Lower Elementary:
Question: Mary baked 4 loaves of bread. She cut each loaf in half, and then she cut each half in half again. How many pieces of bread does Mary have?
Answer: 16 pieces of bread
Solution: Since she cut each piece loaf of bread in half, there are twice as many pieces of bread than what Mary started with. So, 4 doubled is 8. Then she cuts each of those 8 pieces in half, so there will be twice as many pieces of bread from before. 8 doubled is 16. Mary will have 16 pieces of bread.
Upper Elementary:
Question: Miguel’s mom thinks he watches too much TV so she limited the amount of TV he can watch. Miguel does not watch TV before school, gets home from school at 3PM, and goes to bed at 9PM. His mom will only let him watch TV for 1/6 of the time that he is home from school and before he goes to bed. If Miguel already watched 30 minutes of TV, how much more TV can he watch before he goes to bed?
Answer: 30 minutes
Solution: First, we have to find out how much TV Miguel’s mom will allow him to watch. From 3PM to 9PM is 6 hours and his mom will allow him to watch TV for 1/6 of this time. 1/6 of 6 is 1, so Miguel can watch 1 hour of TV. He already watched 30 minutes, so he is allowed to watch 30 more minutes of TV before he goes to bed.
Middle School:
Question: Penelope plans to tip her waitress twice the tax. The bill came to $20 and the tax is 8% of the bill. How much will Penelope tip?
Answer: $3.20
Solution: One way to do this is to find the amount the tax will be and double it. Percent means for each hundred. 20 is 1/5 of 100, so to find 8% of 20, divide 8 by 5. 8 ÷ 5 = 1.6. The tax will be $1.60. To find the tip amount, double the tax amount. 1.60 doubled = 1 doubled + 0.6 doubled = 2 + 1.2 = 3.2. Penelope will tip $3.20.
Algebra and Up:
Question: What is the smallest number greater than 100 that is not divisible by 2, 3, 5, and is not prime?
Answer: 119
Solution: For a number not to be prime, it has to have at least one pair factors other than 1 and itself. If we multiply 2 prime numbers together, we will get a composite number that is only divisible by the 2 prime numbers used. Since the number cannot be divisible by 2, 3, or 5, the next prime numbers are 7, 11, 13, and 17. Let’s multiply 7, the smallest prime number in the list, by each of the prime numbers until we get a number greater than 100. 7 × 7 = 49, 7 × 11 = 77, 7 × 13 = 91, 7 × 17 = 119. Recall that 11 × 11 = 121, and 119 is less than 121. The smallest product is 119, which means that the smallest number greater than 100 that is not divisible by 2, 3, and 5 and is not a prime number is 119.
If you go up from 100, all the even numbers are divisible by 2 and all numbers ending in a 5 or 0 are divisible by 5. This leaves 101, 103, 107, 109, 111, 113, 117, 119, 121, 123, etc. Starting from the beginning, 101 is prime, 103 is prime, 107 is prime, 109 is prime, 111 is divisible by 3, 113 is prime, 117 is divisible by 3, and 119 is composite (7 × 17), which means 119 is the smallest number greater than 100 that is not divisible by 2, 3, or 5 and not prime.
(925) 292-8854
