Add And Subtract Fractions

Mechanics working on some car engines use common fractions.

Many drill bits, sockets and Allen keys are in Imperial sizes such as ¹⁄₂ inch, ¹⁄₄ inch, ¹⁄₈ inch and so on.

Steps to add and subtract common fractions are:

• Step 1 - find the common denominator (the number that both bottom numbers will divide into without a remainder)
• Step 2 - find the equivalent fractions
• Step 3 - add or subtract the equivalent fractions
• Step 4 - change to a mixed number or simplify if needed.

---

Example One - Adding Allen Keys

Allen keys are used to measure gaps in car engines. Into a gap, Allen keys with thicknesses of ¹⁄₂ inch and ¹⁄₄ inch can fit. What is the width of the gap?

Answer:
¹⁄₂ + ¹⁄₄
= ²⁄₄ + ¹⁄₄ (Steps 1 and 2)
= ³⁄₄ (Step 3)

---

Example Two - Adding Allen Keys

What is the width of a gap into which Allen keys with thicknesses of ³⁄₈ inch and ¹⁄₁₆ inch can fit?

Answer:
³⁄₈ + ¹⁄₁₆
= ⁶⁄₁₆ + ¹⁄₁₆ (Steps 1 and 2)
= ⁷⁄₁₆ (Step 3)

---

Example Three - Adding Pizza Slices

What is the total of ³⁄₄ pizza and ²⁄₃ pizza?

Answer:
³⁄₄ + ²⁄₃
= ⁹⁄₁₂ + ⁸⁄₁₂ (Steps 1 and 2)
= ¹⁷⁄₁₂ (Step 3)
= 1 ⁵⁄₁₂ (Step 4)

---

Example Four - Subtracting Pizza Slices

There is ³⁄₄ of a pizza. If I eat ²⁄₃ pizza, how much is left?

Answer:
³⁄₄ – ²⁄₃
= ⁹⁄₁₂ – ⁸⁄₁₂ (Steps 1 and 2)
= ¹⁄₁₂ (Step 3)

Example Five - Adding Mixed Numbers

Add 1 ³⁄₄ and 1 ²⁄₃.

Answer:
Change these mixed numbers to improper fractions first.
1 ³⁄₄ + 1 ²⁄₃
= ⁷⁄₄ + ⁵⁄₃
= ²¹⁄₁₂ + ²⁰⁄₁₂
= ⁴¹⁄₁₂
= 3 ⁷⁄₁₂