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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Find an integer which when divided by two given integers leaves two given remainders. This problem may be formulated in two different ways: Let the integer to be found be N, the divisors be a and b, and the remainders be R 1 and R 2. Then the problem is to find N such that; N ≡ R 1 (mod a) and N ≡ R 2 (mod b).
Equations in the book are presently called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes.
Numerical methods for ordinary differential equations approximate solutions to initial value problems of the form ′ = (,), =.. The result is approximations for the value of () at discrete times : = +, where is the time step (sometimes referred to as ) and is an integer.
Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement.
How to Solve It suggests the following steps when solving a mathematical problem: . First, you have to understand the problem. [2]After understanding, make a plan. [3]Carry out the plan.