Fraction Operations Study Guide
5th Grade Math • Student Review
Unit 2: Fractions & Multiplication
Name:
Date: Class:
Directions: Complete the guided rules, visual models, and practice problems to prepare for the test.
1
Fractions as Quotients (\(a \div b = \frac{a}{b}\))
Standard 5.NF.B.3
Key Rule: Division as a fraction: \(a \div b =\) _____ _____
• Numerator (top):
• Denominator (bottom):
Visual Strip Model: Explain \(3 \div 5\)
Shade 1 part in each of the 3 strips to represent 1 share:
\(3 \div 5 = 3 \times \frac{1}{\text{____}} = \) _____ _____
Fill-In Practice Problems
A. 5 friends share 12 doughnuts.
Expression: \(\div\) =
Mixed number: each
B. 18-inch ribbon cut into 4 equal pieces.
Each piece: in. = in.
Tip: The item being shared ALWAYS goes in the numerator!
2
Multiplying Fractions & Whole Numbers
Standard 5.NF.B.4a
"Fraction OF a Whole" =
Problem: "Jada cooks \(\frac{2}{3}\) of an 8-ounce box of pasta."
1. Expression: \(\frac{2}{3}\) \(\times\)
2. Multiply: \(\frac{2 \times \text{____}}{3} = \frac{\text{____}}{3}\)
3. Mixed number: oz
Solve: \(3\frac{9}{10} \times 4\) (Distributive Strategy)
• Whole: \(3 \times 4 =\)
• Fraction: \(\frac{9}{10} \times 4 = \frac{\text{____}}{10}\)
• Combine: + \(\frac{\text{____}}{10} = \frac{\text{____}}{10}\)
• Improper:
3
Equivalent Expressions Check
Standard 5.OA.A.2
Fill in the blanks to complete 4 expressions equivalent to \(\frac{4}{5} \times 3\):
Standard Form: \(\frac{4}{5} \times\)
Division First: \((4 \times 3) \div\)
Unit Fraction: \(\frac{1}{\text{____}} \times (4 \times 3)\)
Commutative: \(\left(\text{____} \times \frac{1}{5}\right) \times 4\)
Trap Alert: Is \(\left(4 \times \frac{1}{5}\right) + \left(3 \times \frac{1}{5}\right)\) equivalent to \(\frac{4}{5} \times 3\)?
Circle: YES NO
Unit 2 Guided Review • Page 1 of 2 Turn page to complete Area Models & Scaling →
Part 2: Area Models, Scaling & Multi-Step Problems
Apply visual representations and reasoning to complete each section.
5.NF.B.4b • 5.NF.B.5b • 5.NF.B.6
4
Area Models with Fractional Dimensions
Standard 5.NF.B.4b
Area Formula: \(\text{Area} =\) \(\times\)
Example A: Shaded Grid Region
4 units 1
• Number of whole unit columns =
• Shaded fraction of each unit height =
• Multiplication: \(\times \frac{\text{____}}{5} = \frac{\text{____}}{5}\) sq units
Check: Denominator is 5 because 1 whole unit is divided into 5 equal parts.
Example B: Multi-Unit Expressions
A grid is 5 units wide and 3 units high. Each unit height is partitioned into 4 equal fourths. The top \(2\frac{3}{4}\) is shaded.
Form 1: (Total area) − (Unshaded area)
\((5 \times 3) - (5 \times\) )
Form 2: (Shaded height) × (Width)
\(\times 5\)
Form 3: Count total shaded fourths:
\(\times \frac{1}{4} = \frac{\text{____}}{4}\)
Tip: Look for both subtraction & mixed-number multiplication forms!
5
Multiplication as Scaling (Comparing Without Calculating)
Standard 5.NF.B.5b
Consider the expression: \(6 \times \text{Factor}\). Complete the scaling rules:
Factor < 1 (e.g., \(\frac{1}{2}\))
Product will:
DECREASE INCREASE
\(6 \times \frac{1}{2} = 3\)
3 is between and
Factor = 1 (e.g., \(\frac{4}{4}\))
Product will:
STAY EQUAL
\(6 \times \frac{4}{4} =\)
(Identity Property)
Factor > 1 (e.g., \(1\frac{1}{2}\))
Product will:
INCREASE DECREASE
Product is (circle):
> 6 or < 6
Multi-Step Word Problem Practice
"A farm is 2 km long and 3 km wide. It is divided into 5 equal parts. What is the area of 1 part?"
• Total Area = \(\times\) = sq km
• Divide by 5 = \(\div\) 5 = sq km
• Mixed number = sq km
Check units: Area must always be in square units!
My Test-Day Readiness Checklist
Check each box once you understand the strategy:
- I write sharing problems as \(\frac{\text{Total}}{\text{Shares}}\) without flipping.
- For grid areas, my denominator is the partitions of 1 unit.
- In scaling, I compare fraction factor to 1 (less, equal, greater).
- For "Explain" items, I include BOTH equations & solutions.
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Unit 2 Guided Review • Page 2 of 2 ✓ Completed Study Guide
