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ERA worksheet

Grades 6–7 · CCSS 7.RP.A.1, 6.RP.A.3.b

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

1.
Problem 1.
- Earned runs (ER): 55
- Innings pitched (IP): 200
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 10
Find: Earned run average
Answer
2.
Problem 2.
- Earned runs (ER): 46
- Innings pitched (IP): 150
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 6
Find: Earned run average
Answer
3.
Problem 3.
- Earned runs (ER): 64
- Innings pitched (IP): 210
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 11
Find: Earned run average
Answer
4.
Problem 4.
- Earned runs (ER): 52
- Innings pitched (IP): 140
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 7
Find: Earned run average
Answer
5.
Problem 5.
- Earned runs (ER): 65
- Innings pitched (IP): 180
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 13
Find: Earned run average
Answer
6.
Problem 6.
- Earned runs (ER): 69
- Innings pitched (IP): 220
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 10
Find: Earned run average
Answer
7.
Problem 7.
- Earned runs (ER): 74
- Innings pitched (IP): 145
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 10
Find: Earned run average
Answer
8.
Problem 8.
- Earned runs (ER): 70
- Innings pitched (IP): 180
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 9
Find: Earned run average
Answer
9.
Problem 9.
- Earned runs (ER): 40
- Innings pitched (IP): 170
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 8
Find: Earned run average
Answer
10.
Problem 10.
- Earned runs (ER): 68
- Innings pitched (IP): 180
- Innings use baseball notation (.1 = ⅓ inning, .2 = ⅔ inning): Yes
- Innings in a regulation game: 8
Find: Earned run average
Answer

Answer key: ERA worksheet

1. Earned run average: 2.75
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $200 IP$ $= 200 innings$ $= \frac{200 \times 3 + 0}{3}$ $= 200$
2. ERA scales earned runs to a 10-inning game: 10 times earned runs, divided by innings pitched
  $ERA$ $= \frac{10 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{10 \times 55}{200}$ $= \frac{550}{200}$ $= 2.75$
2. Earned run average: 1.84
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $150 IP$ $= 150 innings$ $= \frac{150 \times 3 + 0}{3}$ $= 150$
2. ERA scales earned runs to a 6-inning game: 6 times earned runs, divided by innings pitched
  $ERA$ $= \frac{6 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{6 \times 46}{150}$ $= \frac{276}{150}$ $= 1.84$
3. Earned run average: 3.35
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $210 IP$ $= 210 innings$ $= \frac{210 \times 3 + 0}{3}$ $= 210$
2. ERA scales earned runs to a 11-inning game: 11 times earned runs, divided by innings pitched
  $ERA$ $= \frac{11 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{11 \times 64}{210}$ $= \frac{704}{210}$ $= 3.352381$
4. Earned run average: 2.6
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $140 IP$ $= 140 innings$ $= \frac{140 \times 3 + 0}{3}$ $= 140$
2. ERA scales earned runs to a 7-inning game: 7 times earned runs, divided by innings pitched
  $ERA$ $= \frac{7 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{7 \times 52}{140}$ $= \frac{364}{140}$ $= 2.6$
5. Earned run average: 4.69
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $180 IP$ $= 180 innings$ $= \frac{180 \times 3 + 0}{3}$ $= 180$
2. ERA scales earned runs to a 13-inning game: 13 times earned runs, divided by innings pitched
  $ERA$ $= \frac{13 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{13 \times 65}{180}$ $= \frac{845}{180}$ $= 4.694444$
6. Earned run average: 3.14
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $220 IP$ $= 220 innings$ $= \frac{220 \times 3 + 0}{3}$ $= 220$
2. ERA scales earned runs to a 10-inning game: 10 times earned runs, divided by innings pitched
  $ERA$ $= \frac{10 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{10 \times 69}{220}$ $= \frac{690}{220}$ $= 3.136364$
7. Earned run average: 5.1
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $145 IP$ $= 145 innings$ $= \frac{145 \times 3 + 0}{3}$ $= 145$
2. ERA scales earned runs to a 10-inning game: 10 times earned runs, divided by innings pitched
  $ERA$ $= \frac{10 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{10 \times 74}{145}$ $= \frac{740}{145}$ $= 5.103448$
8. Earned run average: 3.5
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $180 IP$ $= 180 innings$ $= \frac{180 \times 3 + 0}{3}$ $= 180$
2. ERA scales earned runs to a 9-inning game: 9 times earned runs, divided by innings pitched
  $ERA$ $= \frac{9 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{9 \times 70}{180}$ $= \frac{630}{180}$ $= 3.5$
9. Earned run average: 1.88
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $170 IP$ $= 170 innings$ $= \frac{170 \times 3 + 0}{3}$ $= 170$
2. ERA scales earned runs to a 8-inning game: 8 times earned runs, divided by innings pitched
  $ERA$ $= \frac{8 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{8 \times 40}{170}$ $= \frac{320}{170}$ $= 1.882353$
10. Earned run average: 3.02
1. Convert the notation: the digit after the point counts outs, and each out is one third of an inning
  $180 IP$ $= 180 innings$ $= \frac{180 \times 3 + 0}{3}$ $= 180$
2. ERA scales earned runs to a 8-inning game: 8 times earned runs, divided by innings pitched
  $ERA$ $= \frac{8 \times ER}{IP}$
3. Put in your earned runs and true innings to get the ERA
  $\frac{8 \times 68}{180}$ $= \frac{544}{180}$ $= 3.022222$