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Reading from the right, the digits occupy units, tens, hundreds, thousands, ten-thousands, hundred-thousands. The 7 sits in the fifth place from the right, which is the ten-thousands column, so its value is 70 000.
A number is divisible by 9 when the sum of its digits is a multiple of 9. The digits of 4 512 add to 12, which is not a multiple of 9, so this option is not divisible by 9 either - wait, rechecking: 4+5+1+2 = 12. The correct choice must have a digit sum of 9, 18, 27 and so on.
The highest common factor of 36 and 48 is 12. Dividing numerator and denominator by 12 gives 3/4, and 3 and 4 share no common factor, so the fraction is fully reduced.
Two hundred and five thousand is 205 000, and forty adds 40 in the tens column. Combining them gives 205 040, with a zero in the hundreds place and a zero in the units place.
To round to the nearest hundred, look at the tens digit. Here the tens digit is 4, which is less than 5, so the hundreds digit stays at 7 and the following digits become zeros, giving 6 700.
Following the order of operations, multiplication and division are done before addition and subtraction. This gives 3 + 8 − 2, which evaluates to 9.
A prime number has exactly two factors, 1 and itself. The number 29 is not divisible by 2, 3, or 5, and its square root is about 5.4, so no other factor exists; it is prime.
0.75 means 75 hundredths, that is 75/100. Dividing numerator and denominator by 25 gives 3/4, which is the simplest form.
Listing multiples of 12 gives 12, 24, 36, 48…, and multiples of 18 give 18, 36, 54…. The smallest value appearing in both lists is 36. Equivalently, LCM = (12 × 18) ÷ HCF = 216 ÷ 6 = 36.
If the original price is 100, a 20% increase gives 120, and a 20% reduction of 120 gives 96. The final price is 96 compared with 100, a net decrease of 4%.
When multiplying powers with the same base, add indices: 2³ × 2⁴ = 2⁷. When dividing, subtract indices: 2⁷ ÷ 2² = 2⁵. The result is 32.
Standard form requires a number between 1 and 10 multiplied by a power of 10. Moving the decimal point four places to the right gives 3.05, so the exponent is −4.
The square root of 144 is 12 because 12 × 12 = 144. The cube root of 27 is 3 because 3 × 3 × 3 = 27. Adding gives 12 + 3 = 15.
The lowest common denominator of 5 and 7 is 35. Converting gives 21/35 + 10/35 = 31/35, and 31 is prime, so the fraction cannot be reduced further.
An increase of 15% means the new value is 115% of the original. Divide 92 by 1.15 to get 80. Checking: 80 × 1.15 = 92.
On a number line, values increase from left to right. The most negative number, −5, is smallest, followed by −2, then 0, then 3, so the ascending order is −5, −2, 0, 3.
Repeated division by primes gives 84 = 2 × 42 = 2 × 2 × 21 = 2² × 3 × 7. All factors are prime, so this is the correct prime factorisation.
Let x = 0.333…; then 10x = 3.333…. Subtracting gives 9x = 3, so x = 3/9 = 1/3. The recurring decimal is exactly one third.
For two numbers, HCF × LCM = product of the numbers. So 6 × 72 = 432, and the other number is 432 ÷ 24 = 18. Checking: HCF(24, 18) = 6 and LCM(24, 18) = 72, both correct.
Multiplying by 10³ shifts the decimal point three places to the right, turning 4.2 into 4 200. This matches the meaning of the exponent 3.
A prime number must have exactly two distinct factors, and a composite number must have more than two. The number 1 has only one factor, itself, so it belongs to neither category.
Check 23: 23 ÷ 5 leaves remainder 3, and 23 ÷ 3 leaves remainder 2. Both conditions hold, so 23 is a valid value of N.
Dividing 2 by 3 gives 0.6666…, a recurring decimal. To round to 3 decimal places, look at the fourth digit, which is 6, so round the third digit up, giving 0.667.
The ratio 5 : 3 means there are 8 parts in total. Each part is 480 ÷ 8 = 60 pupils, and girls make up 3 parts, so there are 3 × 60 = 180 girls.
After one year the value is 81 000 × 0.9 = 72 900. After the second year it is 72 900 × 0.9 = 65 610. Equivalently, 81 000 × 0.9² = 65 610.
Reading from the right, the digits occupy units, tens, hundreds, thousands and ten-thousands places. In 47 382 the 7 sits in the thousands column, so its value is 7 × 1000 = 7000.
A number is a multiple of both 6 and 9 exactly when it is a multiple of their LCM, which is 18. Checking the options, only 54 = 18 × 3 is divisible by 18, and indeed 54 ÷ 6 = 9 and 54 ÷ 9 = 6.
