![]() įinally, we can add rational numbers with the same denominator by just adding their numerators. We now rewrite each fraction to have a denominator of 40 as follows:ġ 8 + 3 5 = 1 × 5 8 × 5 + 3 × 8 5 × 8 = 5 4 0 + 2 4 4 0. (or their highest powers) of the two numbers. We then find the product of all of the different prime factors We can find this by factoring each of the denominators into primes. To do this, we first need toįind the lowest common multiple of all of the denominators. We now want to rewrite the fractions in the expression so that they have the same denominators. ![]() We can simplify this by adding the fractions with same denominator. ![]() To do this, let’s first evaluate the decimal part of this expression. We recall that we can evaluate the sum of rational numbers by first converting them into fractions with equal denominators. In our final example, we will evaluate an expression involving the sum of multiple fractions and decimals giving our answer asĮxample 7: Simplifying an Expression Involving Fractions and Decimalsįind the value of 1 8 + ( − 0. Since 13 and 10 have no common factors greater than 1, we cannot simplify this any further. We can then substitute these into the expression and evaluate to get We can then rewrite 3 5 to have a denominator of 10 by multiplying both the numerator and denominator Since 5 is a factor of 10, we must have that 10 is their lowest common multiple. Lowest common multiple of the two denominators. To write these fractions with the same denominator, we first need to find the We can evaluate the sum of two rational numbers by first converting them into fractions with equal denominators. 7 giving the answer as a fraction in its simplest form. In our next example, we find the sum of a fraction and decimal value giving our answer as a fraction in its simplest form.Įxample 6: Adding Fractions to Decimals and Simplifying the AnswerĮvaluate 3 5 + 0. Therefore, we want to rewrite all of these fractions with a denominator of 12. Taking the product of all theĭifferent prime factors (or their highest powers) of the three numbers gives their lowest common multiple ![]() We have 4 = 2 and 6 = 2 × 3, and 3 is prime. We will do this by factoring each denominator Toĭo this, we first need to find the lowest common multiple of all the denominators. However, it is not always possible to combine fractions in this way we may need to write them with a common denominator. We can then add the fractions with equal denominators by adding the numerators. Substituting this into the expression givesġ 4 + 1 3 + 3 4 + − 2 6 = 1 4 + 1 3 + 3 4 + − 1 3 . Simplified since the numerator and denominator share a factor of 2. The easiest way is to note that − 2 6 can be There are two ways to evaluate this expression. Example 5: Evaluating Numerical Expressions Involving the Addition of Rational NumbersĮvaluate 1 4 + 1 3 + 3 4 + − 2 6 giving the answer in ![]()
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