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In 4,782 the digits from left to right sit in the thousands, hundreds, tens, and ones places. The 7 is in the hundreds place, so its value is 7 hundreds, which equals 700.
The words name 605 thousands and then 40 ones. Writing the thousands group as 605 and the ones group as 040 gives 605,040, because the ones group must always keep three digits.
Place each digit in its named column: ten-thousands 8, thousands 3, hundreds 0, tens 5, ones 2. Reading left to right gives 83,052, and the zero must be written to hold the hundreds place.
All four numbers have the same thousands digit, so compare hundreds first: 0, then 5, then 5, then 9. For the two numbers with 5 hundreds, compare tens: 0 is less than 9, so 3,509 comes before 3,590.
Add the parts by placing each value in its column: 6 thousands, 4 hundreds, 3 tens, and 8 ones. Combined, they form the number 6,438.
The parts give 5 ten-thousands, 2 thousands, 7 hundreds, 0 tens, and 9 ones. Writing each digit in its column, with a zero for the empty tens place, gives 52,709.
One ten equals 10, so 40 tens equals 40 x 10 = 400. Moving a digit one place to the left multiplies its value by ten.
A whole number is even when its ones digit is 0, 2, 4, 6, or 8. The number 8,634 ends in 4, so it is even.
Add the ones, tens, hundreds, and thousands, regrouping when a column reaches ten or more. 1,248 + 675 = 1,923, because 8 + 5 = 13 ones, giving 3 ones and 1 regrouped ten.
Regroup across the zeros: borrow from the 5 thousands to make 4,000 + 900 + 90 + 12, then subtract. 5,002 - 1,468 = 3,534.
To compare two amounts, subtract the smaller from the larger: 2,375 - 1,896. Regrouping gives 479, so Friday had 479 more tickets.
Break 47 into 40 and 7. Then 40 x 6 = 240 and 7 x 6 = 42, and 240 + 42 = 282.
Equal rows mean division: 96 divided by 8. Since 8 x 12 = 96, each row has 12 chairs.
To round to the nearest hundred, look at the tens digit. The tens digit is 0, which is less than 5, so the hundreds digit stays 6 and the answer is 3,600.
A number rounds to 5,000 when it lies from 4,500 up to but not including 5,500. The number 4,500 is exactly at the lower boundary, and the hundreds digit 5 means it rounds up to 5,000.
Use place value: 25 x 32 = 25 x 30 + 25 x 2. That gives 750 + 50 = 800.
Multiplying by 10 shifts each digit one place to the left, so dividing by 10 shifts it back. 4,700 divided by 10 is 470.
The distributive property says a x (b + c) = a x b + a x c. Applying it to 6 x (4 + 5) gives 6 x 4 + 6 x 5, and both equal 54.
Order of operations says to multiply before adding. So 3 x 4 = 12 first, and then 8 + 12 = 20.
The divisibility rule for 3 checks the digit sum: if the digits add to a multiple of 3, the whole number is a multiple of 3. For example, 4,281 has digit sum 15, so it is divisible by 3.
A common multiple must appear in both times tables. Multiples of 4 include 24, and 6 x 4 = 24, so 24 is a multiple of both 4 and 6.
List the factors of each number: 36 has 1, 2, 3, 4, 6, 9, 12, 18, 36, and 48 has 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest factor they share is 12.
The bells coincide at common multiples of 6 and 8 minutes. The least common multiple is 24, since 24 is the smallest number both divide, so the next shared ring is 24 minutes after 9:00, at 9:24 a.m.
First find the total bottles shipped: 24 bottles per crate times 15 crates, or 24 x 15. Then subtract the 7 broken bottles, giving 24 x 15 - 7.
To stay below 7,000 the thousands digit must be 5, the largest available digit under 7. To make the number as large as possible, place the remaining digits 9, 7, and 3 in decreasing order, giving 5,973, which is odd.
Each digit's value depends on its place: ten-thousands means the digit is multiplied by 10,000, thousands by 1,000, and so on. Writing the digits in order from ten-thousands to ones gives 7 0 4 2 9, which is 70,429.
To compare whole numbers, compare digits from left to right. 4,099 and 4,199 both start with 4, but the next digit 0 is less than 1, so 4,099 is actually less than 4,199; the true statement among the choices is 3,876 < 3,867? Wait, check each: 4,099 > 4,199 is false; 5,010 < 5,001 is false; 6,305 = 6,350 is false; 3,876 < 3,867 is false because 3,876 has 7 tens and 3,867 has 6 tens, so 3,876 > 3,867. None are true, so the question is flawed. Let's re-evaluate: Actually 4,099 > 4,199 is false. 5,010 < 5,001 is false. 6,305 = 6,350 is false. 3,876 < 3,867 is false. So no correct option. I need to fix this question. I'll change the options to have one true. For example: 4,099 < 4,199 is true. But I must have one correct. So I'll rewrite the question: Which comparison is true? Options: A) 4,099 < 4,199 (true), B) 5,010 < 5,001 (false), C) 6,305 = 6,350 (false), D) 3,876 < 3,867 (false). Then correct is A. But I need to ensure exactly one correct. So I'll set correctIndex 0 with option0 being "4,099 < 4,199". Let's do that.
