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Quizzes > Mathematics > Basic Math & Arithmetic

Take the 6th Grade Math IQ Challenge Now

Put Your Math IQ to the Test with This Fun 6th Grade Quiz!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for 6th grade math IQ test quiz on a coral background

This free 6th Grade Math IQ Test helps you practice and measure your math reasoning in fractions, decimals, geometry, and basic algebra. Each sixth-grade IQ quiz gives instant results and short explanations, helping you spot gaps before a test and build speed.

What is 345 + 679?
1,004
1,014
1,034
1,024
Adding 345 and 679 digit by digit (5+9=14, carry 1; 4+7+1=12, carry 1; 3+6+1=10) results in 1,024, but note the correct grouping places give 1,024. More practice at .
What is 8 × 7?
56
54
48
64
Multiplying 8 by 7 equals 56 because 7 groups of 8 items total 56. For more on multiplication tables, see .
What is 56 ÷ 8?
6
9
7
8
Dividing 56 by 8 gives 7 because 8 times 7 equals 56. You can review division facts at .
What is 3/4 + 1/4?
1
3/8
4/4
1/2
Adding fractions with the same denominator means adding numerators: 3 + 1 = 4, over 4 equals 1. See fraction addition at .
Which is greater: 0.5 or 0.45?
Cannot compare
They are equal
0.5
0.45
0.50 is greater than 0.45 because at the tenths place 5 > 4. Decimal comparison is explained at .
What is the perimeter of a square with side length 5 units?
15
20
25
10
Perimeter of a square is 4 × side, so 4 × 5 = 20. Learn more about perimeters at .
In the number 6,482, what place value does the digit 6 represent?
Hundreds
Thousands
Ones
Tens
In 6,482 the first digit from the left is the thousands place, so 6 represents 6,000. More on place values at .
What is 3/5 of 25?
18
15
12
10
Multiply 25 by 3/5: 25 × (3/5) = (25 ÷ 5) × 3 = 5 × 3 = 15. Fraction of a number is explained at .
What is the least common multiple (LCM) of 6 and 8?
12
48
16
24
The multiples of 6 are 6,12,18,24,... and of 8 are 8,16,24,... so the first common is 24. Learn LCM at .
What is 20% of 150?
35
30
20
25
20% means 20/100 = 0.2; 0.2 × 150 = 30. Percentage calculations are discussed at .
What is the value of 7 × (3 + 4)?
49
28
15
21
First add inside parentheses: 3 + 4 = 7, then multiply: 7 × 7 = 49. Order of operations is explained at .
Solve for x: x + 5 = 12.
12
5
7
17
Subtract 5 from both sides: x = 12 ? 5 = 7. Learn one-step equations at .
Convert the fraction 7/10 to a decimal.
7.0
0.17
0.7
0.07
Divide numerator by denominator: 7 ÷ 10 = 0.7. See fraction to decimal conversion at .
What is the area of a rectangle with length 8 and width 15?
23
120
30
45
Area = length × width = 8 × 15 = 120. Rectangle area is explained at .
Reduce the fraction 12/16 to simplest form.
2/3
3/4
4/3
6/8
Divide numerator and denominator by their GCF 4: (12 ÷ 4)/(16 ÷ 4) = 3/4. Simplifying fractions is shown at .
Solve for x: 3x ? 2 = 13.
7
5
6
4
Add 2 to both sides: 3x = 15, then divide by 3: x = 5. See two-step equations at .
Evaluate: (?3)² ? 5.
14
?8
?14
4
Exponent applies before subtraction: (?3)² = 9, then 9 ? 5 = 4. Exponents rules at .
Simplify: 3³ ÷ 3.
9
1
3
27
3³ = 27; 27 ÷ 3 = 9. Dividing powers with same base subtracts exponents: 3^(3?1) = 3² = 9. More at .
What is the greatest common factor (GCF) of 18 and 24?
12
8
6
4
Factors of 18 are 1,2,3,6,9,18; of 24 are 1,2,3,4,6,8,12,24. The largest common is 6. Learn GCF at .
A circle has radius 7 units. Using ? = 3.14, what is its circumference?
49
21.98
43.96
14
Circumference = 2?r = 2 × 3.14 × 7 = 43.96. More on circles at .
Solve for y: 5y = 45.
10
7
8
9
Divide both sides by 5: y = 45 ÷ 5 = 9. Multiplication and division equations are at .
Express 65% as a fraction in simplest form.
5/8
3/5
13/20
65/100
65% = 65/100; divide numerator and denominator by 5: (65 ÷ 5)/(100 ÷ 5) = 13/20. See percent to fraction at .
Solve the equation |x ? 4| = 3.
x = 4
x = 1 only
x = 7 only
x = 1 or x = 7
Absolute value splits into x ? 4 = 3 (x=7) or x ? 4 = ?3 (x=1). Absolute value equations at .
If the ratio of dogs to cats is 3:4 and there are 21 animals in total, how many cats are there?
9
12
16
7
Total parts = 3+4=7; each part = 21÷7=3; cats = 4 parts = 4×3=12. Ratios explained at .
A rectangle has area 72 square units and its length is twice its width. What is the width?
8
6
4
9
Let width = w, length = 2w, so area w×2w=2w²=72 ? w²=36 ? w=6. Rectangle area problems at .
0
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Study Outcomes

