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Reach Advantage worksheet

Grade 6 · CCSS 6.RP.A.1, 6.RP.A.3.d, 6.NS.B.3

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Units: Centimeters
- Fighter A: Fighter A
- Fighter A height: 70
- Fighter A reach (arm span): 80
- Fighter B: Fighter B
- Fighter B height: 85
- Fighter B reach (arm span): 55
Find: Reach advantage
Answer
2.
Problem 2.
- Units: Inches
- Fighter A: Fighter A
- Fighter A height: 70
- Fighter A reach (arm span): 65
- Fighter B: Fighter B
- Fighter B height: 65
- Fighter B reach (arm span): 75
Find: Reach advantage
Answer
3.
Problem 3.
- Units: Centimeters
- Fighter A: Fighter A
- Fighter A height: 85
- Fighter A reach (arm span): 62
- Fighter B: Fighter B
- Fighter B height: 70
- Fighter B reach (arm span): 72
Find: Reach advantage
Answer
4.
Problem 4.
- Units: Centimeters
- Fighter A: Fighter A
- Fighter A height: 70
- Fighter A reach (arm span): 110
- Fighter B: Fighter B
- Fighter B height: 82
- Fighter B reach (arm span): 90
Find: Reach advantage
Answer
5.
Problem 5.
- Units: Centimeters
- Fighter A: Fighter A
- Fighter A height: 75
- Fighter A reach (arm span): 70
- Fighter B: Fighter B
- Fighter B height: 55
- Fighter B reach (arm span): 60
Find: Reach advantage
Answer
6.
Problem 6.
- Units: Centimeters
- Fighter A: Fighter A
- Fighter A height: 55
- Fighter A reach (arm span): 65
- Fighter B: Fighter B
- Fighter B height: 49
- Fighter B reach (arm span): 74
Find: Reach advantage
Answer
7.
Problem 7.
- Units: Centimeters
- Fighter A: Fighter A
- Fighter A height: 72
- Fighter A reach (arm span): 116
- Fighter B: Fighter B
- Fighter B height: 64
- Fighter B reach (arm span): 76
Find: Reach advantage
Answer
8.
Problem 8.
- Units: Centimeters
- Fighter A: Fighter A
- Fighter A height: 80
- Fighter A reach (arm span): 66
- Fighter B: Fighter B
- Fighter B height: 90
- Fighter B reach (arm span): 72
Find: Reach advantage
Answer
9.
Problem 9.
- Units: Inches
- Fighter A: Fighter A
- Fighter A height: 70
- Fighter A reach (arm span): 52
- Fighter B: Fighter B
- Fighter B height: 68
- Fighter B reach (arm span): 80
Find: Reach advantage
Answer
10.
Problem 10.
- Units: Inches
- Fighter A: Fighter A
- Fighter A height: 65
- Fighter A reach (arm span): 80
- Fighter B: Fighter B
- Fighter B height: 66
- Fighter B reach (arm span): 85
Find: Reach advantage
Answer

