the constant term is 3.

terms $7x$, $3$; coefficient 7; constant 3

Exercise 9 – Three terms

Terms: $4a$, $9b$, $2$.

Coefficients: 4 (of a) and 9 (of b). Constant: 2.

3 terms; coefficients 4 and 9; constant 2

Exercise 10 – Read a product

It is the product of 3 and the sum $x + 5$.

Factors: 3 and $(x + 5)$

Exercises 11 and up

Exercise 11 – Words for a difference

Sample answers: “9 less than twice a number n” or “the difference of 2 times n and 9.”

9 less than twice n

Exercise 12 – Words for a quotient

$\frac{n}{3}$ is the quotient of n and 3. Adding 4 makes it a sum.

the sum of the quotient of n and 3, and 4

Exercise 13 – Sum of a product

“4 times a” is $4a$. The sum of that and 7 is $4a + 7$.

$4a + 7$

Exercise 14 – Hourly pay

Pay = rate times hours: $12h$.

For 5 hours: $12 \times 5 = 60$.

$12h$; $60.00

The expression 12h gives the pay for h hours.

Exercise 15 – Notebooks and a pen

The notebooks cost $3n$ dollars. Adding the pen gives $3n + 2$ dollars.

$3n + 2$

Cost of notebooks and one pen.

Exercise 16 – More stickers

“5 more than x” means add 5.

$x + 5$

Exercise 17 – Perimeter of a square

The perimeter is s + s + s + s, which is $4s$.

$4 \times 7 = 28$

$4s$; 28 inches

Four sides of 7 inches make 28 inches.

Exercise 18 – Distance

Distance = rate times time: $14t$.

$14 \times 3 = 42$

$14t$; 42 miles

Exercise 19 – Read a product of a sum

It is 5 times the sum of 2 times x and 1.

Factors: 5 and $(2x + 1)$. Terms inside: $2x$ and $1$.

product of 5 and the sum $2x + 1$

Exercise 20 – Tickets

Cost: $8a + 5c$.

$8 \times 3 + 5 \times 4 = 24 + 20 = 44$

$8a + 5c$; $44.00

Key facts behind this write expressions answers

Key facts

Sum, plus, more than: add. Difference, less than, decreased by: subtract.
Product and times: multiply; quotient and divided by: divide.
A term is a part of an expression separated by plus or minus signs.
A coefficient is the number multiplied by a variable; a constant has no variable.
Read an expression in parentheses as one quantity.

How to use this write expressions answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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All Grade 6 chapters: Grade 6 math.

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