Learning Outcomes
Show To add or subtract fractions with different denominators, we first must write them as equivalent fractions having the same denominator. We’ll use the techniques from the previous section to find the LCM of the denominators of the fractions. Recall that we call this the LCD (the least common denominator). We only use the denominators of the fractions, not the numerators, when finding the LCD. Then we can use the Equivalent Fractions Property to algebraically change a fraction to an equivalent one. Remember, two fractions are equivalent if they have the same value. The steps for finding the LCD and the Equivalent Fractions Property are repeated below for reference. Least Common DenominatorThe least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators. Equivalent Fractions PropertyIf [latex]a,b,c[/latex] are whole numbers where [latex]b\ne 0,c\ne 0,\text{then}[/latex] [latex]\Large\frac{a}{b}=\Large\frac{a\cdot c}{b\cdot c}\normalsize\text{ and }\Large\frac{a\cdot c}{b\cdot c}=\Large\frac{a}{b}[/latex] Once we have converted two fractions to equivalent forms with common denominators, we can add or subtract them by adding or subtracting the numerators. Try the examples and practice problems below to refresh these skills. Add or subtract fractions with different denominators
ExampleAdd: [latex]\Large\frac{1}{2}+\Large\frac{1}{3}[/latex] Solution:
Remember, always check to see if the answer can be simplified. Since [latex]5[/latex] and [latex]6[/latex] have no common factors, the fraction [latex]\Large\frac{5}{6}[/latex] cannot be reduced. Try ItWatch the following video to see more examples and explanation about how to add two fractions with unlike denominators. ExampleSubtract: [latex]\Large\frac{1}{2}-\left(-\Large\frac{1}{4}\right)[/latex] Try ItThe following video provides two more examples of how to subtract two fractions with unlike denominators. ExampleAdd: [latex]\Large\frac{7}{12}+\Large\frac{5}{18}[/latex] Try ItWhen we use the Equivalent Fractions Property, there is a quick way to find the number you need to multiply by to get the LCD. Write the factors of the denominators and the LCD just as you did to find the LCD. The “missing” factors of each denominator are the numbers you need. The LCD, [latex]36[/latex], has [latex]2[/latex] factors of [latex]2[/latex] and [latex]2[/latex] factors of [latex]3[/latex]. Twelve has two factors of [latex]2[/latex], but only one of [latex]3[/latex] —so it is ‘missing‘ one [latex]3[/latex]. We multiplied the numerator and denominator of [latex]\Large\frac{7}{12}[/latex] by [latex]3[/latex] to get an equivalent fraction with denominator [latex]36[/latex]. Eighteen is missing one factor of [latex]2[/latex] —so you multiply the numerator and denominator [latex]\Large\frac{5}{18}[/latex] by [latex]2[/latex] to get an equivalent fraction with denominator [latex]36[/latex]. We will apply this method as we subtract the fractions in the next example. ExampleSubtract: [latex]\Large\frac{7}{15}-\Large\frac{19}{24}[/latex] Try ItExampleAdd: [latex]-\Large\frac{11}{30}+\Large\frac{23}{42}[/latex] Try ItHow do you add fractions with unlike denominators step by step?To add fractions with unlike denominators, you should:. Find the common denominator.. Rewrite each fraction using the common denominator.. Add the numerators.. Carry across the common denominator.. If possible, reduce the final fraction.. What is an example of a Unlike fraction?Fractions with different denominators are called the unlike fractions. Here the denominators of fractions have different values. For example, 2/3, 4/9, 6/67, 9/89 are unlike fractions.
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