Mathematics
Grade 5
15 min
Multiply fractions and whole numbers: sorting
Multiply fractions and whole numbers: sorting
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify whole numbers and fractions within a multiplication problem.
Convert a whole number into an equivalent fraction.
Multiply a fraction by a whole number.
Multiply a whole number by a fraction.
Simplify the product of a fraction and a whole number to its simplest form.
Express improper fraction products as mixed numbers when appropriate.
Ever wondered how to share 🍕 pizza slices equally among friends, even if you only have part of a whole pizza?
In this lesson, you'll learn how to multiply fractions by whole numbers and whole numbers by fractions. We'll focus on 'sorting' the numbers correctly to make multiplication easy and accurate, helping you solve everyday sharing and scaling problems.
Real-World Applications
Scaling a...
2
Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing a part of a whole, written as a numerator over a denominator.$ rac{3}{4}$ represents three out of four equal parts.
Whole NumberA number without fractions or decimals (e.g., 0, 1, 2, 3...).5 is a whole number.
NumeratorThe top number in a fraction, indicating how many parts are being considered.In $ rac{2}{5}$, 2 is the numerator.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts in the whole.In $ rac{2}{5}$, 5 is the denominator.
ProductThe result obtained when two or more numbers are multiplied together.The product of 3 and 4 is 12.
Improper FractionA fraction where the numerator is greater than or equal to the denominator.$ rac{7}{3}$ is an improper fraction.
Simplest FormA fraction where the numer...
3
Core Formulas
Converting a Whole Number to a Fraction
Any whole number $W$ can be written as a fraction $\frac{W}{1}$.
This rule helps us prepare whole numbers for multiplication with fractions by giving them a denominator.
Multiplying a Fraction by a Whole Number
To multiply a fraction $\frac{a}{b}$ by a whole number $W$, first convert $W$ to $\frac{W}{1}$. Then, multiply the numerators and multiply the denominators: $\frac{a}{b} \times \frac{W}{1} = \frac{a \times W}{b \times 1} = \frac{a \times W}{b}$.
This rule shows how to combine the parts of the numbers to find the product.
Simplifying Fractions
To simplify a fraction $\frac{N}{D}$, divide both the numerator $N$ and the denominator $D$ by their greatest common factor (GCF).
Always simplify your answer to its simplest form,...
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A baker has 20 cups of sugar. A recipe for one batch of cookies requires 2/3 cup of sugar. If the baker makes 15 batches, how much sugar will be used?
A.20 cups
B.10 cups
C.30/3 cups
D.15 2/3 cups
Challenging
If W is a whole number greater than 1, and a/b is a proper fraction (a < b), when will the product W x a/b be a whole number?
A.When W is a multiple of the denominator b.
B.When W is a multiple of the numerator a.
C.Always.
D.Never.
Challenging
A student solved 9 x 2/6. Their work was: Step 1: 9/1 x 2/6 = 18/6. Step 2: 18/6 = 2 6/6. What is the final, correct answer and what was the student's mistake?
A.The answer is 2 1/3; the student simplified incorrectly.
B.The answer is 18/6; the student should not have converted to a mixed number.
C.The answer is 3; the student converted to a mixed number incorrectly.
D.The answer is 2; the student made a multiplication error.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free