Whole Numbers and Integers — Free Pre-Algebra Review Games.

-8 + 5 = -3. Adding a positive to a negative moves right on the number line.

The absolute value of any number is its distance from zero, so |-12| = 12.

Order of operations: multiply first (4*2=8), then add (3+8=11).

A negative times a negative is positive: -6 * -3 = 18.

Zero is the only integer that is neither positive nor negative.

Subtracting a negative is adding: 5+3+2 = 10.

A negative divided by a negative is positive: -24 / -6 = 4.

Parentheses first: 3+5=8, then 2*8=16, then 16-4=12.

On a number line, -5 is farthest left, then -1, 0, and 2.

(-2)^3 = (-2)*(-2)*(-2) = 4*(-2) = -8. Odd powers of negatives are negative.

|(-3)*4| = |-12| = 12, and |-2| = 2, so 12 + 2 = 14.

-3^2 = -(9) = -9 and (-3)^2 = 9, so -9 + 9 = 0.

Exponent first: 2^3=8. Then multiply: 3*4=12. Then 15-12+8=11.

a^2 = 16, 2*a*b = 2*(-4)*3 = -24, so 16 - (-24) = 40.

(-1)^50 = 1 (even power) and (-1)^51 = -1 (odd power), so 1 + (-1) = 0.

Adding a positive number to a negative moves you toward zero and beyond, so \(-7+10=3\) because you subtract the smaller absolute value from the larger and keep the sign of the number with greater magnitude. The choice "\(-17\)" is wrong because it treats both numbers as if they had the same sign, adding their magnitudes instead of finding the difference. Always identify which number has the larger absolute value first when combining opposite signs.

Rewriting the subtraction as \(9+(-15)\) shows that combining a smaller positive with a larger negative gives \(-6\), the sign of the larger magnitude. The choice "\(6\)" is wrong because it drops the negative sign that must appear when the number being subtracted exceeds the starting value. Turning subtraction into addition of the opposite is a reliable strategy for these problems.

Absolute value measures distance from zero, so \(|-20|=20\) regardless of the original sign. The choice "\(-20\)" is wrong because absolute value output is defined to always be non-negative. Remember that absolute value strips the sign and reports only the magnitude.

The absolute value of a positive number equals the number itself, so \(|7|=7\). The choice "\(-7\)" is wrong because absolute value can never return a negative result by definition. Applying absolute value to an already-positive number simply returns that same number.

Multiplying a negative number by a positive number produces a negative product, so \(-4\times5=-20\). The choice "\(20\)" is wrong because it ignores the sign rule that opposite signs multiply to give a negative result. Memorize that same signs multiply to positive and opposite signs multiply to negative.

Dividing a positive number by a negative number yields a negative quotient, so \(12\div(-4)=-3\). The choice "\(3\)" is wrong because it drops the sign that results from dividing numbers with opposite signs. Division follows the same sign rules as multiplication.

Order of operations requires multiplication before addition, so \(2\times3=6\) first and then \(6+6=12\). The choice "\(24\)" is wrong because it comes from adding \(6+2\) first and then multiplying by \(3\), evaluating left to right instead of following the precedence rules. Multiplication and division always come before addition and subtraction.

On the number line, \(-3\) lies closer to zero than \(-8\), and numbers closer to zero on the negative side are greater. The choice "\(-8\)" is wrong because it is farther from zero in the negative direction, making it the smaller value. For negative numbers, the one with the smaller absolute value is always greater.

When adding two negative numbers, you add their magnitudes and keep the negative sign, so \(-9+(-6)=-15\). The choice "\(15\)" is wrong because it drops the negative sign that must remain when combining two negative values. Same-signed numbers always combine by adding magnitudes and preserving the shared sign.

The opposite, or additive inverse, of a number has the same magnitude but the reversed sign, so the opposite of \(-15\) is \(15\). The choice "\(-15\)" is wrong because it is the original number, not its opposite. Finding an opposite simply flips the sign while keeping the magnitude unchanged.

Addition and subtraction share equal precedence and are performed left to right, so \(10-4=6\) first, then \(6+2=8\). The choice "\(4\)" is wrong because it incorrectly evaluates \(4+2\) before subtracting, violating the left-to-right rule for same-precedence operations. Always process addition and subtraction in the order they appear from left to right.

A negative number divided by a positive number gives a negative quotient, so \(-18\div3=-6\). The choice "\(6\)" is wrong because it ignores the sign rule for dividing numbers with opposite signs. Opposite-signed division always results in a negative answer.

A negative integer is a whole number less than zero, and \(-5\) fits that definition exactly. The choice "\(0\)" is wrong because zero is neither positive nor negative. Negative integers are whole numbers found to the left of zero on the number line.

Order of operations requires multiplying \(3\times4=12\) before adding, giving \(-5+12=7\). The choice "\(-8\)" is wrong because it results from adding \(-5+3\) first and then multiplying by \(4\), which violates the required order of operations. Always perform multiplication and division before addition and subtraction.

