Mixed to Improper Worksheet Math Guide & Practice Grade 5–6 Fraction Skills
Mixed Numbers to Improper Fractions
Master the conversion method, connect to visual models, and compute with ease.
Name:
Date: Period:
1. Essential Vocabulary
Mixed Number
A whole number and a fraction combined.
\( 2\frac{3}{4} \)
Improper Fraction
A fraction where the numerator \( \ge \) denominator .
\( \frac{11}{4} \)
Numerator & Denominator
Numerator (top): parts counted.Denominator (bottom): parts in 1 whole.
2. Visual Model: Why Does It Work?
In \( 2\frac{3}{4} \) , each whole has 4 equal fourths :
• 2 wholes = \( 2 \times 4 = 8 \text{ fourths} \) (\( \frac{8}{4} \))
Total fourths: \( 8 + 3 = 11 \text{ fourths} = \frac{11}{4} \)
\( \frac{4}{4} \)
\( \frac{4}{4} \)
\( \frac{3}{4} \)
=
\( \frac{11}{4} \)
3. The 3-Step "M-A-D" Method
M MULTIPLY
Denominator \( \times \) whole number .
\( 4 \times 2 = 8 \)
A ADD
Add the original numerator .
\( 8 + 3 = 11 \)
D DENOMINATOR
Keep the same denominator .
\( \frac{11}{4} \)
4. Practice: Convert to Improper Fractions
Multiply \( \rightarrow \) Add \( \rightarrow \) Keep Denominator
1. Guided Model \( 3\frac{1}{2} \)
M ultiply denominator \( \times \) whole: \( 2 \times 3 = 6 \)
A dd the numerator: \( 6 + 1 = 7 \)
D enominator stays the same: bottom = \( 2 \)
Improper Fraction:
\( \frac{7}{2} \)
2. Practice \( 2\frac{3}{5} \)
Improper Fraction:
3. Practice \( 4\frac{2}{3} \)
Improper Fraction:
4. Practice \( 5\frac{1}{4} \)
Improper Fraction:
Mixed Numbers to Improper Fractions Guide Page 1 of 2 • Continue to Operations on Page 2 →
Part 2 • Operations
Multiplying & Dividing with Improper Fractions
Golden Rule: Convert mixed numbers to improper fractions FIRST!
Multiplying Fractions
Convert any mixed number to an improper fraction.
Multiply straight across: \( \frac{\text{top} \times \text{top}}{\text{bottom} \times \text{bottom}} \).
Simplify to simplest form (mixed or proper).
Dividing Fractions (Keep • Change • Flip)
Convert mixed numbers to improper fractions first.
Keep 1st fraction, Change \( \div \) to \( \times \), Flip 2nd fraction.Multiply straight across, then simplify .
A
Multiplication Practice (Convert & Multiply)
Simplify all answers completely
\( 1\frac{1}{2} \times \frac{4}{5} \)
Convert \( 1\frac{1}{2} \rightarrow \) improper:
Multiply & show work:
Answer:
\( 2\frac{1}{4} \times 1\frac{1}{3} \)
Convert both mixed numbers:
Multiply & show work:
Answer:
\( 3\frac{1}{3} \times \frac{3}{5} \)
Convert \( 3\frac{1}{3} \rightarrow \) improper:
Multiply & show work:
Answer:
B
Division Practice (Convert & Keep • Change • Flip)
Multiply by the reciprocal of the 2nd fraction
\( 2\frac{1}{2} \div \frac{3}{4} \)
Convert \( 2\frac{1}{2} \rightarrow \) improper:
Keep • Change • Flip & solve:
Answer:
\( 1\frac{3}{4} \div 2\frac{1}{3} \)
Convert both mixed numbers:
Keep • Change • Flip & solve:
Answer:
\( 3\frac{1}{2} \div 1\frac{3}{4} \)
Convert both mixed numbers:
Keep • Change • Flip & solve:
Answer:
Final Accuracy Checklist:
Converted to improper first Flipped only 2nd fraction (division) Reduced to simplest form
Mixed Numbers to Improper Fractions Guide Page 2 of 2 • Complete & Turn In
Fraction Kickoff Do Now Fraction Warm-Up • Do Now
Prerequisite review: Wholes, parts, and counting pieces
Name:
Date:
1 Making 1 Whole: Fill in the missing numerator or denominator.
\( 1 \text{ whole} = \)
/ 2
\( 1 \text{ whole} = \)
3 /
\( 1 \text{ whole} = \)
