Fraction Flip Reference Sheet
\(\frac{a}{b}\)
5th Grade Math Anchor Sheet Keep in Math Binder 📁
Mixed Numbers \(\rightarrow\) Improper Fractions
Name:
Date:
Mixed Number
A whole number combined with a proper fraction.
\(2\frac{3}{4}\)
Improper Fraction
Numerator is greater than or equal to the denominator.
\(\frac{11}{4}\)
The Golden Rule
Use the M.A.D. Trick!
Go in a "C" circle shape ↻
M
Multiply
Multiply the denominator by the whole number.
\(4 \times 2 = \mathbf{8}\)
A
Add
Add that answer to the top numerator.
\(8 + 3 = \mathbf{11}\)
D
Denominator
Keep the bottom number exactly the same.
Bottom stays \(\mathbf{4}\)
Formula in Action Watch all three pieces assemble:
\(2\frac{3}{4}\) \(\rightarrow\) \(\frac{(4 \times 2) + 3}{4}\) = \(\frac{11}{4}\)
Visual Proof: Why Does It Work?
Looking at \(2\frac{3}{4}\) as pizza slices or fraction bars:
1st Whole = 4 fourths
¼
¼
¼
¼
\(\frac{4}{4}\)
2nd Whole = 4 fourths
¼
¼
¼
¼
\(\frac{4}{4}\)
Plus Fraction = 3 fourths
¼
¼
¼
Empty
\(\frac{3}{4}\)
Count all shaded pieces: \(4 + 4 + 3 = \) 11 fourths total \(\rightarrow \mathbf{\frac{11}{4}}\)
Step-by-Step Examples
\(3\frac{1}{2}\) \((2 \times 3) + 1 = 7\) \(\frac{7}{2}\)
\(4\frac{2}{5}\) \((5 \times 4) + 2 = 22\) \(\frac{22}{5}\)
\(1\frac{5}{6}\) \((6 \times 1) + 5 = 11\) \(\frac{11}{6}\)
Watch Out! Common Traps
- ✗ Don't change the bottom: The denominator represents slice size—it never changes!
- ✗ Don't add first: Always multiply bottom \(\times\) whole before adding the top.
- ✓ Sanity check: The numerator in your answer must be larger than the original whole number!
Quick Try-It (Test Your MAD Skills!) Upside down answers below:
\(5\frac{1}{3} =\) ____
\(2\frac{4}{7} =\) ____
\(6\frac{1}{2} =\) ____
\(3\frac{3}{8} =\) ____
Answers: (1) \(\frac{16}{3}\) | (2) \(\frac{18}{7}\) | (3) \(\frac{13}{2}\) | (4) \(\frac{27}{8}\)
