Additive vs multiplicative: 36 and 4. Additive difference is ___, multiplicative ratio is ___. — 32 and 9.36 − 4 = 32 (additive). 36 ÷ 4 = 9 (multiplicative).
Country A has 7 times the population of Country B. If Country A has 350,000 people, how many does Country B have? — 50,000.350,000 ÷ 7 = 50,000.
A pool holds 4 times as much water as a tank. If the pool holds 2,400 L, what does the tank hold? — 600 L.2,400 ÷ 4 = 600 L.
After tripling, a number becomes 99. What was the original number? — 33.If tripled = 99, then original = 99 ÷ 3 = 33.
Emma saved 6 times as much as Finn. Emma saved $90 more than Finn. How much did Finn save? — $18.6f − f = 5f = 90 → f = 18. Finn saved $18.
Which word problem uses multiplicative comparison? (A) "I have 3 more than you." (B) "I have 3 times as many as you." (C) "We have 3 in total." (D) "I gave you 3." — B."3 times as many" is a multiplicative comparison. The others involve addition or subtraction.
Which number is a common factor of both 24 and 36? — 12.24 ÷ 12 = 2 and 36 ÷ 12 = 3, so 12 is a factor of both.
A rectangle has area 30 square units. How many different rectangles with whole-number sides are possible? — 4.Factor pairs of 30: 1×30, 2×15, 3×10, 5×6 — that is 4 distinct rectangles.
Twin primes are pairs of primes differing by 2. Which is a twin prime pair? — (11, 13).11 and 13 are both prime and differ by 2, making them twin primes.
How many factors does 100 have? — 9.Factors of 100: 1,2,4,5,10,20,25,50,100 — that is 9 factors.
What is the prime factorization of 36? — 2² × 3².36 = 2×2×3×3 = 2²×3². This expresses 36 as a product of prime numbers only.
A number less than 50 has exactly 1 factor. What is it? — 1.Only 1 has exactly one factor (itself). Every other positive integer has at least 2 factors.
If you know 6 is a factor of n, which other numbers must also be factors of n? — 1, 2, 3, and 6.If 6|n then 1, 2, 3, and 6 all divide n (since 6 = 2×3, any factor of 6 is also a factor of n).
Pattern: 1, 1, 2, 3, 5, 8, 13, ___. Each term = sum of the two before it. — 21.8 + 13 = 21. This is the famous Fibonacci sequence!
An arithmetic pattern has first term 4 and common difference 7. What is the 8th term? — 53.Term n = 4 + (n−1)×7. Term 8 = 4 + 7×7 = 4 + 49 = 53.
The pattern 2, 6, 18, 54 — how many times greater is each term than the previous? — 3.6/2=3, 18/6=3, 54/18=3. Each term is 3 times the previous.
An additive pattern: 0, 4, 8, 12, 16. An even number added to an even number is always: — Even.Even + even = even. All terms in this pattern are even, confirming even numbers added together always stay even.
A pattern has terms 6, 10, 14, 18. The rule is +4. Which property do all terms share? — All are multiples of 2 (even).6, 10, 14, 18 are all even. Even + even = even, so adding 4 to an even number always gives an even number.
Which term of 3, 9, 27, 81 equals 3^4? — 4th.3¹=3, 3²=9, 3³=27, 3⁴=81. The 4th term equals 3⁴ = 81.
In 100, 95, 90, 85, ..., what is the FIRST negative term? — −5.100, 95, 90, ..., 5, 0, −5. After reaching 0, the next term is −5 (the first negative term).
Two patterns start at 1: Pattern A adds 2, Pattern B multiplies by 2. After 5 steps, which is larger? — Pattern B (1,2,4,8,16,32).After 5 steps: A=11, B=32. Multiplicative patterns grow much faster!
Fill in the missing term: 2, 5, 11, 23, ___, 95 — 47.Pattern: each term = (previous × 2) + 1. 2→5 (2×2+1), 5→11, 11→23, 23→47, 47→95. Missing term is 47.