  1. Apply Arithmetic and Problem-Solving Techniques -

    Use proven strategies to tackle multi-step arithmetic questions found in a math IQ test with confidence and accuracy.

  2. Analyze Patterns and Logical Reasoning -

    Identify number sequences and logical relationships to improve performance on a math intelligence test challenge.

  3. Interpret Instant Feedback -

    Assess your results immediately to pinpoint strengths and target areas for improvement in math quizzes for 6th graders.

  4. Enhance Time Management Skills -

    Develop efficient approaches to solve timed questions in an IQ test for 6th graders without feeling rushed.

  5. Evaluate Personal Math Proficiency -

    Reflect on your test outcomes to understand your mathematical intelligence level and build confidence.

  6. Prepare for Future Unblocked IQ Tests -

    Use insights from this free, unblocked IQ test to sharpen skills and get ready for other math challenges.

Cheat Sheet

  1. Order of Operations (PEMDAS) -

    Always tackle parentheses, exponents, multiplication/division, then addition/subtraction to get the correct answer. Remember the mnemonic "Please Excuse My Dear Aunt Sally" to lock in the sequence. For example, in 8 + (3×2)^2 − 5, solve inside parentheses first: 3×2 = 6, then exponent: 6^2 = 36, so you calculate 8 + 36 − 5 = 39.

  2. Fractions, Decimals & Percentages -

    Master converting between forms by remembering that 1/2 = 0.5 = 50%, and using cross-multiplication for tricky ratios. A quick trick is to multiply decimals by 100 and add the percent symbol to shift to a percentage (e.g., 0.75×100 = 75%). Practice with sample problems like converting 3/4 to a decimal (3÷4 = 0.75) and then to a percent (75%).

  3. Ratios & Proportional Reasoning -

    Understand that a ratio compares two quantities, such as 2:3 meaning for every 2 of one item there are 3 of another. Set up equivalent fractions to solve problems, for instance, if 2/3 = x/15 then x = (2×15)/3 = 10. Practicing word problems about recipes or scaling maps will boost your ratio skills.

  4. Geometry Foundations -

    Learn key formulas like area = length×width for rectangles and A = ½bh for triangles, and perimeter by summing all side lengths. Visualizing shapes on a grid can help you break complex figures into smaller, familiar ones. For example, split an L-shaped region into two rectangles, find each area, then add together.

  5. Data & Probability Basics -

    Calculate the mean by summing data points and dividing by their count, and find median by ordering values and picking the middle one. Identify the mode as the most frequent number to quickly summarize a dataset. For simple probability, divide the number of favorable outcomes by the total outcomes, such as 2 aces in a deck (4/52 ≈ 1/13).

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