Section 1: Fractions and Decimals

Fractions, decimals and percents are all numbers that represent a part of the whole. We often need to convert from fractions to decimals or percents or from decimals to percents or fractions.

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Converting a fraction to a decimal

Divide the numerator (the top number) by the denominator (the bottom number) in your calculator.

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Note that the final decimal in this example is expressed to three decimal places. When you round a decimal, you round up if the number following is 5, 6, 7, 8, or 9 (as we did here) and you round down if the number following is 0, 1, 2, 3, or 4

Converting a decimal to a percent

Move the decimal point two places to the right. What you are doing is multiplying the decimal by 100 and attaching a “%” sign.

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Converting a percent to a decimal

Move the decimal point two places to the left. What you are doing is dividing the percentage by 100 and removing the “%” sign.

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Converting a percent to a fraction

Put the number over 100 and reduce (i.e. simplify the fraction so that the top number and bottom number cannot be divided by the same number.)

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Convert a decimal to a fraction

Determine how many numbers follow the decimal place (i.e. the number of “decimal places.) If there is one decimal place, place the number over 10 and reduce. If there are two decimal places, place the number over 100 and reduce. If there are three decimal places, place the number over 1000 and reduce. And so on.

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Adding and subtracting fractions

To add or subtract fractions, each fraction must have the same denominator (i.e. the same number in the bottom of the fraction.) If the denominators are different, you must find the lowest common denominator (LCD.) The LCD is the smallest number that is divisible by the denominator of each fraction. Once you determine the LCD, you multiply the top and the bottom by the number that will make the denominator of the fraction equal to the LCD. Then add the two numerators (i.e. numbers in the top) and put that sum over the LCD.

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These fractions have different denominators (3 and 4.) The LCD is 12 because it is the smallest number into which both 3 and 4 are evenly divided. To make the denominator of the first fraction equal to 12, multiply the top and the bottom of the fraction by 4. To make the denominator of the second fraction equal to 12, multiply the top and the bottom of the fraction by 3:

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Multiplying and dividing fractions

To multiply fractions, simply multiply across the top and across the bottom of the fractions.

To divide fractions, take the reciprocal of the second fraction (i.e. “flip” the second fraction) and multiply it by the first.

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To divide fractions, take the reciprocal of the second fraction (i.e. “flip” the second fraction) and multiply it by the first.

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Take Fractions and Decimals Assessment
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