Answer key: Reach Advantage worksheet

1. Reach advantage: 25 cm
1. Reach advantage: the longer reach minus the shorter one (Fighter A has the edge)
  $80 cm - 55 cm$ $= 25 cm$
2. Fighter A's ape index as a difference: reach minus height
  $80 cm - 70 cm$ $= 10 cm$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{80 cm}{70 cm}$ $= 1.1429$
4. Fighter B's ape index as a difference: reach minus height
  $55 cm - 85 cm$ $= −30 cm$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{55 cm}{85 cm}$ $= 0.6471$
6. The reach advantage in inches (divide by 2.54)
  $\frac{25}{2.54}$ $= 9.84 in$
2. Reach advantage: 10 in
1. Reach advantage: the longer reach minus the shorter one (Fighter B has the edge)
  $75 in - 65 in$ $= 10 in$
2. Fighter A's ape index as a difference: reach minus height
  $65 in - 70 in$ $= −5 in$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{65 in}{70 in}$ $= 0.9286$
4. Fighter B's ape index as a difference: reach minus height
  $75 in - 65 in$ $= 10 in$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{75 in}{65 in}$ $= 1.1538$
6. The reach advantage in centimeters (1 in = 2.54 cm exactly)
  $10 \times 2.54$ $= 25.4 cm$
3. Reach advantage: 10 cm
1. Reach advantage: the longer reach minus the shorter one (Fighter B has the edge)
  $72 cm - 62 cm$ $= 10 cm$
2. Fighter A's ape index as a difference: reach minus height
  $62 cm - 85 cm$ $= −23 cm$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{62 cm}{85 cm}$ $= 0.7294$
4. Fighter B's ape index as a difference: reach minus height
  $72 cm - 70 cm$ $= 2 cm$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{72 cm}{70 cm}$ $= 1.0286$
6. The reach advantage in inches (divide by 2.54)
  $\frac{10}{2.54}$ $= 3.94 in$
4. Reach advantage: 20 cm
1. Reach advantage: the longer reach minus the shorter one (Fighter A has the edge)
  $110 cm - 90 cm$ $= 20 cm$
2. Fighter A's ape index as a difference: reach minus height
  $110 cm - 70 cm$ $= 40 cm$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{110 cm}{70 cm}$ $= 1.5714$
4. Fighter B's ape index as a difference: reach minus height
  $90 cm - 82 cm$ $= 8 cm$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{90 cm}{82 cm}$ $= 1.0976$
6. The reach advantage in inches (divide by 2.54)
  $\frac{20}{2.54}$ $= 7.87 in$
5. Reach advantage: 10 cm
1. Reach advantage: the longer reach minus the shorter one (Fighter A has the edge)
  $70 cm - 60 cm$ $= 10 cm$
2. Fighter A's ape index as a difference: reach minus height
  $70 cm - 75 cm$ $= −5 cm$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{70 cm}{75 cm}$ $= 0.9333$
4. Fighter B's ape index as a difference: reach minus height
  $60 cm - 55 cm$ $= 5 cm$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{60 cm}{55 cm}$ $= 1.0909$
6. The reach advantage in inches (divide by 2.54)
  $\frac{10}{2.54}$ $= 3.94 in$
6. Reach advantage: 9 cm
1. Reach advantage: the longer reach minus the shorter one (Fighter B has the edge)
  $74 cm - 65 cm$ $= 9 cm$
2. Fighter A's ape index as a difference: reach minus height
  $65 cm - 55 cm$ $= 10 cm$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{65 cm}{55 cm}$ $= 1.1818$
4. Fighter B's ape index as a difference: reach minus height
  $74 cm - 49 cm$ $= 25 cm$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{74 cm}{49 cm}$ $= 1.5102$
6. The reach advantage in inches (divide by 2.54)
  $\frac{9}{2.54}$ $= 3.54 in$
7. Reach advantage: 40 cm
1. Reach advantage: the longer reach minus the shorter one (Fighter A has the edge)
  $116 cm - 76 cm$ $= 40 cm$
2. Fighter A's ape index as a difference: reach minus height
  $116 cm - 72 cm$ $= 44 cm$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{116 cm}{72 cm}$ $= 1.6111$
4. Fighter B's ape index as a difference: reach minus height
  $76 cm - 64 cm$ $= 12 cm$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{76 cm}{64 cm}$ $= 1.1875$
6. The reach advantage in inches (divide by 2.54)
  $\frac{40}{2.54}$ $= 15.75 in$
8. Reach advantage: 6 cm
1. Reach advantage: the longer reach minus the shorter one (Fighter B has the edge)
  $72 cm - 66 cm$ $= 6 cm$
2. Fighter A's ape index as a difference: reach minus height
  $66 cm - 80 cm$ $= −14 cm$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{66 cm}{80 cm}$ $= 0.825$
4. Fighter B's ape index as a difference: reach minus height
  $72 cm - 90 cm$ $= −18 cm$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{72 cm}{90 cm}$ $= 0.8$
6. The reach advantage in inches (divide by 2.54)
  $\frac{6}{2.54}$ $= 2.36 in$
9. Reach advantage: 28 in
1. Reach advantage: the longer reach minus the shorter one (Fighter B has the edge)
  $80 in - 52 in$ $= 28 in$
2. Fighter A's ape index as a difference: reach minus height
  $52 in - 70 in$ $= −18 in$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{52 in}{70 in}$ $= 0.7429$
4. Fighter B's ape index as a difference: reach minus height
  $80 in - 68 in$ $= 12 in$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{80 in}{68 in}$ $= 1.1765$
6. The reach advantage in centimeters (1 in = 2.54 cm exactly)
  $28 \times 2.54$ $= 71.12 cm$
10. Reach advantage: 5 in
1. Reach advantage: the longer reach minus the shorter one (Fighter B has the edge)
  $85 in - 80 in$ $= 5 in$
2. Fighter A's ape index as a difference: reach minus height
  $80 in - 65 in$ $= 15 in$
3. Fighter A's ape index as a ratio: reach divided by height
  $\frac{80 in}{65 in}$ $= 1.2308$
4. Fighter B's ape index as a difference: reach minus height
  $85 in - 66 in$ $= 19 in$
5. Fighter B's ape index as a ratio: reach divided by height
  $\frac{85 in}{66 in}$ $= 1.2879$
6. The reach advantage in centimeters (1 in = 2.54 cm exactly)
  $5 \times 2.54$ $= 12.7 cm$