Before viewing this page, it would be helpful to learn how to calculate Equivalent 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.

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)

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)

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)

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)

**Q1.** ^{1}⁄_{2} + ^{1}⁄_{3}
**Q2.** ^{3}⁄_{4} + ^{1}⁄_{3}
**Q3.** ^{7}⁄_{8} + ^{3}⁄_{4}
**Q4.** ^{5}⁄_{6} – ^{3}⁄_{8}

**Answers**
**A1.** ^{5}⁄_{6}
**A2.** 1 ^{1}⁄_{12}
**A3.** 1 ^{5}⁄_{8}
**A4.** ^{11}⁄_{24}

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}

**Q1.** 2 ^{1}⁄_{8} + 3 ^{3}⁄_{4}
**Q2.** 3 ^{1}⁄_{4} – 1 ^{1}⁄_{5}

**Answers**
**A1.** 5 ^{7}⁄_{8}
**A2.** 2 ^{1}⁄_{20}

Bob loves to count. One day, his teacher put a pile of pencils on Bob's desk. Bob began to count the pencils. He told his teacher the following facts about the pencils:

- When I count the pencils by two, I have one left over.
- When I count the pencils by threes, I have one left over.
- When I count the pencils by fours, I have one left over.
- When I count them by sevens, I have none left over.

How many pencils are there?