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Adding a positive integer to a negative integer means moving to the right on the number line. Starting at −7 and moving 12 units right lands on 5. Equivalently, 12 − 7 = 5, and the answer is positive because 12 has the larger absolute value.
Absolute value measures distance from zero, so it is never negative: |−9| = 9 and |4| = 4. Adding the two distances gives 9 + 4 = 13. The signs inside the bars do not carry over to the result.
The order of operations requires multiplication before addition. So compute 4 × 2 = 8 first, then add 3 to get 11. Working strictly left to right would give the wrong result.
Subtracting a negative number is the same as adding its opposite, so −5 − (−8) becomes −5 + 8. Moving 8 units right from −5 lands on 3. The two negative signs together produce an increase.
Multiply first: the product of two negative numbers is positive, so (−6) × (−4) = 24. Then 24 ÷ (−8) = −3, since a positive divided by a negative gives a negative quotient. With two negative factors and one negative divisor, the overall sign is negative.
Evaluate the exponent first: (−2)³ = −8 because three negative factors give a negative product. Then 4 × (−3) = −12. Adding −8 and −12 gives −20.
For negative numbers, the value closer to zero is greater. Converting to decimals gives −0.6, about −0.667, −0.06, and −1.25. Of these, −0.06 is nearest to zero, so it lies furthest right on the number line and is the greatest.
Write each number in prime form: 12 = 2² × 3 and 18 = 2 × 3². The LCM uses the highest power of every prime that appears, giving 2² × 3² = 4 × 9 = 36.
Simplify inside the parentheses first: 2 − 5 = −3. Then −3 × (−3) = 9, and (−4)² = 16 because a negative squared is positive. Finally 9 + 16 = 25.
The equation |x| = 7 has two solutions, x = 7 and x = −7, and the condition x < 0 selects x = −7. Then x − |x| = −7 − 7 = −14. Subtracting a positive distance from a negative number always decreases the value.
Exponents are evaluated first, then multiplication, then subtraction. Since 3^2 = 9, the product 3^2 × 2 equals 18, and 20 − 18 = 2.
Two numbers are additive inverses when their sum is zero. The opposite of −3/4 is 3/4, because −3/4 + 3/4 = 0.
The greatest common factor is the largest number that divides both values evenly. Since 24 = 2^3 × 3 and 36 = 2^2 × 3^2, the shared prime factors give 2^2 × 3 = 12.
An odd power of −1 stays negative, so (−1)^15 = −1, while an even power clears the sign, so (−2)^4 = 16. Multiplying gives −1 × 16 = −16.
Factoring −3 out of each term gives −6x ÷ (−3) = 2x and 15 ÷ (−3) = −5. Distributing −3 over (2x − 5) returns −6x + 15.
Distance on a number line is the absolute value of the difference between the coordinates. Here |7 − (−4)| = |11| = 11, and a distance is never negative.
The decimal 0.45 means 45 hundredths, or 45/100. Dividing the numerator and denominator by 5 gives 9/20, and 9 and 20 share no common factor other than 1.
Rewrite both fractions over the common denominator 12: −2/3 = −8/12 and 1/4 = 3/12. Adding the numerators gives −8/12 + 3/12 = −5/12.
The even exponent in (−2)^4 makes the result positive, so it equals 16. The other expressions equal −16, 8, and −8 respectively, so 16 is the largest.
Starting at −48 m, a 30 m rise gives −18 m. Descending 15 m gives −33 m, and descending 12 m more gives −45 m.
On a number line, values increase from left to right, and every negative integer is less than zero and also less than any positive integer. Between −8 and −2, the number −8 lies farther left, so it is the smaller one. Putting the four values in increasing order gives −8, −2, 0, 3.
The hundreds digit of 4,782 is 7, and the digit immediately to its right in the tens place is 8. Because 8 is 5 or greater, the hundreds digit increases from 7 to 8 and both digits to the right become zeros. The result is 4,800.
A factor divides a number with a remainder of zero. Since 36 ÷ 9 = 4 exactly, 9 is a factor of 36, but 24 ÷ 9 does not give a whole number. Each of the other choices divides both 36 and 24 evenly.
A rise of 13 °C means adding 13 to the starting reading: −8 + 13 = 5 °C at noon. A fall of 9 °C means subtracting 9 from the noon reading: 5 − 9 = −4 °C. Keeping the sign of each change gives the correct final temperature.
Dividing by 3/8 is the same as multiplying by its reciprocal 8/3. So −3/4 × 8/3 = −24/12 = −2. The quotient is negative because the dividend and the divisor have opposite signs.
