Mathematics
Grade 5
15 min
Multiply a mixed number by a fraction
Multiply a mixed number by a fraction
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert mixed numbers into improper fractions.
Multiply an improper fraction by a proper fraction.
Simplify fractions before or after multiplication to find the product in simplest form.
Convert improper fraction products back into mixed numbers.
Solve real-world word problems involving the multiplication of a mixed number by a fraction.
Explain the steps involved in multiplying a mixed number by a fraction.
Ever wonder how much flour you need if a recipe calls for 2 ½ cups, but you only want to make ½ of the recipe? 🥣 Let's find out!
In this lesson, you'll learn how to multiply a mixed number by a fraction. This skill is super useful for scaling recipes, calculating portions, and understanding how parts of parts work in real life!
Real-World...
2
Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number that combines a whole number and a fraction.$2 \frac{1}{2}$ (two and one-half)
Improper FractionA fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).$\frac{5}{2}$ (five-halves)
NumeratorThe top number in a fraction, which tells you how many parts of the whole you have.In $\frac{3}{4}$, the numerator is 3.
DenominatorThe bottom number in a fraction, which tells you how many equal parts the whole is divided into.In $\frac{3}{4}$, the denominator is 4.
ProductThe result or answer obtained when two or more numbers are multiplied together.The product of 2 and 3 is 6.
Simplifying FractionsReducing a fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common...
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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 multiply a mixed number, you must first convert it into an improper fraction. Multiply the whole number (A) by the denominator (C), then add the numerator (B). Keep the original denominator (C).
Multiplying Two Fractions
$\frac{A}{B} \times \frac{C}{D} = \frac{A \times C}{B \times D}$
To multiply two fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
Converting an Improper Fraction to a Mixed Number
$\frac{N}{D} = Q \frac{R}{D}$ (where $N = Q \times D + R$)
If your answer is an improper fraction, you can convert it back to a mixed number. Divide the numerator (N) by the denominator (D)....
5 more steps in this tutorial
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Challenging
When you multiply a mixed number greater than 1 (like $2 \frac{1}{2}$) by a proper fraction (like $\frac{1}{3}$), the product will be:
A.Larger than the original mixed number.
B.Smaller than the original mixed number.
C.Equal to the original mixed number.
D.Always a whole number.
Challenging
Find the value of N that makes the following equation true: $2 \frac{1}{2} \times \frac{N}{5} = 1$.
A.2
B.1
C.3
D.4
Challenging
A large square tile has a side length of $4 \frac{1}{2}$ inches. A smaller tile has a side length that is $\frac{2}{3}$ of the large tile's side length. What is the area of the SMALLER tile?
A.3 inches
B.9 square inches
C.6 \frac{3}{4} square inches
D.20 \frac{1}{4} square inches
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