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A digit's value depends on its place: each place to the left is worth ten times the place to its right. The 7 sits in the hundreds place, so its value is 7 × 100 = 700.
To round to the nearest hundred, look at the tens digit. Since 7 is 5 or greater, the hundreds digit increases from 8 to 9 and the digits to its right become zeros, giving 6,900.
A number is divisible by 3 exactly when the sum of its digits is divisible by 3. The digits of 351 sum to 3 + 5 + 1 = 9, which is a multiple of 3.
A prime number has exactly two factors, 1 and itself. The number 37 has no factor other than 1 and 37.
Going from a denominator of 4 to a denominator of 12 multiplies the denominator by 3, so the numerator must also be multiplied by 3. Thus 3/4 = (3 × 3)/(4 × 3) = 9/12.
The decimal 0.6 means 6 tenths, or 6/10. Dividing the numerator and denominator by their common factor 2 gives 3/5, which is in simplest form.
In the order of operations, multiplication is performed before addition. So 2 × 5 = 10 first, and then 8 + 10 = 18.
The number 5,038 has 5 thousands, 0 hundreds, 3 tens, and 8 ones. Expanded form writes each place value separately, so it is 5,000 + 30 + 8.
The factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, and 36, and the factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The largest factor the two numbers share is 12.
Multiples of 8 are 8, 16, 24, 32, ... and multiples of 12 are 12, 24, 36, ... The first multiple the two lists share is 24.
Rewrite 1/3 as an equivalent fraction with denominator 6: 1/3 = 2/6. Then 5/6 − 2/6 = 3/6, which simplifies to 1/2.
Write 2 1/2 as the improper fraction 5/2. Dividing by 1/2 is the same as multiplying by 2, so 5/2 × 2 = 5.
Multiply 4 × 25 = 100, then place the decimal point so the answer has as many decimal places as the two factors combined (1 + 2 = 3). This gives 0.100, which equals 0.1.
A percent is a ratio out of 100, so 15% = 0.15. Multiplying 0.15 × 80 gives 12.
Find the unit price first: $1.20 ÷ 3 = $0.40 per pencil. Then 5 × $0.40 = $2.00.
Adding a positive number moves to the right on the number line: starting at −7 and moving 12 units right lands on 5. Equivalently, 12 − 7 = 5 and the result is positive because 12 has the greater absolute value.
Scientific notation writes a number as a factor between 1 and 10 times a power of 10. Moving the decimal point 4 places to the right to get from 0.00045 to 4.5 means the exponent is −4.
A unit rate is found by dividing the quantity by the number of units: 180 miles ÷ 3 hours = 60 miles per hour.
Rewrite each fraction with the common denominator 120: 3/5 = 72/120, 5/8 = 75/120, 2/3 = 80/120, and 7/12 = 70/120. The largest numerator belongs to 80/120, so 2/3 is the greatest.
Comparing decimals means comparing place values from left to right, so pad with zeros where helpful: 0.600, 0.590, 0.065, 0.605. The tenths and hundredths digits tie for 0.6 and 0.605, and the thousandths digit 5 makes 0.605 larger.
When multiplying powers with the same base, add the exponents: 3⁴ × 3² = 3⁶. When dividing, subtract the exponents: 3⁶ ÷ 3³ = 3³ = 27.
Evaluate the parentheses first: 4 + 2 = 6. Then the exponent gives 6² = 36, the division gives 36 ÷ 9 = 4, and finally 4 − 1 = 3.
Dividing the total amount by the amount per batch gives 9 ÷ 3/4. Dividing by a fraction is the same as multiplying by its reciprocal: 9 × 4/3 = 36/3 = 12.
The greatest common factor of 48 and 72 is 24. Since 48 = 24 × 2 and 72 = 24 × 3, the sum can be written as 24(2 + 3).
After a 20% discount, the sale price is 80% of the original price, so 0.8 × original = $40. Dividing gives $40 ÷ 0.8 = $50.
Each place in a whole number is worth ten times the place to its right. Counting from the right, the digits are ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions, so the 7 sits in the hundred-thousands place. Therefore its value is 7 × 100,000 = 700,000.
