Fraction Blueprint Worksheet Fraction Blueprint
Unlike Denominators • Numerical Analysis
Engineer:
Page 01 of 02
Method Guide
Multiply denominators for the Common Denominator (CD).
Cross-multiply: Top-Left × Bottom-Right (C1).
Cross-multiply: Bottom-Left × Top-Right (C2).
\( \frac{1}{2} + \frac{1}{3} \)
3 + 2
6
\( \frac{5}{6} \)
#01
\( \frac{1}{2} + \frac{1}{4} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
#02
\( \frac{3}{5} - \frac{1}{10} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
#03
\( \frac{2}{3} + \frac{1}{6} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
#04
\( \frac{5}{8} - \frac{1}{2} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
#05
\( \frac{1}{3} + \frac{1}{9} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
Fraction Blueprint
Page 02 of 02
#06
\( \frac{5}{6} - \frac{1}{3} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
#07
\( \frac{3}{4} + \frac{2}{8} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
#08
\( \frac{9}{10} - \frac{1}{2} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
#09
\( \frac{2}{5} + \frac{2}{10} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
#10
\( \frac{4}{5} - \frac{2}{10} \)
Common Denom
Cross Prod 1
Cross Prod 2
Result
Simplify
/
Fraction Blueprint Answer Key Answer Key
Project: Fraction Blueprint
Teacher Reference
CD: Common Denominator
C1: Cross Product 1
C2: Cross Product 2
1
\( \frac{1}{2} + \frac{1}{4} \)
CD: 8
C1: 4 | C2: 2
Final: 6/8 → 3/4
2
\( \frac{3}{5} - \frac{1}{10} \)
CD: 50
C1: 30 | C2: 5
Final: 25/50 → 1/2
3
\( \frac{2}{3} + \frac{1}{6} \)
CD: 18
C1: 12 | C2: 3
Final: 15/18 → 5/6
4
\( \frac{5}{8} - \frac{1}{2} \)
CD: 16
C1: 10 | C2: 8
Final: 2/16 → 1/8
5
\( \frac{1}{3} + \frac{1}{9} \)
CD: 27
C1: 9 | C2: 3
Final: 12/27 → 4/9
6
\( \frac{5}{6} - \frac{1}{3} \)
CD: 18
C1: 15 | C2: 6
Final: 9/18 → 1/2
7
\( \frac{3}{4} + \frac{2}{8} \)
CD: 32
C1: 24 | C2: 8
Final: 32/32 → 1
8
\( \frac{9}{10} - \frac{1}{2} \)
CD: 20
C1: 18 | C2: 10
Final: 8/20 → 2/5
9
\( \frac{2}{5} + \frac{2}{10} \)
CD: 50
C1: 20 | C2: 10
Final: 30/50 → 3/5
10
\( \frac{4}{5} - \frac{2}{10} \)
CD: 50
C1: 40 | C2: 10
Final: 30/50 → 3/5
Fraction Link Worksheet Fraction Link
Project: Opposite Denominator Strategy
Engineer:
Numerical Set • Page 1 of 4
Example: Multiplying by Opposites
\( \frac{1}{2} + \frac{1}{3} \)
1 × 3
2 × 3
1 × 2
3 × 2
\( \frac{3+2}{6} = \frac{5}{6} \)
1
\( \frac{2}{3} + \frac{1}{4} \)
Step 1: Link & Multiply
Fraction A × Denom B
Fraction B × Denom A
Step 2: Simplify
2
\( \frac{4}{5} - \frac{1}{10} \)
Step 1: Link & Multiply
-
Step 2: Simplify
Fraction Link
Page 2 of 4
3
\( \frac{2}{3} + \frac{1}{6} \)
Step 1: Link & Multiply
Step 2: Simplify
4
\( \frac{5}{8} - \frac{1}{2} \)
Step 1: Link & Multiply
-
Step 2: Simplify
5
\( \frac{1}{3} + \frac{1}{9} \)
Step 1: Link & Multiply
Step 2: Simplify
Fraction Link
Page 3 of 4
6
\( \frac{5}{6} - \frac{1}{3} \)
Step 1: Link & Multiply
-
Step 2: Simplify
7
\( \frac{3}{4} + \frac{2}{8} \)
Step 1: Link & Multiply
Step 2: Simplify
8
\( \frac{9}{10} - \frac{1}{2} \)
Step 1: Link & Multiply
-
Step 2: Simplify
Fraction Link
Page 4 of 4
9
\( \frac{2}{5} + \frac{2}{10} \)
Step 1: Link & Multiply
Step 2: Simplify
10
\( \frac{4}{5} - \frac{2}{10} \)
Step 1: Link & Multiply
-
Step 2: Simplify
Conversion Reference
Mixed → Improper
Multiply denominator by whole number, then add the numerator.
Ex: 3 1/2 = (2×3)+1 = 7/2
Improper → Mixed
Divide numerator by denominator. Use the remainder as the numerator.
