Algebraic Expressions and Properties of Real Numbers: math practice, Grade 9 – download the PDF

1 Parts of an expression ★★★

Consider the expression \(7x^2-4x+9\).

1. How many terms does it have, and what are they?
2. Give the coefficient of each variable term.
3. What is the constant term?

2 Order of operations ★★★

Compute each expression and write every step.

1. \(5+3\cdot 4\)
2. \((5+3)\cdot 4\)
3. \(20-12\div 4\)
4. \(2\cdot 3^2\)

3 Evaluate a linear expression ★★★

Evaluate \(4n+7\) for each value of \(n\).

1. \(n=3\)
2. \(n=-2\)
3. \(n=0\)
4. \(n=\dfrac{1}{2}\)

4 Name the property ★★★

Name the property that justifies each statement.

1. \(6\cdot 9=9\cdot 6\)
2. \((4+5)+1=4+(5+1)\)
3. \(3(x+2)=3x+6\)
4. \(8+0=8\)
5. \(5\cdot\dfrac{1}{5}=1\)

5 Combine the like terms ★★★

Simplify each expression.

1. \(6a+2a\)
2. \(9y-4y+y\)
3. \(3x+5-x+2\)
4. \(4m+3n-m+2n\)

6 Which set is smallest? ★★★

For each number, name the smallest set it belongs to: natural, whole, integer, rational, or irrational.

1. \(-9\)
2. \(\dfrac{2}{5}\)
3. \(\sqrt{25}\)
4. \(\sqrt{10}\)

7 Words to symbols ★★★

Write an expression, using \(n\) for the number.

1. the sum of a number and 9
2. 7 times a number
3. a number decreased by 4
4. the quotient of a number and 6

8 Evaluate a quadratic expression ★★★

Evaluate \(2x^2-5x+1\) for \(x=3\), \(x=-1\), and \(x=0.5\).

9 Grouping symbols ★★★

Compute.

1. \(-6+4\cdot(-3)^2\div 9\)
2. \(3-2[5-(1+3)]\)

10 Use the distributive property ★★★

Expand.

1. \(5(2x-3)\)
2. \(-3(4y+1)\)
3. \(-(7-2z)\)
4. \(\dfrac{1}{2}(8a+6)\)

11 Distribute and combine ★★★

Simplify \(3(x+4)+2(5x-1)\), then check your answer for \(x=1\).

12 Mental math with properties ★★★

Use properties to compute these without a calculator, and name the property you use.

1. \(25\cdot 17\cdot 4\)
2. \(8\cdot 53\)
3. \(99\cdot 6\)

13 Concert tickets ★★★

A school concert sells adult tickets for $12 and student tickets for $8.

1. Write an expression for the money collected from \(a\) adult tickets and \(s\) student tickets.
2. Evaluate it for \(a=15\) and \(s=22\).

14 True or false? ★★★

Decide whether each statement is true for all numbers. If it is false, give a counterexample.

1. \(5-x=x-5\)
2. \(4+x=x+4\)
3. \(2(x+3)=2x+3\)
4. \(12\div(3\cdot 2)=(12\div 3)\cdot 2\)

15 A longer simplification ★★★

Simplify \(4(3x-2)-2(5x-7)+x\).

16 Perimeter of a rectangle ★★★

The rectangle below has length \((3x+2)\) cm and width \((x+5)\) cm.

1. Write and simplify an expression for the perimeter.
2. Find the perimeter when \(x=3\).

17 Phone plan ★★★

Plan A costs $25 per month plus $0.10 per text message.

1. Write an expression for the monthly cost with \(t\) texts.
2. What is the bill for 240 texts?
3. One month the bill was $60. How many texts were sent?

18 Find the error ★★★

A student simplified \(3(x-4)+2x\) and wrote \(3x-4+2x=5x-4\). Explain the error and give the correct answer.

19 Shopping for notebooks ★★★

A notebook costs \(n\) dollars. Ava buys 4 notebooks and a $3 pen. Ben buys 6 notebooks and uses a $2 coupon.

1. Write and simplify an expression for their combined spending.
2. Evaluate it for \(n=2.50\).

20 Always, sometimes, or never? ★★★

Decide whether each statement is always, sometimes, or never true, and justify.

1. The sum of two rational numbers is rational.
2. The sum of two irrational numbers is irrational.
3. The product of a nonzero rational number and an irrational number is irrational.
4. The square root of a positive integer is irrational.

21 Evaluate a fraction expression ★★★

Evaluate \(\dfrac{(a-b)^2}{2c}+ab\) for \(a=7\), \(b=-3\), and \(c=5\).

22 Fractions with distribution ★★★

Simplify \(\dfrac{3}{4}(8x-12)+\dfrac{1}{2}(6x+4)\).