In 352,718, the digits from left to right are in the hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones places. The digit 5 is in the ten-thousands place, so its value is 5 × 10,000 = 50,000.
Adding the hundreds, tens, and ones gives 300 + 40 + 9 = 349. The digits appear in order from hundreds to ones, so the number is 349.
Standard form writes the number using digits, with each place value in its correct position. 6,000 + 70 + 5 means 6 thousands, 0 hundreds, 7 tens, and 5 ones, which is written as 6,075.
When rounding to the nearest thousand, look at the hundreds digit. If it is 4 or less, round down; if 5 or more, round up. 7,450 has a hundreds digit of 4, so it rounds down to 7,000? Wait, 7,450 rounded to nearest thousand: the hundreds digit is 4, so we keep the thousands digit 7 and change the rest to zeros, giving 7,000. But the target is 8,000. So 7,450 rounds to 7,000, not 8,000. So option0 is wrong. Let's check others: 8,620 has hundreds digit 6, so rounds up to 9,000? Actually 8,620: hundreds digit 6, so round up the thousands digit from 8 to 9, giving 9,000. 7,399: hundreds digit 3, rounds down to 7,000. 8,501: hundreds digit 5, rounds up to 9,000. None round to 8,000. So the question is flawed. I need to fix. Numbers that round to 8,000 are those from 7,500 to 8,499. So I should pick an option in that range. For example, 7,650 rounds to 8,000 because hundreds digit 6 >=5, so round up 7 to 8. So I'll change options to: A) 7,650 (correct), B) 8,620, C) 7,399, D) 8,501. Then correctIndex 0. Let's do that.
To round to the nearest hundred, look at the tens digit. In 4,827, the tens digit is 2, which is less than 5, so keep the hundreds digit (8) and change the tens and ones to zeros. The result is 4,800.
Subtract by regrouping: 6,000 - 2,475. Since 0 ones is less than 5 ones, regroup from the thousands. 6,000 becomes 5 thousands, 9 hundreds, 9 tens, and 10 ones. Then subtract: 10 - 5 = 5 ones; 9 - 7 = 2 tens; 9 - 4 = 5 hundreds; 5 - 2 = 3 thousands. The result is 3,525.
Add column by column from right to left: ones: 6 + 9 = 15, write 5, carry 1. Tens: 5 + 8 + 1 = 14, write 4, carry 1. Hundreds: 4 + 7 + 1 = 12, write 2, carry 1. Thousands: 3 + 2 + 1 = 6. The sum is 6,245.
First find the total sold: 1,275 + 850 = 2,125. Then subtract from the starting amount: 2,500 - 2,125 = 375. So 375 books are left.
Add the numbers in columns: ones: 4 + 8 + 6 = 18, write 8, carry 1. Tens: 3 + 7 + 7 + 1 = 18, write 8, carry 1. Hundreds: 2 + 6 + 8 + 1 = 17, write 7, carry 1. Thousands: 1 + 5 + 9 + 1 = 16. The sum is 16,788.
Multiplying by 20 is the same as multiplying by 2 and then by 10. 43 × 2 = 86, and 86 × 10 = 860. So 43 × 20 = 860.
Multiply the number of boxes by the number of pencils per box: 15 × 24. Break 24 into 20 + 4: 15 × 20 = 300, and 15 × 4 = 60. Then 300 + 60 = 360 pencils.
Division asks how many groups of 12 are in 144. Since 12 × 12 = 144, the quotient is 12.
Divide the total number of eggs by the number of eggs per carton: 372 ÷ 12. Since 12 × 30 = 360 and there are 12 left, 12 × 31 = 372. So the farmer can fill 31 cartons.
Divide each place value: 2,408 ÷ 4. 2,400 ÷ 4 = 600, and 8 ÷ 4 = 2, so the quotient is 602.
Find the greatest multiple of 7 that is less than or equal to 50. 7 × 7 = 49, and 50 - 49 = 1. So the quotient is 7 with a remainder of 1.
The distributive property says that a × (b + c) = a × b + a × c. Applying this to 8 × (7 + 3) gives 8 × 7 + 8 × 3.
Follow the order of operations: first evaluate the parentheses, 6 - 2 = 4. Then divide: 24 ÷ 4 = 6. Finally add 3: 6 + 3 = 9.
Evaluate each expression using the order of operations. For 6 + 3 × 10, multiply first: 3 × 10 = 30, then add 6: 6 + 30 = 36. The other expressions do not equal 36.
Work backward: start with 35, subtract 7 to undo the addition, giving 28. Then divide by 4 to undo the multiplication: 28 ÷ 4 = 7. So the number is 7.
A factor of 36 divides 36 evenly, and a multiple of 3 is 3, 6, 9, 12, ... Among the choices, 9 is a factor of 36 (36 ÷ 9 = 4) and a multiple of 3 (3 × 3 = 9).
List multiples of 6: 6, 12, 18, 24, 30, ... and multiples of 8: 8, 16, 24, 32, ... The smallest number that appears in both lists is 24. So the LCM of 6 and 8 is 24.
A whole number is divisible by 9 exactly when the sum of its digits is divisible by 9. This is a divisibility rule for 9.
A prime number has exactly two factors: 1 and itself. 29 is not divisible by 2, 3, 5, 7, 11, 13, ... and has no factors other than 1 and 29, so it is prime.