Parentheses are resolved first giving \(6\), then division gives \(6\div3=2\), and finally addition gives \(2+1=3\). The choice "\(4\)" is wrong because it results from adding \(3+1\) before dividing, which ignores the required order of operations. Parentheses are always evaluated first, followed by multiplication or division, then addition or subtraction.

Subtracting a negative number is equivalent to adding its opposite, so \(-7-(-9)=-7+9=2\). The choice "\(-16\)" is wrong because it incorrectly treats the expression as \(-7-9\), adding the magnitudes with the wrong sign. Subtracting a negative always converts to addition of the positive counterpart.

The exponent gives \(4^2=16\) and the multiplication gives \(3\times5=15\), so subtracting yields \(16-15=1\). The choice "\(-7\)" is wrong because it comes from computing \(4^2\) as \(4\times2=8\) instead of \(4\times4=16\), a common exponent mistake. Exponents represent repeated multiplication of the base by itself, not the base times the exponent value.

Multiplying two negative numbers gives a positive product, so \(-3\times(-3)=9\), and adding \(2\) gives \(11\). The choice "\(-7\)" is wrong because it would result from computing the product as \(-9\), misapplying the sign rule for two negatives. Two negatives multiplied together always yield a positive result.

Ordering from greatest to least places the largest positive value first, then continues down through zero to the most negative value, giving \(4, 0, -2, -7\). The choice "\(-7,-2,0,4\)" is wrong because it is actually the least to greatest order, the reverse of what was requested. Always double-check whether a question asks for ascending or descending order before answering.

Absolute value converts both numbers to positive before combining, so \(|-6|=6\) and \(|-9|=9\), and \(6+9=15\). The choice "\(-3\)" is wrong because it results from subtracting the absolute values instead of adding them as the expression requires. Absolute value bars must be resolved before combining the results with other operations.

Division and multiplication share equal precedence and are evaluated left to right, so \(20\div(-5)=-4\) first, then \(-4\times2=-8\). The choice "\(8\)" is wrong because it would result from multiplying the divisors together without following the correct left-to-right order and sign rules. Multiplication and division are always performed from left to right, not chosen arbitrarily.

Working left to right, \(-12+15=3\), and then \(3-8=-5\). The choice "\(5\)" is wrong because it flips the sign of the final subtraction step, mishandling the order of the operations. Addition and subtraction must always be processed in the order they appear from left to right.

The parentheses give \(4-6=-2\), and squaring a negative number always produces a positive result, \((-2)^2=4\), so \(3\times4=12\). The choice "\(-12\)" is wrong because it incorrectly keeps the squared term negative, forgetting that squaring any real number yields a non-negative result. Squaring a negative value always results in a positive number.

Distance is found using the absolute value of the difference between two points, so \(|3-(-5)|=|8|=8\). The choice "\(2\)" is wrong because it fails to properly combine the signs when subtracting a negative from a positive value. Distance between any two points on a number line is always the absolute value of their difference.

Multiplying first gives \(-2\times3=-6\), and subtracting a negative four adds it, so \(-6+4=-2\). The choice "\(-10\)" is wrong because it treats \(-(-4)\) as \(-4\) rather than correctly flipping it to \(+4\). Subtracting a negative number is always equivalent to adding its positive counterpart.

Order of operations requires multiplication before addition, so \(2+4\times2=2+8=10\). The choice "\((2+4)\times2\)" is wrong because the parentheses force addition first, changing the value to \(12\) instead of \(10\). Parentheses and multiplication precedence can dramatically change the outcome of an expression.

Squaring a negative number placed inside parentheses multiplies \(-4\) by itself, giving a positive result of \(16\). The choice "\(-16\)" is wrong because that would be the value of \(-4^2\) without parentheses, an entirely different expression. Parentheses around a negative base change how the exponent applies to the sign.

Dividing two negative numbers gives a positive quotient, \(-16\div(-4)=4\), and adding \(3\) gives \(7\). The choice "\(-1\)" is wrong because it treats the quotient as negative, misapplying the rule that same-signed division produces a positive result. Dividing two negative numbers always yields a positive quotient.

The parentheses give \(3-1=2\), multiplying by \(2\) gives \(4\), and subtracting from \(7\) gives \(3\). The choice "\(10\)" is wrong because it results from subtracting before multiplying, ignoring the correct order of operations. Operations inside parentheses and multiplication must be completed before subtraction.

Multiplying first, two negatives give a positive product, \((-3)\times(-2)=6\), and then \(-8+6=-2\). The choice "\(-14\)" is wrong because it incorrectly adds \(-8\) and \(-3\) before multiplying by \(-2\), ignoring the required order of operations. Multiplication takes precedence over addition even when negative signs are involved.

The expression inside the absolute value bars simplifies first, \(-5+2=-3\), and then the absolute value gives \(3\). The choice "\(7\)" is wrong because it incorrectly adds the absolute values of \(5\) and \(2\) separately instead of combining them first. Always simplify the expression inside absolute value bars before applying the absolute value.

The exponent and multiplication are computed first, \(3^2=9\) and \(5\times2=10\), so subtracting gives \(10-9=1\). The choice "\(19\)" is wrong because it results from adding the two terms instead of subtracting, treating the expression as \(10+9\). Exponents and multiplication must be evaluated before the final subtraction step.

