Which expression would you rather add? \(\dfrac{51}{684}+\dfrac{43}{684}+\dfrac{738}{684}\) OR \(\dfrac{1}{8}+\dfrac{4}{5}+\dfrac{1}{9}\) Explain to a 3rd grader why: ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Now, we will explore why fractions behave the way they do for adding, subtracting, multiplying and dividing: Example \(\PageIndex{1}\): Add Fractions with a Drawing, Number Line, then with Common Denominators Add \(\dfrac{1}{2}+\dfrac{1}{3}\). Why 6 boxes? Example \(\PageIndex{2}\): Subtract Fractions with a Drawing, Number Line, then with Common Denominators Subtract \(\dfrac{1}{2} - \dfrac{1}{3}\). Why 6 boxes? Example \(\PageIndex{3}\): Multiply Fractions with a Drawing, Number Line, then with Common Denominators Add \(\dfrac{1}{2} \times \dfrac{1}{3}\). Why 6 boxes? Example \(\PageIndex{4}\): Divide Fractions with a Drawing, Number Line, then with Common Denominators Divide \(\dfrac{1}{2} \div \dfrac{1}{3}\). “Think portions, when it comes to division! Why 6 boxes? Example \(\PageIndex{5}\) Why does “multiply and flip the second fraction” work when dividing fractions? Solution We know that: \[\dfrac{a}{b} \times \dfrac{b}{a}=\dfrac{a b}{a b}=1 \nonumber \] \[\begin{aligned} Partner Activity 2Which Operation is Correct? A stretch of highway is \(3 \dfrac{1}{2}\) miles long. Each day, \(\dfrac{2}{3}\) of a mile is repaved. How many days are needed to repave the entire section? How would you explain to a 5th grader which operation is correct? Do we add? \(3 \dfrac{1}{2}+\dfrac{2}{3}=\dfrac{7}{2}+\dfrac{2}{3}=\dfrac{21}{6}+\dfrac{4}{6}=\dfrac{25}{6}=4 \dfrac{1}{6}\) days Do we subtract? \(3 \dfrac{1}{2}-\dfrac{2}{3}=\dfrac{7}{2}-\dfrac{2}{3}=\dfrac{21}{6}-\dfrac{4}{6}=\dfrac{17}{6}=2 \dfrac{5}{6}\) days Do we multiply? \(3 \dfrac{1}{2} \times \dfrac{2}{3}=\dfrac{7}{2} \times \dfrac{2}{3}=\dfrac{14}{6}=2 \dfrac{2}{6}=2 \dfrac{1}{3}\) days Do we divide? \(3 \dfrac{1}{2} \div \dfrac{2}{3}=\dfrac{7}{2} \times \dfrac{3}{2}=\dfrac{21}{4}=5 \dfrac{1}{4}\) days Practice ProblemsAdd, subtract, multiply or divide the expressions. Use any method.
Calculator UseUse this fraction calculator for adding, subtracting, multiplying and dividing fractions. Answers are fractions in lowest terms or mixed numbers in reduced form. Input proper or improper fractions, select the math sign and click Calculate. This is a fraction calculator with steps shown in the solution. If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator. Sometimes math problems include the word "of," as in What is 1/3 of 3/8? Of means you should multiply so you need to solve 1/3 × 3/8. To do math with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator. Math on Fractions with Unlike DenominatorsThere are 2 cases where you need to know if your fractions have different denominators:
How to Add or Subtract Fractions
How to Multiply Fractions
How to Divide Fractions
Fraction FormulasThere is a way to add or subtract fractions without finding the least common denominator (LCD). This method involves cross multiplication of the fractions. See the formulas below. You may find that it is easier to use these formulas than to do the math to find the least common denominator. The formulas for multiplying and dividing fractions follow the same process as described above. Adding FractionsThe formula for adding fractions is: \( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd} \) Example steps: \( \dfrac{2}{6} + \dfrac{1}{4} = \dfrac{(2\times4) + (6\times1)}{6\times4} \) \( = \dfrac{14}{24} = \dfrac {7}{12} \) Subtracting FractionsThe formula for subtracting fractions is: \( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - bc}{bd} \) Example steps: \( \dfrac{2}{6} - \dfrac{1}{4} = \dfrac{(2\times4) - (6\times1)}{6\times4} \) \( = \dfrac{2}{24} = \dfrac {1}{12} \) Multiplying FractionsThe formula for multiplying fractions is: \( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd} \) Example steps: \( \dfrac{2}{6} \times \dfrac{1}{4} = \dfrac{2\times1}{6\times4} \) \( = \dfrac{2}{24} = \dfrac {1}{12} \) Dividing FractionsThe formula for dividing fractions is: \( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc} \) Example steps: \( \dfrac{2}{6} \div \dfrac{1}{4} = \dfrac{2\times4}{6\times1} \) \( = \dfrac{8}{6} = \dfrac {4}{3} = 1 \dfrac{1}{3} \) Related CalculatorsTo perform math operations on mixed number fractions use our Mixed Numbers Calculator. This calculator can also simplify improper fractions into mixed numbers and shows the work involved. If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator. For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator. If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values. NotesFollow
CalculatorSoup: How do you add and subtract fractions step by step?Note: The rules for adding and subtracting improper fractions are the same as working with proper fractions. Step 1: Keep the denominator the same. Step 2: Add or subtract the numerators. Step 3: If the answer is an improper form, reduce the fraction into a mixed number.
How do you know when to add subtract multiply or divide?Order of operations tells you to perform multiplication and division first, working from left to right, before doing addition and subtraction. Continue to perform multiplication and division from left to right. Next, add and subtract from left to right.
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