Mathematics
Grade 5
15 min
Multiplication with mixed numbers: word problems
Multiplication with mixed numbers: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify mixed numbers and fractional quantities within word problems.
Convert mixed numbers to improper fractions accurately.
Multiply improper fractions to find a product.
Convert improper fractions back to mixed numbers or whole numbers in simplest form.
Interpret the numerical answer in the context of the original word problem.
Solve multi-step word problems involving multiplication of mixed numbers.
Estimate the product of mixed numbers to check for reasonableness.
Imagine you're baking cookies and the recipe calls for 1 1/2 cups of sugar. What if you want to make 3 batches? 🍪 How much sugar do you need in total?
In this lesson, you'll learn how to tackle word problems that require multiplying mixed numbers. This skill is super practica...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a proper fraction.$2 \frac{1}{2}$ (two and one-half)
Improper FractionA fraction where the numerator is greater than or equal to the denominator.$\frac{5}{2}$ (five-halves)
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.
ProductThe result obtained when two or more numbers are multiplied together.The product of 3 and 4 is 12.
Word ProblemA mathematical problem presented in a narrative or descriptive form, requiring students to extract information and apply operations.Sarah has $2 \frac{1}{4}$ yards...
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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 to an improper fraction, multiply the whole number part by the denominator, add the numerator, and place the result over the original denominator. This makes it easier to multiply.
Multiplying Fractions
$\frac{A}{B} \times \frac{C}{D} = \frac{A \times C}{B \times D}$
To multiply two fractions, multiply their numerators together to get the new numerator, and multiply their denominators together to get the new denominator.
Converting an Improper Fraction to a Mixed Number
Divide the numerator by the denominator. The quotient is the whole number part, the remainder is the new numerator, and the denominator stays the same.
After multiplying, if your an...
5 more steps in this tutorial
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Challenging
A large jug of water holds 20 cups. A soccer team drinks $1 \frac{3}{4}$ cups of water after each of their 9 practices. After the 9 practices, how much water is left in the jug?
A.4 \frac{1}{4} cups
B.5 \frac{3}{4} cups
C.15 \frac{3}{4} cups
D.4 \frac{3}{4} cups
Challenging
A farmer has a field that is $12 \frac{1}{2}$ acres. He plants corn on $\frac{2}{5}$ of the field. He then plants soybeans on $1 \frac{1}{2}$ times the area of the corn. How many acres are planted with soybeans?
A.5 acres
B.7 \frac{1}{2} acres
C.8 acres
D.7 acres
Challenging
On a scale drawing of a new park, 1 inch represents $8 \frac{1}{2}$ feet. The length of the main path on the drawing is $4 \frac{1}{2}$ inches. What is the actual length of the path?
A.32 \frac{1}{2} feet
B.36 feet
C.38 \frac{1}{4} feet
D.40 feet
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