Mathematics
Grade 5
15 min
Subtract mixed numbers with unlike denominators
Subtract mixed numbers with unlike denominators
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Introduction & Learning Objectives
Learning Objectives
Identify the components of mixed numbers.
Find the least common denominator (LCD) for fractions with unlike denominators.
Convert mixed numbers to equivalent fractions with a common denominator.
Subtract mixed numbers when the fraction part of the minuend is greater than or equal to the fraction part of the subtrahend.
Subtract mixed numbers by regrouping (borrowing) when the fraction part of the minuend is smaller than the fraction part of the subtrahend.
Simplify the resulting fractional part of the difference to its lowest terms.
Ever tried to share a pizza 🍕 but realized you had different sized slices left? Subtracting mixed numbers helps us figure out exactly how much is left!
In this lesson, you'll learn how to subtract mixed numbers even whe...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a proper fraction.$3 \frac{1}{2}$ (three and one-half)
NumeratorThe top number in a fraction, representing the number of parts being considered.In $\frac{3}{4}$, $3$ is the numerator.
DenominatorThe bottom number in a fraction, representing the total number of equal parts in the whole.In $\frac{3}{4}$, $4$ is the denominator.
Unlike DenominatorsFractions that have different denominators.$\frac{1}{2}$ and $\frac{1}{3}$ have unlike denominators.
Least Common Multiple (LCM)The smallest positive number that is a multiple of two or more numbers. It helps find the LCD.The LCM of 4 and 6 is 12.
Least Common Denominator (LCD)The least common multiple of the denominators of two or more fractions. It's the smallest com...
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Core Formulas
Finding the Least Common Denominator (LCD)
To find the LCD of two fractions, find the Least Common Multiple (LCM) of their denominators.
This rule is used as the first step to make the denominators of fractions the same, allowing for addition or subtraction. For example, for $\frac{1}{3}$ and $\frac{1}{4}$, the LCM of 3 and 4 is 12, so the LCD is 12.
Subtracting Fractions with Like Denominators
$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$
Once fractions have the same denominator, subtract only the numerators and keep the common denominator. The denominator does not change.
Regrouping (Borrowing) from a Whole Number
When subtracting mixed numbers and the first fraction is smaller than the second, 'borrow' 1 from the whole number part. Convert the borrowed 1 int...
5 more steps in this tutorial
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Challenging
Maria started with a ribbon that was $5 \frac{1}{4}$ meters long. After she used some for a project, she had $1 \frac{2}{3}$ meters left. How much ribbon did she use?
A.$4 \frac{1}{12}$ meters
B.$3 \frac{7}{12}$ meters
C.$4 \frac{7}{12}$ meters
D.$3 \frac{1}{1}$ meters
Challenging
Find the missing number in the equation: $8 \frac{1}{5} - ? = 3 \frac{1}{2}$
A.$5 \frac{3}{10}$
B.$5 \frac{7}{10}$
C.$4 \frac{3}{10}$
D.$4 \frac{7}{10}$
Challenging
Which expression has a greater value? Expression X: $5 \frac{1}{3} - 2 \frac{1}{2}$ or Expression Y: $4 \frac{1}{4} - 1 \frac{5}{6}$
A.Expression X is greater.
B.Expression Y is greater.
C.Both expressions have the same value.
D.It is impossible to tell.
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