Without parentheses, \(-2^4\) means the negative of \(2^4\), giving \(-16\), while \((-2)^2\) with parentheses squares the full negative value to give \(4\), so \(3\times4=12\) and \(-16+12=-4\). The choice "\(28\)" is wrong because it treats \(-2^4\) as \((-2)^4=16\), ignoring the crucial difference parentheses make to how the exponent applies. Without parentheses, an exponent applies only to the number immediately before it, not to a preceding negative sign.

Simplifying inside each set of bars gives \(|-11|=11\) and \(|-7|=7\), so subtracting yields \(11-7=4\). The choice "\(18\)" is wrong because it incorrectly adds the two absolute values instead of subtracting them as the expression specifies. Absolute value expressions must be fully simplified inside the bars before combining with operations outside them.

Substituting \(-5\) gives \((-5)^2-3(-5)+1=25+15+1=41\), since squaring removes the negative and subtracting a negative becomes addition. The choice "\(-39\)" is wrong because it mishandles \(-3x\) as \(-15\) and then subtracts it instead of correctly adding, an incorrect sign application. Substitute negative values carefully using parentheses to preserve correct sign handling throughout the expression.

The innermost exponent gives \((-2)^2=4\), so the bracket becomes \(3-4=-1\); multiplying by \(2\) gives \(-2\), and \(4-(-2)=6\). The choice "\(2\)" is wrong because it fails to correctly subtract the negative result at the final step, treating it as \(4-2=2\). Work from the innermost grouping symbol outward, resolving exponents before other operations within each group.

Multiplying first gives \(-4\times(-2)=8\), squaring gives \((-5)^2=25\), and combining left to right yields \(-3+8+25=30\). The choice "\(-10\)" is wrong because it incorrectly evaluates \((-5)^2\) as \(-25\), ignoring that parentheses force the entire negative base to be squared. Parenthesized negative bases squared always produce positive results, and multiplication must be completed before addition.

An odd exponent preserves the sign of its base, so \((-2)^3=-8\), while \(2^3=8\), giving \(-8-8=-16\). The choice "\(0\)" is wrong because it assumes the two terms cancel out, ignoring that subtraction of two equal-magnitude values with the same intended sign actually doubles the result rather than canceling it. Odd exponents keep the sign of the base, unlike even exponents which always produce positive results.

Since \(|-7|=7\), the term \(-|-7|\) becomes \(-7\), and subtracting \(-3\) adds it, giving \(-7+3=-4\). The choice "\(-10\)" is wrong because it treats \(-(-3)\) as \(-3\) instead of correctly converting it to \(+3\). Apply absolute value first, then handle any outside negative signs and subtraction of negatives carefully.

Substituting gives \((-2)(-5)-(-2)^2=10-4=6\), since two negatives multiply to a positive and squaring \(-2\) also produces a positive \(4\). The choice "\(14\)" is wrong because it results from adding \(a^2\) instead of subtracting it, or from mistakenly evaluating \((-2)^2\) as \(-4\). Evaluate each term separately with correct sign rules before combining them into a final answer.

Working from the innermost parentheses outward, \(5-8=-3\), then \(4-(-3)=7\), and finally \(6-7=-1\). The choice "\(13\)" is wrong because it results from adding all the numbers together instead of following the nested subtraction structure of the expression. Nested grouping symbols must be resolved one layer at a time, starting from the innermost group.

Without parentheses, \(-5^2=-25\) because the exponent applies before the negative sign, while \(|-5|^2\) first converts \(-5\) to \(5\) and then squares it to get \(25\), so \(-25+25=0\). The choice "\(-50\)" is wrong because it treats both terms as negative after squaring, ignoring that absolute value always removes the sign first. The placement of absolute value bars versus a plain negative sign dramatically changes how an exponent interacts with the sign.

Since \((-2)^3=-8\), \(3\times(-8)=-24\), and since \((-1)^5=-1\), \(4\times(-1)=-4\); subtracting this negative gives \(-24-(-4)=-20\). The choice "\(-28\)" is wrong because it results from adding the two products instead of correctly subtracting a negative value. Odd exponents retain the sign of a negative base, and subtracting a negative term always increases the result.

Simplifying inside the bars gives \(-6+2=-4\), taking the absolute value gives \(4\), multiplying by \(-3\) gives \(-12\), and adding \(5\) gives \(-7\). The choice "\(-17\)" is wrong because it results from adding \(5\) before multiplying by \(-3\), violating the correct order of operations. Absolute value acts like a grouping symbol and must be resolved before any surrounding multiplication or addition.

Here \(|x|^2=|-3|^2=9\) since absolute value removes the sign before squaring, while \(x^3=(-3)^3=-27\) because odd exponents preserve sign, so \(9-(-27)=36\). The choice "\(-18\)" is wrong because it mishandles the subtraction of a negative cube, treating it as \(9-27\) instead of correctly as \(9+27\). Distinguish carefully between an absolute value squared and a variable raised to an odd power, since they behave very differently with negative inputs.