Repeatedly divide 180 by the smallest primes: 180 = 2 × 90 = 2 × 2 × 45 = 2² × 3 × 15 = 2² × 3² × 5. Checking by multiplication, 4 × 9 × 5 = 180, so the factorization is complete.
Powers and division are done before addition. Here 24 ÷ (−6) = −4, and (−5)² = (−5)(−5) = 25. Adding the two results gives −4 + 25 = 21, which is positive.
A fraction can be rewritten as a decimal by dividing the numerator by the denominator, so 7 ÷ 8 = 0.875. Checking the result, 0.875 × 8 = 7, which confirms the conversion. The digits come from the division, not from copying the digits of the fraction.
The inequality |n| ≤ 4 means that the distance from n to 0 on the number line is at most 4. So n can be any integer from −4 through 4 inclusive. Listing them as −4, −3, −2, −1, 0, 1, 2, 3, 4 gives a total of 9 integers.
Work through the exponents and operations in order: (−2)³ = −8, so (−8) × (−3) = 24. Also (−4)² = 16 and 16 ÷ (−2) = −8, so the expression becomes 24 − (−8), which equals 24 + 8 = 32.
An integer is a whole number that can be positive, negative, or zero, with no fractional or decimal part. The number −7 is a whole number, while 0.5, 2/3, and 3.2 all have fractional parts.
The absolute value bars make the inside value nonnegative, so |−12| = 12. The minus sign in front then negates that result, giving −12.
On a number line, values increase from left to right. Since −4 is to the right of −9, the true statement is −4 > −9.
Subtracting a negative is the same as adding its opposite, so −14 − (−9) becomes −14 + 9. Combining a negative and a positive gives −5.
First multiply (−8) × (−3); a negative times a negative is positive, so the product is 24. Then divide 24 by (−4), and a positive divided by a negative is negative, giving −6.
Distribute −4 across both terms: −4(x − 3) = −4x + 12. Then combine −4x with 2x to get −2x, leaving −2x + 12.
To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. 3 ÷ 8 = 0.375, and 0.375 × 100 = 37.5%.
First evaluate the expression inside each absolute value: −7 + 3 = −4, so |−7 + 3| = |−4| = 4. Also |−5| = 5, so the expression becomes 4 − 5 = −1.
For negative numbers, the value closest to zero is greatest. Converting to decimals gives −0.666…, −0.625, −0.75, and −0.700, so −5/8 = −0.625 is closest to zero and therefore greatest.
In a whole number, place values from right to left are ones, tens, hundreds, thousands, and ten-thousands. The digits of 48,206 are 4 ten-thousands, 8 thousands, 2 hundreds, 0 tens, and 6 ones, so the thousands digit is 8.
The opposite of a number is the same distance from 0 but on the other side of the number line. Since −13 is 13 units to the left of 0, its opposite is 13 units to the right of 0, which is 13.
List the factors of each number and find the largest factor they share. The factors of 18 include 1, 2, 3, 6, 9, and 18; the factors of 30 include 1, 2, 3, 5, 6, 10, 15, and 30. The greatest shared factor is 6.
Rewrite both fractions with the least common denominator, 12. 2/3 becomes 8/12 and 1/4 becomes 3/12, so the sum is 11/12.
Evaluate the parentheses first: 3 − 8 = −5. Then multiply −5 by −5, and the product of two negative numbers is positive, so the value is 25.
The decimal 0.75 means 75 hundredths, or 75/100. Dividing the numerator and denominator by 25 gives 3/4, so 3/4 is equivalent to 0.75.
The distance between two points on a number line is the absolute value of their difference. |4 − (−7)| = |4 + 7| = 11, so the distance is 11 units.
In −3², the exponent applies only to 3, so the value is −(3 × 3) = −9. In (−3)², the parentheses make the base −3, so the value is (−3) × (−3) = 9. Adding gives −9 + 9 = 0.
Convert each fraction to a decimal: −3/4 = −0.75 and −5/8 = −0.625. For negative numbers, the value closer to zero is greater, so −0.625 is the greatest of the four numbers.
Subtracting a negative number is the same as adding its opposite, so −9 + 4 − (−3) becomes −9 + 4 + 3. Adding from left to right gives −5 + 3, and that sum is −2.
The hundreds digit is 8, so the deciding digit is the tens digit, which is 4. Because 4 is less than 5, the 8 stays the same and the tens and ones digits become zeros, giving 6,800.