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In the base-ten place value system, each position is ten times the value of the position to its right. In 4,782 the digit 7 sits in the hundreds place, so it represents 7 hundreds, which equals 700.
Each named place value contributes its digit to that position, and a zero must be written in the thousands place. Placing 3 in ten-thousands, 0 in thousands, 6 in hundreds, 5 in tens, and 2 in ones gives 30,652.
When two numbers have the same number of digits, compare from the left until the digits differ. All four options share the digits 5,4,9 in the hundreds and tens positions, so compare the ones digits: 5,500 has 0 ones against 9 ones in 5,499, making 5,500 the larger value.
To round to the nearest hundred, look at the tens digit. The tens digit of 6,847 is 4, which is less than 5, so the hundreds digit stays at 8 and the remaining digits become zeros, giving 6,800.
Adding the ones gives 8 + 7 = 15, so write 5 and carry 1 ten. Adding the tens gives 3 + 4 + 1 = 8 tens, so the total is 85.
Regrouping across the zeros of 500 gives 4 hundreds, 9 tens, and 10 ones. Subtracting 2 hundreds, 6 tens, and 8 ones leaves 2 hundreds, 3 tens, and 2 ones, which is 232.
Multiplication is commutative, so 4 × 6 equals 6 × 4, and both equal 24. The other choices give 10, 36, and 12, none of which equals 24.
A fraction compares the number of equal parts selected to the total number of equal parts. Here 3 parts are shaded out of 8 equal parts, so the shaded fraction is 3/8.
The cost of 7 notebooks is 7 × $2 = $14. Subtracting that cost from the $20 paid gives $20 − $14 = $6 in change.
Order of operations requires multiplication and division before addition. First 24 ÷ 6 = 4 and 3 × 2 = 6, then 4 + 6 = 10, so the correct value is 10; among the listed choices the intended answer follows that same left-to-right evaluation of the two operations before adding.
When the denominators are the same, larger numerators mean larger fractions. With denominator 4, the fractions are 1/4, 2/4, and 3/4, so the order from least to greatest is 1/4, 1/2, 3/4.
A fraction with denominator 10 converts to a decimal by placing the numerator in the tenths position. The numerator 7 goes in the tenths place, giving 0.7. Note that 0.70 is the same value but is listed separately as a trap for place-value confusion.
Multiplying a fraction by a whole number repeats the fraction that many times: 3 × 2/3 = 6/3. Since 6 divided by 3 equals 2, three batches require 2 cups of sugar.
List the factors of each number: 24 has 1, 2, 3, 4, 6, 8, 12, 24, and 36 has 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest factor appearing in both lists is 12.
A multiple of both 4 and 6 must be divisible by each. The multiples of 4 include 4, 8, 12, 16, 20, 24, and the multiples of 6 include 6, 12, 18, 24, 30. The smallest shared value in the list is 24.
The nth term of an arithmetic pattern starting at 5 with a common difference of 7 is 5 + 7(n − 1). For n = 10, this gives 5 + 7 × 9 = 5 + 63 = 68.
Line up the decimal points and write 4.6 as 4.60 so both numbers have two decimal places. Adding 4.60 + 3.75 gives 8.35.
The divisibility rule for 9 states that a number is divisible by 9 exactly when the sum of its digits is divisible by 9. For example, 738 has digit sum 18, so it is divisible by 9.
Rounding to the nearest thousand gives 5,000 for any number from 4,500 through 5,499. The number 4,650 lies in that interval, so it rounds to 5,000.
The distributive property states that a × (b + c) = a × b + a × c. Applying it with a = 3, b = 8, and c = 4 gives 3 × 8 + 3 × 4, and both expressions equal 36.
A remainder of 3 when dividing by 5 means the number is 3 more than a multiple of 5. Since 25 is a multiple of 5, 25 + 3 = 28 satisfies the condition, and 28 ÷ 5 = 5 remainder 3.
First find the red marbles: 3/8 of 48 is 48 ÷ 8 × 3 = 18. The marbles that are not red are 48 − 18 = 30, which also equals 5/8 of 48.
A fraction between 0 and 1 represents a part of a whole, so multiplying a whole number by it produces only that part. For example, 12 × 1/4 = 3, which is less than 12, and this reasoning holds for every positive whole number.
In a five-digit number the places from left to right are ten-thousands, thousands, hundreds, tens, ones. The number 46,208 has 6 in the thousands place and 0 in the tens place, so it matches both conditions.
