![]() ![]() We see that 3 and 6 are both factors of 12, so we need to find We can combine all of these fractions by rewriting them to have a commonĭenominator. To have the same denominator and then evaluating the numerators. We can evaluate the sum or difference of multiple fractions by writing them Number is the same as adding its additive inverse. Properties of the addition of rational numbers since subtracting a rational We first note that we can evaluate this expression in any order by using the ![]() Giving the answer as a fraction in the simplest form. In our next example, we will determine the difference between two rational numbers,Įxample 5: Evaluating the Difference of Four Proper Fractions It is also worth noting that we could answer this question by convertingġ 5 = 2 0 1 0 0 = 0. We can substitute this into the expression and evaluate to getġ 3 2 0 − 1 5 = 1 3 2 0 − 4 2 0 = 1 3 − 4 2 0 = 9 2 0. We can do this by noting that 5 is a factor of 20. ![]() ![]() To subtract these fractions, we want to write them with a common denominator. We can then use the fact that 5 goes into 65 thirteen times to rewrite this as a Since we need to give our answer as a fraction, we will instead convert intoĠ. For example, we could convertīoth rational numbers into decimals and then evaluate the subtraction. We could answer this question in different ways. In our next example, we will find the difference between rational numbers where oneĮxample 3: Finding the Difference between Rational Numbers Given inĮvaluate 0. However, we want to give our answer as a mixed number. We could now evaluate this expression by writing both numbers as fractions. We can do this by noting that 4 is a divisor of 8, so the lowest common multipleġ 4 − 5 8 = 1 × 2 4 × 2 − 5 8 = 2 8 − 5 8 = 2 − 5 8 = − 3 8. To do this, we need to rewrite both fractions to have the same denominator. We have that 7 − 4 = 3, so we need to determineġ 4 − 5 8. Subtraction of the whole parts and fractional parts separately sinceħ 1 4 − 4 5 8 = 7 1 4 + − 4 5 8 = 7 + 1 4 + − 4 − 5 8 = ( 7 − 4 ) + 1 4 − 5 8 . Instead, we first note that we can evaluate the We could start by converting both mixed numbers into fractions however, In our first example, we will evaluate the difference between two rational numbersĮxample 2: Subtraction of Rational Numbers as Mixed Numbers withĬalculate 7 1 4 − 4 5 8. This is the most general way to determine the difference between rational numbers. Now, we evaluate the subtraction since they have a common denominator: However, we can simplify this process by noting that the lowest common We then cancel the shared factor of 2 in the numerator and denominator to get We can use the above definition to evaluateġ 2 − 1 4 = 1 ( 4 ) − 2 ( 1 ) 2 ( 4 ) = 4 − 2 8 = 2 8. □ as the common denominator when subtracting fractions. It is also worth noting that we can also use the lowest common multiple of □ and Definition: Difference between Rational Numbers ![]()
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