Mathematics
Grade 5
15 min
Complete the mixed-number multiplication sentence
Complete the mixed-number multiplication sentence
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1
Introduction & Learning Objectives
Learning Objectives
Identify mixed numbers and improper fractions.
Convert mixed numbers to improper fractions accurately.
Multiply two improper fractions.
Simplify fractions before or after multiplication to find the product in simplest form.
Convert improper fraction products back to mixed numbers.
Complete multiplication sentences involving mixed numbers.
Ever wonder how much flour you need if a recipe calls for 1 ½ cups, but you want to make 2 ½ batches? 🍪 Let's find out how to multiply those tricky numbers!
In this lesson, you'll learn the essential steps to multiply mixed numbers. We'll turn them into improper fractions, multiply, and then convert them back to get our final answer, helping you solve real-world problems.
Real-World Applications
Scal...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number written as a whole number and a proper fraction (e.g., $2 rac{1}{2}$).$3 rac{1}{4}$ means 3 whole units and $ rac{1}{4}$ of another unit.
Improper FractionA fraction where the numerator (top number) is greater than or equal to the denominator (bottom number) (e.g., $ rac{5}{2}$).$ rac{7}{3}$ is an improper fraction because 7 is greater than 3.
Proper FractionA fraction where the numerator is less than the denominator (e.g., $ rac{1}{2}$).$ rac{2}{5}$ is a proper fraction because 2 is less than 5.
NumeratorThe top number in a fraction, showing how many parts are being considered.In $ rac{3}{4}$, the numerator is 3.
DenominatorThe bottom number in a fraction, showing the total number of equal parts in the whole.In $ rac{3}{4}$, the denominator is...
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Core Formulas
Converting a Mixed Number to an Improper Fraction
$A \frac{B}{C} = \frac{(A \times C) + B}{C}$
To convert a mixed number, multiply the whole number (A) by the denominator (C), add the numerator (B), and place this sum over the original denominator (C). This is the first step in multiplying mixed numbers.
Multiplying Fractions
$\frac{A}{B} \times \frac{C}{D} = \frac{A \times C}{B \times D}$
To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. This rule applies after converting mixed numbers.
Converting an Improper Fraction to a Mixed Number
$\frac{\text{Numerator}}{\text{Denominator}} = \text{Whole Number } \frac{\text{Remainder}}{\text{Denominator}}$ (where Whole Number = Nu...
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Challenging
Complete the sentence by finding the missing mixed number: $1 \frac{1}{3} \times \text{?} = 3 \frac{1}{3}$
A.2 \frac{1}{3}
B.2
C.2 \frac{1}{2}
D.3
Challenging
A rectangular painting is $2 \frac{1}{2}$ feet long and $1 \frac{1}{5}$ feet wide. What is the area of the painting in square feet?
A.2 \frac{1}{10} \text{ sq. feet}
B.3 \frac{7}{10} \text{ sq. feet}
C.3 \text{ sq. feet}
D.4 \text{ sq. feet}
Challenging
Sam solved $2 \frac{2}{3} \times 1 \frac{1}{4}$. His steps were:
Step 1: $2 \frac{2}{3} = \frac{8}{3}$
Step 2: $1 \frac{1}{4} = \frac{5}{4}$
Step 3: $\frac{8}{3} \times \frac{5}{4} = \frac{40}{12}$
Step 4: The answer is $3 \frac{4}{12}$.
In which step did Sam make his first mistake?
A.Step 1
B.Step 2
C.Step 3
D.Step 4
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