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Quizzes > Mathematics > Basic Math & Arithmetic

Test Your Number Sense: Take the Quiz Now!

Ready for a Sample Number Sense Test? Practice and Perfect Your Skills!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for a free number sense practice test on a teal background

Ready to boost your number sense practice? Take the Ace Your Number Sense Practice: Free Quiz Challenge - your gateway to mastering expressions, equations, and ratios through a fun number sense test. Start with a quick sample number sense test to find your baseline, then tackle a full number sense practice test that's designed for speed and accuracy. Dive into targeted mental math practice tips and stretch your skills with an arithmetic quiz . Perfect for students and lifelong learners alike, this quiz will sharpen your mind and build confidence. Start now and see how far you can go!

Simplify the expression 7 + 3 × 2.
12
20
13
9
According to the order of operations, multiplication is performed before addition. First, compute 3 × 2 = 6, then add 7 to get 13. Therefore, the simplified result is 13. For more details on order of operations, see Khan Academy.
What is 15% of 200?
30
35
15
25
To find 15% of 200, convert 15% to decimal form (0.15) and multiply by 200. Thus, 0.15 × 200 = 30. This method works for any percentage problem. Learn more at Khan Academy.
Evaluate the expression 5(2 + 3).
10
30
15
25
First, add inside the parentheses: 2 + 3 = 5. Then multiply by 5: 5 × 5 = 25. Parentheses indicate which operation to perform first. For more on order of operations, visit Khan Academy.
Which fraction is greater: 3/4 or 2/3?
1/2
3/4
2/3
1
Convert both fractions to decimals or compare cross-products. 3/4 = 0.75 while 2/3 ? 0.6667, so 3/4 is larger. Cross-multiplying (3×3 vs. 2×4) also shows 9 > 8. See Khan Academy for fraction comparisons.
Simplify the ratio 4:6.
4:6
2:3
1:1.5
3:4
Divide both terms by their greatest common divisor, which is 2. Thus, 4 ÷ 2 = 2 and 6 ÷ 2 = 3, giving 2:3. Ratios are simplified similarly to fractions. For more, see Khan Academy.
What is the value of x if x + 5 = 12?
-7
7
17
5
Subtract 5 from both sides of the equation: x + 5 ? 5 = 12 ? 5, so x = 7. Solving linear equations involves isolating the variable. Learn more at Khan Academy.
Calculate 9².
81
27
72
18
An exponent of 2 means multiply the base by itself: 9 × 9 = 81. This is the definition of a square number. To review exponents, visit Khan Academy.
Simplify the expression (8 + 2) × (6 ? 4).
14
20
10
24
First compute inside each parenthesis: 8 + 2 = 10 and 6 ? 4 = 2. Multiply the results: 10 × 2 = 20. Parentheses indicate priority. See Khan Academy.
Solve for x: 3x ? 5 = 16.
7
5.667
3.67
21
Add 5 to both sides: 3x = 21, then divide by 3: x = 7. This is a standard linear equation solution. Learn more at Khan Academy.
Simplify 2³ × 2².
8
64
32
16
When multiplying like bases, add the exponents: 3 + 2 = 5, so 2? = 32. This exponent rule applies generally to a? × a? = a???. See Khan Academy.
If 5 out of 20 marbles are red, what is the ratio of red to blue marbles?
1:3
5:20
3:1
5:15
There are 20 ? 5 = 15 blue marbles. The ratio red:blue = 5:15, which simplifies by dividing both by 5 to 1:3. Ratios simplify like fractions. More at Khan Academy.
Compute 2/5 + 3/10.
1/2
1
7/10
11/15
Convert 2/5 to tenths by multiplying numerator and denominator by 2, giving 4/10. Then add 4/10 + 3/10 = 7/10. Adding fractions requires common denominators. See Khan Academy.
Solve for x: x/4 + 2 = 5.
12
2
20
3
Subtract 2 from both sides: x/4 = 3. Then multiply by 4: x = 12. This isolates x in a one-step equation. More practice at Khan Academy.
Simplify the expression 3(x ? 2) + 4x.
x ? 6
6x ? 6
7x + 6
7x ? 6
Distribute 3 across (x ? 2) to get 3x ? 6, then add 4x for a total of 7x ? 6. Combining like terms is key in simplification. See Khan Academy.
Convert the decimal 0.75 to a fraction.
1/2
75/100
3/4
2/3
0.75 equals 75 hundredths, or 75/100. Simplify by dividing numerator and denominator by 25 to get 3/4. Decimal-to-fraction conversion is based on place value. Learn more at Khan Academy.
Simplify (x² × x³) ÷ x?.
x
x?
x?¹
x²
Combine exponents in numerator: x² × x³ = x?, then subtract exponent in division by x?: x? ÷ x? = x^(5?4) = x. This uses exponent rules. See Khan Academy.
Solve for x: 2(x ? 1) + 3 = 11.
4
5
6
-5
Distribute 2: 2x ? 2 + 3 = 11, so 2x + 1 = 11. Subtract 1 then divide by 2: 2x = 10, x = 5. This is solving a multi-step linear equation. More at Khan Academy.
If A:B = 3:4 and B:C = 2:5, what is A:C?
6:20
5:12
3:10
3:8
To combine ratios, match B terms: A:B = 3:4 can become 6:8; B:C = 2:5 becomes 8:20; so A:C = 6:20, which simplifies to 3:10. Ratio chaining uses common terms. See Khan Academy.
Evaluate the expression |?5 + 2 × 3|.
-1
1
11
-11
Compute inside absolute value: ?5 + (2×3) = ?5 + 6 = 1. The absolute value of 1 is 1. Absolute value measures distance from zero. More at Khan Academy.
Simplify (6y²) ÷ (2y).
3y²
y
6y
3y
Divide coefficients: 6 ÷ 2 = 3. Subtract exponents on y: y² ÷ y¹ = y^(2?1) = y. Combined result is 3y. See Khan Academy.
Solve for x: 4x/3 ? 2 = 6.
3
24
6
18
Add 2 to both sides: 4x/3 = 8. Multiply by 3: 4x = 24, then divide by 4: x = 6. This is a two-step equation. More examples at Khan Academy.
Compute (2/3) ÷ (4/9).
4/3
1/2
9/8
3/2
Dividing by a fraction is multiplying by its reciprocal: (2/3) × (9/4) = 18/12 = 3/2. Simplify the fraction by dividing numerator and denominator by 6. See Khan Academy.
Simplify the expression (3x²y? × 4xy²)².
144x?y?
24x³y²
144x?y²
12x?y?
First simplify inside: y? = 1, so 3x² × 4x y² = 12x³y². Squaring gives 12² = 144, x^(3×2) = x?, y^(2×2) = y?, yielding 144x?y?. This uses exponent and zero-exponent rules. For more, see Khan Academy.
Solve for x: 5^(x ? 1) = 125.
4
3
2
1
Recognize that 125 = 5³, so x ? 1 = 3 and x = 4. Solving exponential equations often requires rewriting in common bases. See Khan Academy.
Given a:b = 2:3 and b:c = 4:9, find a:b:c.
2:3:4
8:12:27
4:9:6
2:6:9
Set b common: from a:b=2:3 let b=12 (multiply by 4), so a=8. From b:c=4:9 let b=12 (multiply by 3), so c=27. Hence a:b:c = 8:12:27. Combining ratios uses a shared term. See Khan Academy.
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Study Outcomes

