Mathematics
Grade 6
15 min
Perform multiple operations with fractions
Perform multiple operations with fractions
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1
Introduction & Learning Objectives
Learning Objectives
Identify and apply the correct order of operations (PEMDAS/BODMAS) when solving problems involving fractions.
Accurately add and subtract fractions with different denominators within multi-step problems.
Correctly multiply fractions, including mixed numbers, within complex expressions.
Proficiently divide fractions by applying the reciprocal method in multi-step calculations.
Simplify fractions to their lowest terms at appropriate stages within a multi-operation problem.
Solve word problems that require performing multiple operations with fractions.
Convert between mixed numbers and improper fractions as needed to perform operations.
Have you ever followed a recipe that asks you to add 1/2 cup of flour, then take out 1/4 of the mixture, and then divide...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole. It is written as a numerator (top number) over a denominator (bottom number).In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator.
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $\frac{2}{5}$, the numerator is 2, meaning we have 2 out of 5 equal parts.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts that make up the whole.In $\frac{7}{8}$, the denominator is 8, meaning the whole is divided into 8 equal parts.
Order of Operations (PEMDAS/BODMAS)A set of rules that dictates the sequence in which mathematical operations should be performed to ensure a consistent result. (Parentheses/Brackets, Exponents/Or...
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Core Formulas
Order of Operations (PEMDAS/BODMAS)
1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
Always follow this order to solve any multi-operation problem, including those with fractions, to get the correct answer.
Adding and Subtracting Fractions
To add or subtract fractions, they must have a common denominator. Find the least common multiple (LCM) of the denominators, convert the fractions, then add or subtract the numerators. The denominator stays the same.
Formula (after finding common denominator): $\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}$
This rule ensures you are combining or separating parts of the same size. Remember to simplify your final answer if possible.
Multiply...
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Challenging
Simplify the complex fraction: \(\frac{1\frac{1}{4} + \frac{1}{8}}{3 - \frac{1}{4}}\)
A.\(\frac{1}{2}\)
B.\(\frac{11}{22}\)
C.\(\frac{9}{11}\)
D.\(\frac{1}{3}\)
Challenging
A number is multiplied by \(\frac{3}{4}\), and then \(\frac{1}{2}\) is subtracted from the result. If the final answer is \(\frac{1}{8}\), what was the original number?
A.\(\frac{1}{6}\)
B.\(\frac{3}{4}\)
C.\(\frac{5}{6}\)
D.\(\frac{7}{8}\)
Challenging
Sam is baking a cake that requires \(2\frac{1}{2}\) cups of flour. He has a measuring cup that holds \(\frac{1}{4}\) cup. He has already put in 5 scoops. He then realizes he needs to double the recipe. How many MORE scoops does he need to add?
A.15
B.10
C.20
D.5
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