Suppose b is any integer. If b mod 12 = 5, what is 6b mod 12? In other words, if division of b by 12 gives a remainder of 5, what is the remainder when 6b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 5, there is an integer m such that b = 12m + 12m + 5 1. Multiply both sides of this equation by 6 and then simplify the right-hand side to find values of g and r such that 6b = 12g +r with osr< 12. The results is and r= Now 0sr< 12, and a is an integer because -Select--- V. So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 6b is divided by 12 is
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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