How Do I Do Math Problems With Exponents & Parentheses Without a Calculator?
Even complicated math problems can be solved without the aid of a calculator. Armed with basic knowledge of the four math operations, an understanding of the order of operations, and perhaps paper and a pencil, most basic equations can be solved even when they involve parentheses and exponents. In fact, it is important to have the skill to solve them without the aid of a calculator. This will allow you to use unfamiliar or less powerful calculators, or to solve the problems when your calculator is not available.
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Instructions
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Scan the entire problem. Look for portions written inside of grouping symbols such as parentheses or brackets. Work the math within the innermost grouping symbols first. For example, in the problem 7+(56/8), solve the division problem 56/8 first. In the problem (2 * 6) + 2 * [10 - (2*4)], solve the 2*4 first, because it is in the innermost grouping symbols. Next, do 2 * 6 and 10-8, because those problems are still within grouping symbols.
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Scan the problem to find exponents. Simplify numbers with exponents by multiplying the base number by itself the number of times indicated by the exponent. For five raised to the third power, multiply 5 * 5 * 5. If necessary, use paper and a pencil to solve these problems.
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Search the problem for multiplication and division steps. Work from left to right and multiply or divide numbers in the order they are presented. For the problem 4 + 7 * 3, solve 7 * 3 first. Again, use paper and a pencil to solve these simple portions of the problem, if necessary.
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Complete the problem by solving addition and subtraction, again working from left to right. Consider the example problem 30 - (3 + 2^2) * 4. Address the problem inside the parentheses first. 3 + 2^2 contains an exponent to simplify. This yields 3 + 4, which is 7. Now the problem reads 30 - (7) * 4. Solve the multiplication next, which leaves 30-28. The answer is 2.
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References
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