  1. Understand Number Sense Foundations -

    Identify and articulate the core concepts in number sense practice, including place value, order of operations, and mental math strategies.

  2. Simplify Algebraic Expressions -

    Apply algebraic rules to streamline expressions, mastering techniques to simplify variables, exponents, and fractions in our number sense practice test.

  3. Solve Linear Equations Swiftly -

    Use systematic methods to solve one- and two-step linear equations, boosting speed and accuracy in sample number sense test questions.

  4. Master Ratios and Proportions -

    Analyze and compare ratios through real-world examples, enhancing your ability to solve proportion problems quickly in any quiz setting.

  5. Enhance Mental Calculation Skills -

    Implement effective mental math shortcuts to perform rapid arithmetic operations, reducing reliance on paper and improving test efficiency.

  6. Interpret Feedback for Continuous Improvement -

    Review detailed explanations and tips provided after each question to pinpoint areas for growth and track progress in your number sense practice.

Cheat Sheet

  1. Simplifying Algebraic Expressions -

    Master the order of operations (PEMDAS) to simplify expressions quickly, as outlined by Khan Academy and MIT OpenCourseWare. Practice combining like terms and using the distributive property (a(b + c) = ab + ac) to streamline complex problems during your number sense practice. A handy mnemonic is "Please Excuse My Dear Aunt Sally" to recall parentheses, exponents, multiplication/division, and addition/subtraction.

  2. Solving Linear Equations -

    Learn to isolate variables by applying inverse operations, a technique emphasized by the College Board in their algebra resources. For example, solve 3x + 5 = 20 by subtracting 5 and then dividing by 3 to get x = 5. Regularly timed drills from sample number sense test collections can build speed and accuracy.

  3. Ratios and Proportions -

    Understand that a:b = c:d implies ad = bc, which helps solve real-world mixture and scale problems, as recommended by the National Council of Teachers of Mathematics (NCTM). Convert ratios to fractions or use cross-multiplication to find missing values quickly in a number sense practice test. Visualizing with ratio tables can also reinforce the concept and prevent common mistakes.

  4. Number Properties & Factoring -

    Review prime factorization and the greatest common divisor (GCD) to simplify fractions and solve divisibility queries, following guidelines from reputable math journals like the Journal of Integer Sequences. Use the factor tree method to break down numbers quickly in a timed number sense test. Remember that any integer's factors come in pairs, which is especially useful for spotting square numbers.

  5. Mental Math & Estimation Tricks -

    Develop mental shortcuts such as rounding and compensation to approximate sums, products, or quotients fast, as suggested by research at Stanford's Math Education Lab. For example, to multiply 49 × 8, think (50 - 1) × 8 = 400 - 8 = 392. Frequent practice with a number sense practice test improves both your speed and confidence under time constraints.

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