Ex: 11/4 = 11÷4 = 2 R 3 = 2 3/4
Fraction Link Answer Key Answer Key
Project: Fraction Link • Opposite Denominator Strategy
Teacher Resource
1
\( \frac{2}{3} + \frac{1}{4} \)
Answer: 11/12
Step 1: Multiply
\( \frac{2 \times 4}{3 \times 4} + \frac{1 \times 3}{4 \times 3} = \frac{8}{12} + \frac{3}{12} \)
Step 2: Combine
\( \frac{11}{12} \) (Already simplest)
2
\( \frac{4}{5} - \frac{1}{2} \)
Answer: 3/10
Step 1: Multiply
\( \frac{4 \times 2}{5 \times 2} - \frac{1 \times 5}{2 \times 5} = \frac{8}{10} - \frac{5}{10} \)
Step 2: Combine
\( \frac{3}{10} \) (Already simplest)
3
\( \frac{1}{6} + \frac{2}{5} \)
Answer: 17/30
Step 1: Multiply
\( \frac{1 \times 5}{6 \times 5} + \frac{2 \times 6}{5 \times 6} = \frac{5}{30} + \frac{12}{30} \)
Step 2: Combine
\( \frac{17}{30} \)
4
\( \frac{7}{8} - \frac{1}{3} \)
Answer: 13/24
Step 1: Multiply
\( \frac{7 \times 3}{8 \times 3} - \frac{1 \times 8}{3 \times 8} = \frac{21}{24} - \frac{8}{24} \)
Step 2: Combine
\( \frac{13}{24} \)
5
\( \frac{1}{2} + \frac{3}{7} \)
Answer: 13/14
Step 1: Multiply
\( \frac{1 \times 7}{2 \times 7} + \frac{3 \times 2}{7 \times 2} = \frac{7}{14} + \frac{6}{14} \)
Step 2: Combine
\( \frac{13}{14} \)
6
\( \frac{5}{9} - \frac{1}{4} \)
Answer: 11/36
Step 1: Multiply
\( \frac{5 \times 4}{9 \times 4} - \frac{1 \times 9}{4 \times 9} = \frac{20}{36} - \frac{9}{36} \)
Step 2: Combine
\( \frac{11}{36} \)
7
\( \frac{3}{10} + \frac{2}{3} \)
Answer: 29/30
Step 1: Multiply
\( \frac{3 \times 3}{10 \times 3} + \frac{2 \times 10}{3 \times 10} = \frac{9}{30} + \frac{20}{30} \)
Step 2: Combine
\( \frac{29}{30} \)
8
\( \frac{5}{6} - \frac{2}{5} \)
Answer: 13/30
Step 1: Multiply
\( \frac{5 \times 5}{6 \times 5} - \frac{2 \times 6}{5 \times 6} = \frac{25}{30} - \frac{12}{30} \)
Step 2: Combine
\( \frac{13}{30} \)
9
\( \frac{3}{8} + \frac{1}{10} \)
Answer: 19/40
Fraction Conversion Cheat Sheet Fraction Field Guide
Conversions • Improper Fractions & Mixed Numbers
Key Definitions
Numerator
The top number. It represents the count of parts you currently have.
Denominator
The bottom number. It tells you the total size of one whole unit.
Improper Fraction
The numerator is greater than the denominator. (Ex: \( \frac{7}{4} \))
Mixed Number
A combination of a whole number and a proper fraction. (Ex: \( 1 \frac{3}{4} \))
Mixed → Improper Fraction
The "Circle" Strategy
Multiply denominator × whole number.
Add that result to the numerator.
Place answer over original denominator.
Multiply
Add
\( 3 \frac{1}{2} \)
(2 × 3) + 1 = 7
\( \frac{7}{2} \)
Improper Fraction → Mixed
The "Division" Strategy
Divide the top by the bottom.
The Quotient becomes the Whole Number.
The Remainder is the new Numerator.
Keep the Same Denominator.
Example: \( \frac{11}{4} \)
11 ÷ 4 = 2 R 3
Whole
2
Remainder
3
4
Fraction Blueprint Technical Manual • Job Site Reference
Mixed Conversion Worksheet Mixed Conversion
Project: Mixed Numbers to Improper Fractions
Engineer:
Page 1 of 2
The "Circle" Strategy Guide
1. Multiply Denom × Whole #
2. Add Result + Numerator
3. Result: New Top / Same Bottom
3
1
2
(2×3)+1
7
2
1
2
1
3
Show Work
Result:
2
4
3
5
Show Work
Result:
3
1
7
8
Show Work
Result:
4
5
2
7
Show Work
Result:
Mixed Conversion
Page 2 of 2
5
3
3
4
Show Work
Result:
6
6
1
2
Show Work
Result:
7
2
5
6
Show Work
Result:
8
10
1
4
Show Work
Result:
9
8
2
9
Show Work
Result:
10
7
4
7
Show Work
Result:
Mixed Conversion Answer Key Answer Key
Mixed Numbers → Improper Fractions
Teacher Resource
1
\( 2 \frac{1}{3} \)
(3 × 2) + 1 = 7
\( \frac{7}{3} \)
2
\( 4 \frac{3}{5} \)
(5 × 4) + 3 = 23
\( \frac{23}{5} \)
3
\( 1 \frac{7}{8} \)
(8 × 1) + 7 = 15
\( \frac{15}{8} \)
4
\( 5 \frac{2}{7} \)
(7 × 5) + 2 = 37
\( \frac{37}{7} \)
5
\( 3 \frac{3}{4} \)
(4 × 3) + 3 = 15
\( \frac{15}{4} \)
6
\( 6 \frac{1}{2} \)
(2 × 6) + 1 = 13
\( \frac{13}{2} \)
7
\( 2 \frac{5}{6} \)
(6 × 2) + 5 = 17
\( \frac{17}{6} \)
8
\( 10 \frac{1}{4} \)
(4 × 10) + 1 = 41
\( \frac{41}{4} \)
9
\( 8 \frac{2}{9} \)
(9 × 8) + 2 = 74
\( \frac{74}{9} \)
10
\( 7 \frac{4}{7} \)
(7 × 7) + 4 = 53
\( \frac{53}{7} \)
Engineering Answer Set • Verify Before Distribution
