Fractions & Decimals Math Problems
Calculations involving fractions and decimals are easy once you understand them, but it takes practice to learn to solve these math problems. You may need a quick course to remember how to convert decimals to fractions and add and subtract fractions, as well as the rules for multiplication and division.
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Convert Decimals Into Fractions
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Turn a decimal number into a fraction by placing it over the number 1. If you are turning .25 into a fraction, you would now have .25/1. Note how many numbers are after the decimal point and multiply them by 10s. One number after the decimal point is 10, two numbers after the decimal point are 100, three numbers are 1,000. Multiply both the top and bottom of the equation by this number. In this example, you would multiply the top and bottom by 100, as .25 has two numbers after the decimal point. Your equation will look like this: 25/100.
Simplify the fraction by dividing the top and bottom numbers by the greatest common factor, the largest number that both numbers can be divided by. With 25/100, 25 is the greatest common factor. Divide the top and bottom numbers by 25 to reduce the fraction to 1/4.
Convert Fractions to Decimals
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Turning a fraction into a decimal is as easy as dividing the top number of the fraction by the bottom number. Add zeroes to the top number as necessary to make it divisible, but note the location of the decimal point. Each zero, or multiple of 10, is added after a decimal point.
For example, to convert ¼ into a decimal number, divide 1 by 4. But 1 is not divisible by 4, so add one zero, making it 1.0 (or 10). Four goes into 10 twice, with a remainder of 2. Add another zero, making it 1.00 (or 100). Four goes into 100 25 times, after the decimal point, making the answer .25.
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Adding and Subtracting Fractions
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To add or subtract fractions, you must find the lowest common denominator. The denominator is the bottom number of the fraction. Find a number that is divisible by all the denominators of the fractions you are adding and subtracting. Whatever you need to do to the bottom number to get to the common denominator, you must do the same to the top number.
For example, if you are adding 2/5 + ½, the lowest common denominator, divisible by both numbers, is 10. To make the denominator 10 in 2/5, you must multiply it by 2. You must then multiply the top by 2, making it 4/10. To make the denominator in ½ equal 10, you must multiply it by 5. The top also needs to be multiplied by 5, making the fraction 5/10.
Now your equation is 4/10 + 5/10. Add the top numbers and keep the denominator the same. Your answer is 9/10. The formula works the same for subtraction.
Multiplication and Division
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Multiplying fractions is easy. You multiply the top numbers together, then multiply the bottom numbers together. Simplify for a final sum. In the example of 2/5 x ½, you would multiply 2 x 1 for the top numeral (2), and 5 x 2 for the bottom numeral (10). The answer of 2/10, which can be simplified to 1/5.
As in addition and subtraction, dividing fractions requires a common denominator. The division then becomes an equation of one numerator over another.
If you were to divide 2/5 by ½, the common denominator of 10 would turn the equation to 4/10 divided by 5/10, or 4/5.
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References
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