Mathematics
Grade 7
15 min
Divide mixed numbers
Divide mixed numbers
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert mixed numbers to improper fractions.
Recall and apply the rule for dividing fractions.
Perform division operations involving two mixed numbers.
Simplify fractional answers to their lowest terms.
Convert improper fractions back to mixed numbers.
Solve real-world problems that require dividing mixed numbers.
Ever wondered how to equally share 2 and a half cakes among 3 friends? 🍰 Or how many smaller pieces you can cut from a longer piece of wood? 🤔
In this lesson, you'll learn the essential steps to divide mixed numbers. This skill builds on your knowledge of fractions and will help you solve many practical problems, from cooking to construction, making you a more confident problem-solver!
Real-World Applications
Scaling recipes (e.g., h...
2
Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a fraction, representing a value greater than one.$3 \frac{1}{2}$ (three and one-half)
Improper FractionA fraction where the numerator is greater than or equal to the denominator, representing a value greater than or equal to one.$\frac{7}{2}$ (seven-halves)
ReciprocalThe reciprocal of a fraction is found by flipping the fraction, meaning the numerator becomes the denominator and the denominator becomes the numerator. It's also called the multiplicative inverse.The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In the fraction $\frac{3}{4}$, 3 is the numerator.
DenominatorThe bottom number in a fraction, indicati...
3
Core Formulas
Converting Mixed Number to 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 by the denominator, add the numerator, and place the result over the original denominator.
Dividing Fractions (Keep, Change, Flip)
$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$
To divide by a fraction, keep the first fraction, change the division sign to multiplication, and flip (take the reciprocal of) the second fraction. Then multiply the numerators and denominators.
Converting Improper Fraction to 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.
This rule is used to e...
5 more steps in this tutorial
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Challenging
Evaluate the expression: $(2 \frac{1}{2} + 1 \frac{1}{4}) \div 1 \frac{1}{4}$.
A.2
B.2 \frac{1}{2}
C.3 \frac{1}{5}
D.3
Challenging
A student's work for $6 \frac{1}{2} \div 1 \frac{1}{4}$ is shown below. In which step does the first error appear?
Step 1: Convert to improper fractions: $\frac{13}{2} \div \frac{5}{4}$
Step 2: Keep, Change, Flip: $\frac{2}{13} \times \frac{5}{4}$
Step 3: Multiply: $\frac{10}{52}$
Step 4: Simplify: $\frac{5}{26}$
A.Step 1
B.Step 2
C.Step 3
D.Step 4
Challenging
You have a 20-cup bag of flour. A recipe for one batch of cookies requires $1 \frac{1}{2}$ cups of flour. After making the maximum number of full batches, how much flour will be left over?
A.\frac{1}{2} cup
B.\frac{1}{3} cup
C.1 cup
D.No flour will be left over.
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