On a number line, negative integers lie to the left of zero and the further left a number is, the smaller it is. Among the negatives, −7 is further left than −2, so the ascending order is −7, −2, 0, 3.
Standard form requires a single non-zero digit before the decimal point, followed by further digits, multiplied by a power of 10. Only 2.45 × 10³ has its first factor between 1 and 10, so it is the only valid standard form.
Evaluate each power and multiply: 2⁴ = 16, 3² = 9, so 16 × 9 = 144 and 144 × 5 = 720. The prime factorisation therefore represents 720.
Dividing by a fraction is the same as multiplying by its reciprocal, so (2/3) ÷ (4/9) = (2/3) × (9/4) = 18/12. Simplifying 18/12 by dividing both parts by 6 gives 3/2.
Work through powers first, then multiplication and division left to right, then addition and subtraction: 5² = 25, 3 × 4 = 12 and 12 ÷ 6 = 2. So 25 − 12 + 2 = 15, which is 15, not 19 - rechecking: 25 − 12 = 13, then 13 + 2 = 15.
Rounding to 2 significant figures means the answer lies within half of the last retained place of 0.058, which is 0.0005. The lower bound is therefore 0.058 − 0.0005 = 0.0575, and any value from 0.0575 up to (but not including) 0.0585 rounds to 0.058.
Let x = 0.6666…, then 10x = 6.6666… Subtracting gives 9x = 6, so x = 6/9 = 2/3. The fraction is already in simplest form because 2 and 3 share no common factor.
Each part of the ratio is worth 630 ÷ 7 = 90 g. Sugar corresponds to 2 parts, so the mass needed is 2 × 90 = 180 g.
A negative index gives the reciprocal of the corresponding positive power, so 3⁻² = 1/3² = 1/9. Any non-zero number to the power zero equals 1, so 2⁰ = 1, and 1/9 + 1 = 10/9.
If N is divisible by 4 and by 6, then N is a multiple of the LCM of 4 and 6, which is 12. Divisibility by 24 does not follow, because 4 and 6 share the factor 2 and their product is not the LCM.
After a 15% discount the selling price is 85% of the marked price. So the marked price is 68 000 ÷ 0.85 = 80 000, which is larger than the selling price as expected.
For a prime factorisation pᵃ × qᵇ × rᶜ, the number of positive factors is (a+1)(b+1)(c+1). Here that gives (3+1)(2+1)(1+1) = 4 × 3 × 2 = 24 factors.
Write 0.004 × 10⁵ as 4 × 10⁻³ × 10⁵ = 4 × 10². Dividing by 2 × 10⁻³ gives (4 ÷ 2) × 10^(2 − (−3)) = 2 × 10⁵, which is already in standard form.
Subtract by borrowing across place values: 4,608 − 2,749. Working from the ones column, 8 − 9 requires regrouping, and the final result is 1,859. Checking by addition, 1,859 + 2,749 = 4,608, which confirms the answer.
Reading place values from the right, the digits occupy ones, tens, hundreds, thousands, ten-thousands, hundred-thousands and millions. The 7 sits in the hundred-thousands place, so its value is 7 × 100,000 = 700,000.
Each period holds three digits: millions, thousands, then units. Forty million gives 40 in the millions period, six hundred five thousand gives 605 in the thousands period, and ninety-two gives 092 in the units period, so the number is 40,605,092.
Order of operations requires brackets first, so 9 − 3 = 6. Then multiplication precedes addition: 4 × 6 = 24, and finally 26 + 24 = 50.
A number is divisible by 9 exactly when the sum of its digits is a multiple of 9. For 4,536 the digit sum is 4 + 5 + 3 + 6 = 18, which is a multiple of 9.
To round to the nearest hundred, look at the tens digit. Here the tens digit is 4, which is less than 5, so the hundreds digit stays the same and the remaining digits become zeros, giving 6,800.
A prime has exactly two factors, 1 and itself. The number 37 is not divisible by 2, 3, 5 or 7, so it has no factor other than 1 and 37, making it prime.
First find the total: 8 × 24 = 192 books. Then subtract the books given away: 192 − 37 = 155. The two operations must be done in that order because the giveaway applies to the whole purchase.
Multiply 3,205 by 6 to get 19,230, then multiply 3,205 by 40 to get 128,200. Adding the partial products gives 19,230 + 128,200 = 147,430.
Divide the total mass by the number of sacks: 9,450 ÷ 75. Since 75 × 126 = 9,450, each sack holds 126 kg. Multiplying back confirms the division is exact with no remainder.