/ 4
2 Count the shaded pieces. Write the fraction.
2 out of 4 fourths shaded
2 out of 3 thirds shaded
3 Challenge: Count ALL shaded halves. How many total halves?
Total shaded halves: _____
Fraction:
Cut Line • 2 Copies Per Page
Fraction Warm-Up • Do Now
Prerequisite review: Wholes, parts, and counting pieces
Name:
Date:
1 Making 1 Whole: Fill in the missing numerator or denominator.
\( 1 \text{ whole} = \)
/ 2
\( 1 \text{ whole} = \)
3 /
\( 1 \text{ whole} = \)
/ 4
2 Count the shaded pieces. Write the fraction.
2 out of 4 fourths shaded
2 out of 3 thirds shaded
3 Challenge: Count ALL shaded halves. How many total halves?
Total shaded halves: _____
Fraction:
Visual Fractions Worksheet Visual Math Guide Step-by-Step Models
Mixed Numbers to Improper Fractions
Count the pieces to convert mixed numbers using pictures.
Name:
Date:
How to Read the Visual Model
1
Top Number (Numerator) Count ALL shaded pieces in every circle.
2
Bottom Number (Denominator) Count pieces in just ONE whole circle .
Guided Model \( 1\frac{3}{4} \)
4 fourths
3 fourths
Total shaded pieces (4 + 3): 7 (Top)
Pieces in 1 whole circle: 4 (Bottom)
Improper \( \frac{7}{4} \)
Problem 1 \( 2\frac{1}{2} \)
1. Total shaded pieces:
2. Pieces in 1 whole circle:
Improper Fraction
Problem 2 \( 1\frac{2}{3} \)
1. Total shaded pieces:
2. Pieces in 1 whole circle:
Improper Fraction
Visual Fractions Worksheet • Page 1 of 2 Turn page for more practice →
Independent Practice
Count the Pieces • Write the Fractions
Remember: Denominator = pieces in 1 circle!
Problem 3 \( 2\frac{1}{4} \)
Total shaded pieces:
Pieces in 1 whole:
Improper Fraction:
Problem 4 \( 1\frac{3}{5} \)
Total shaded pieces:
Pieces in 1 whole:
Improper Fraction:
Problem 5 \( 3\frac{1}{2} \)
Total shaded pieces:
Pieces in 1 whole:
Improper Fraction:
Problem 6 \( 2\frac{2}{3} \)
Total shaded pieces:
Pieces in 1 whole:
Improper Fraction:
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Visual Fractions Worksheet • Page 2 of 2 Great job! Turn this page in to your teacher.
Fraction Check Exit Ticket Exit Ticket • Fraction Conversion
Show what you know: Use the models to write improper fractions.
Name:
Date:
1. Look at the model for \( 1\frac{3}{4} \):
Pieces in 1 whole:
Total shaded pieces:
Improper
2. Shade the circles to show \( 2\frac{1}{3} \), then write the improper fraction:
Improper
Self-Rating: [ ] Got it! [ ] Need 1 more practice [ ] Need help Score: ___ / 2
Cut Line • 2 Copies Per Page
Exit Ticket • Fraction Conversion
Show what you know: Use the models to write improper fractions.
Name:
Date:
1. Look at the model for \( 1\frac{3}{4} \):
Pieces in 1 whole:
Total shaded pieces:
Improper
2. Shade the circles to show \( 2\frac{1}{3} \), then write the improper fraction:
Improper
Self-Rating: [ ] Got it! [ ] Need 1 more practice [ ] Need help Score: ___ / 2
Fraction Practice Homework Home Practice Visual Math
Fraction Models at Home
Convert mixed numbers to improper fractions using pictures.
Name:
Due Date:
Family & Student Helper Box
1. Denominator (bottom): Count how many pieces make 1 whole circle .2. Numerator (top): Count ALL shaded pieces together.
Example: \( 1\frac{1}{2} = \frac{3}{2} \)
\( 1\frac{1}{2} \)
Pieces in 1 whole circle:
Total shaded pieces:
Improper:
\( 2\frac{2}{3} \)
Pieces in 1 whole circle:
Total shaded pieces:
Improper:
\( 1\frac{3}{4} \)
Pieces in 1 whole circle:
Total shaded pieces:
Improper:
\( 2\frac{1}{4} \)
Pieces in 1 whole circle:
Total shaded pieces:
Improper:
Parent / Guardian Signature:
Turn in tomorrow!
Fraction Transformations Lesson • Visual Conversion Homework
