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A class has from 30 to 40 students. Each boy brings 15 chocolate bars for a Teacher's Day party. The chocolate bars are shared equally among the 20 girl students and their teacher with no left overs. Find the number of Ss and chocolate bars
15 = 3x5, 21 = 3x7. Total bars = 3 x 5 x 7 x b = 105, 210,... if 105 bars -> 7 boys; if 210 bars -> 14 boys. There should be 10-20 boys -> 14 boys -> 34 Ss
Kate wishes to cut some squares from a vanguard sheet of 64 cm x 48 cm. She likes the square to be as big as possible and she doesn't want any left over. Find the length of each square? How many squares can she cut altogether?
a) 64 = 2^6, 48 = 2^4 x 3. Side = GCF = 2^4 = 16 cm, b) 4 x 3 = 12 squares
Michael is an art student who is working on an assignment. He plans to cover a rectangular sheet of paper of dimensions of 12t cm by 108 cm with identical square patterns. What is the least number of square patterns that could be formed?
126 = 2 x 3^2 x 7, 108 = 2^2 x 3^3 -> GCF = 2 x 3^2 = 18 is the side of the square. 126 = 18 x 7 sqrs, 108 = 18 x 6 sqrs -> 7 x 6 = 42 sqrs
Car X and Car Y are at the starting point of a 2-km track race at the same time. Car X and car Y make one lap every 60s and every 80s respectively. How long does it take for both cars to be back at the starting point at the same time?
420s
Which one of the following is a prime number: 501, 509, 3024, 3715
509
Which one of the following is a composite number: 667, 677, 2021, 2027
667 = 23x29; 667: prime number; 2021 = 43x47; 2027: prime number
The area of a square garden is 10000 meter squared. Find the side of this garden?
10000 = 100 x 100 --> The side is 100 meter
The number 176 and 342, written as the products of their prime factors, are 176 = 2^4 x 11 and 342 = 2 x 3^2 x 19. Hence, find the smallest whole number that is divisible by both 175 and 342
LCM = 2^4 x 3^2 x 11 x 19 = 30096
Find the smallest value of n such that the LCM of n and 15 is 45
15 = 3x5, 45 = 3^2 x 5 --> smallest n = 3^2 = 9
Find the square root for 576 by factorization
√576 = √(2³ x3)(2³ x3) = 2³ x3 = 24
Find the cube root for 512 by factorization
∛512 = ∛8³ = 8
Find the highest common factor of each of the following sets of numbers       a) 12 and 30 b) 15, 60 and 75
a) 6 b) 15
Find the lowest common multiple of 24 and 30
120


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