Numbers that round to 800 lie from 750 to 849 inclusive. The greatest number in that interval is 849 and the least is 750, so the greatest possible difference is 849 − 750 = 99.
Working backward reverses each step: first add 4 to 86 to get 90, then divide by 10 to get 9. Checking forward, 9 × 10 − 4 = 86, which matches the output.
Place value means each addend fills one position: 4 thousands, 3 hundreds, 0 tens, and 7 ones. Writing the digits in order gives 4,307, with a zero holding the tens place.
Rewrite 3/4 as 6/8 so both fractions have the same denominator, then add 6/8 + 1/8 = 7/8. The result is less than one meter, which fits a ribbon slightly longer than 3/4 meter.
Compare place by place: both decimals have 0 ones, then 0.6 has 6 tenths while 0.58 has 5 tenths. Since 6 tenths is greater than 5 tenths, 0.6 is larger regardless of the extra digit in 0.58.
48 ÷ 8 equals 6, so the matching expression must also equal 6. Only 6 × 1 gives 6, while the other products give 9, 10, and 16.
Add by place value: 1,250 + 875. The ones give 0 + 5 = 5, the tens give 5 + 7 = 12 (write 2, carry 1), the hundreds give 2 + 8 + 1 = 11 (write 1, carry 1), and the thousands give 1 + 1 = 2, so the total is 2,125.
A factor divides a number with no remainder. 36 ÷ 9 = 4 exactly, but 24 ÷ 9 leaves a remainder, so 9 divides 36 only. The other choices divide both 24 and 36 evenly.
In a decimal, the first place after the point is tenths and the second is hundredths. The number must therefore have 2 tenths and 5 hundredths, written 0.25.
Use eighths as a common denominator: 3/4 = 6/8, so 6/8 + 5/8 = 11/8. Rewriting the improper fraction gives 1 3/8 bags.
The unit price is $4.50 ÷ 3 = $1.50 per notebook. Multiplying by 8 gives 8 × $1.50 = $12.00.
Write 2 1/2 as 5/2 and 1 1/2 as 3/2, then multiply: 5/2 × 3/2 = 15/4. Converting 15/4 gives 3 3/4 cups.
Because 6 = 2 × 3 and the two factors share no common factor, any multiple of 6 is a multiple of both 2 and 3. This is the divisibility rule for 6.
Numbers from 650 through 749 round to 700, since 750 would round up to 800. The greatest whole number in that range is 749.
Order of operations: evaluate the parentheses first to get 5, then multiply 2 × 5 = 10, then add 5 + 10 = 15.
Divide the numerator by the denominator: 3 ÷ 8 = 0.375, since 8 × 375 = 3,000 in thousandths. So 3/8 is exactly 0.375.
Divide the total by the number of bottles: 2.5 ÷ 4 = 0.625. Checking, 4 × 0.625 = 2.5, so each bottle holds 0.625 liter.
Each fraction multiplies the numerator and denominator of 1/2 by the same whole number, so all are equivalent to 1/2. Equivalent fractions name the same value even when the digits differ.
The buses carry 6 × 48 = 288 students and the vans carry 3 × 12 = 36 students. Adding the two groups gives 288 + 36 = 324 students.
A prime number has exactly two factors, 1 and itself. The number 29 has no factor other than 1 and 29, so it is prime.
Compare hundredths: 0.4 = 0.40 and 0.5 = 0.50, so a number between them must be greater than 0.40 and less than 0.50. The value 0.45 lies inside that range.
Undo the steps in reverse order: subtract 7 from 43 to get 36, then divide by 4 to get 9. Checking, 9 × 4 + 7 = 43.
Since 99 = 100 − 1, the distributive property gives 7 × 99 = 7 × 100 − 7 × 1 = 700 − 7 = 693.
Draining 1/4 of the water leaves 3/4 of it, so multiply 2/3 × 3/4 = 6/12 = 1/2. The remaining water fills half the tank.
Numbers with remainder 2 when divided by 5 are 12, 17, 22, 27, ... Testing each for remainder 1 when divided by 3: 12 gives 0, 17 gives 2, and 22 gives 1. So 22 is the least value above 10.
For two numbers, the product of the GCF and LCM equals the product of the numbers: 6 × 36 = 216. Dividing by 12 gives 216 ÷ 12 = 18, and checking, GCF(12, 18) = 6 and LCM(12, 18) = 36.