On a number line, values increase as you move to the right, and negative numbers farther from zero are smaller. So −9 is less than −3, and both are less than 0 and 6. The only list that follows this order is −9, −3, 0, 6.
Multiply 46 by the 3 ones to get 138, then by the 2 tens (20) to get 920. Adding the two partial products, 138 + 920 = 1,058.
Divide 95 by 8: since 8 × 11 = 88 and 8 × 12 = 96, each student gets 11 pencils. Subtracting 88 from 95 leaves a remainder of 7 pencils.
A prime number has exactly two factors, 1 and itself. The number 29 has no factor other than 1 and 29, while the other choices can all be written as products of smaller whole numbers.
To round to the nearest hundred, look at the digit in the tens place. The tens digit is 7, which is 5 or greater, so the hundreds digit 4 is increased to 5 and the digits to its right become zeros. The result is 6,500.
Divide the numerator and denominator by their greatest common factor, 6. That gives 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so the simplified fraction is 2/3.
In a decimal, the places to the right of the decimal point are tenths, hundredths, and thousandths. The digit 5 is in the second place to the right of the point, so it represents 5 hundredths, or 0.05.
Rewrite both fractions with the common denominator 20: 3/4 = 15/20 and 2/5 = 8/20. Adding the numerators gives 15/20 + 8/20 = 23/20, which is greater than 1 and already in lowest terms.
Multiply numerators and denominators: (2 × 9)/(3 × 10) = 18/30. Dividing both parts by their greatest common factor, 6, gives 3/5.
Multiply both the dividend and divisor by 100 to make the divisor a whole number: 480 ÷ 6. Since 6 × 80 = 480, the quotient is 80.
Evaluate the parentheses first: 4 + 2 = 6. Then multiply before subtracting: 3 × 6 = 18, and finally 20 − 18 = 2.
Absolute value gives the distance from zero, so |−7| = 7, |3| = 3, and |−2| = 2. Substituting gives 7 + 3 − 2 = 8.
To convert a decimal to a percent, multiply by 100 and attach the percent symbol. Since 0.075 × 100 = 7.5, the decimal equals 7.5%.
Set up the proportion 1 inch / 25 miles = 4.5 inches / d miles. Cross-multiplying gives d = 4.5 × 25 = 112.5 miles.
A whole number is divisible by 9 exactly when the sum of its digits is divisible by 9. For 5,238 the digit sum is 5 + 2 + 3 + 8 = 18, and 18 is a multiple of 9.
Divide 84 by primes until only primes remain: 84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7. Writing the repeated factor with an exponent gives 2² × 3 × 7, and the product is 4 × 3 × 7 = 84.
Line up the decimal points and write 12.4 as 12.40 so both numbers have the same number of decimal places. Then subtract: 12.40 − 3.65 = 8.75.
Divide the numerator by the denominator: 17 ÷ 5 = 3 with a remainder of 2. The quotient is the whole number and the remainder goes over the original denominator, giving 3 2/5.
The rate is 3 quarts per 6 hours, so in 24 hours (four 6-hour periods) it drips 12 quarts. Since 4 quarts make 1 gallon, 12 quarts equals 3 gallons.
Four walls use 4 × 2/3 = 8/3 = 2 2/3 gallons. Subtracting from 5 gallons gives 5 − 2 2/3 = 2 1/3 gallons remaining.
Multiply the coefficients and add the exponents of the powers of ten: 3 × 2 = 6 and 10⁴ × 10⁻⁶ = 10⁻². The result is 6 × 10⁻², which is already in scientific notation.
A 25% markup makes the price 60 × 1.25 = $75. The 20% discount is taken on $75, so the final price is 75 × 0.80 = $60.
Any nonzero number raised to the zero power equals 1, so 5⁰ = 1. A negative exponent gives the reciprocal, so 2⁻³ = 1/8, and 1 + 1/8 = 1 1/8.
Distribute the 6 to get 6x + 24, then combine like terms with −2x: 6x − 2x = 4x. The simplified expression is 4x + 24.