Mathematics
Grade 10
15 min
Multiply a mixed number by a whole number
Multiply a mixed number by a whole number
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1
Introduction & Learning Objectives
Learning Objectives
Convert mixed numbers to improper fractions with 100% accuracy.
Multiply an improper fraction by a whole number and simplify the resulting fraction.
Apply the distributive property as an alternative method for multiplying a whole number by a mixed number.
Calculate the volume of a rectangular prism when one dimension is a mixed number and it is scaled by a whole number factor.
Determine the total surface area or volume of multiple identical polyhedra where a key measurement is a mixed number.
Solve word problems involving scaling the dimensions of three-dimensional figures using mixed number and whole number multiplication.
Ever wonder how an architect accurately scales up a model with precise, fractional dimensions? 🏗️ This fundamental calculation is the...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number composed of a whole number and a proper fraction.4 ½, which represents four whole units and one half of another unit.
Improper FractionA fraction in which the numerator is greater than or equal to the denominator.9/2, which is the improper fraction equivalent of 4 ½.
Scaling FactorA number by which the dimensions of a geometric figure are multiplied to create a larger or smaller similar figure.If a cube with a side length of 2 cm is scaled by a factor of 3, its new side length is 6 cm.
VolumeThe amount of three-dimensional space an object occupies, measured in cubic units.The volume of a rectangular prism with dimensions 2m x 3m x 4m is 24 m³.
Distributive PropertyA property of multiplication stating that a(b + c) = ab + ac. This can be used to m...
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Core Formulas
Method 1: Conversion to Improper Fraction
a \times (b \frac{c}{d}) = a \times \frac{b \times d + c}{d}
To multiply a whole number by a mixed number, first convert the mixed number into an improper fraction. Then, multiply the whole number by the numerator of the improper fraction, keeping the denominator the same. Simplify the result.
Method 2: The Distributive Property
a \times (b \frac{c}{d}) = (a \times b) + (a \times \frac{c}{d})
Multiply the whole number by the whole number part of the mixed number. Then, multiply the whole number by the fractional part. Finally, add the two products together for the final result.
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
Which of the following correctly converts the mixed number 7 ⅔ into an improper fraction, as required for the first step in Method 1?
A.14/3
B.21/3
C.23/3
D.10/3
Easy
A student incorrectly multiplies 6 by 2 ½ and gets an answer of 12 ½. This is a common pitfall. What did the student do wrong?
A.They added the numbers instead of multiplying.
B.They only multiplied the whole number part (6 × 2).
C.They converted the mixed number to an improper fraction incorrectly.
D.They forgot to simplify the final answer.
Easy
What is the product of 5 and 3 ⅕?
A.15 ⅕
B.16
C.15
D.8 ⅕
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