# Equivalent Fractions

In the pizza on the **left**, what **fraction** is **one slice of pizza**? The answer is 1 part out of the 8 parts, one-eighth or ^{1}⁄_{8}.

In the pizza on the **right**, what **fraction** is **two slices of pizza**? The answer is 2 parts out of the 16 parts, two-sixteenths or ^{2}⁄_{16}.

These pizza servings are the **same** so ** ^{1}⁄_{8} and ^{2}⁄_{16} are equivalent fractions**.

## Examples

**Multiplying** both numerator and denominator by the same number:

^{1}⁄_{2} = ^{2}⁄_{4} = ^{4}⁄_{8} |

To change ^{1}⁄_{2} to ^{2}⁄_{4}, multiply both the numerator and the denominator by 2. |

To change ^{2}⁄_{4} to ^{4}⁄_{8}, multiply both the numerator and the denominator by 2. |

^{2}⁄_{3} = ^{4}⁄_{6} = ^{8}⁄_{12} |

To change ^{2}⁄_{3} to ^{4}⁄_{6}, multiply both the numerator and the denominator by 2. |

To change ^{4}⁄_{6} to ^{8}⁄_{12}, multiply both the numerator and the denominator by 2. |

**Dividing** both numerator and denominator by the same number:

^{4}⁄_{8} = ^{2}⁄_{4} = ^{1}⁄_{2} |

To change ^{4}⁄_{8} to ^{2}⁄_{4}, divide both the numerator and the denominator by 2. |

To change ^{2}⁄_{4} to ^{1}⁄_{2}, divide both the numerator and the denominator by 2. |

^{8}⁄_{12} = ^{4}⁄_{6} = ^{2}⁄_{3} |

To change ^{8}⁄_{12} to ^{4}⁄_{6}, divide both the numerator and the denominator by 2. |

To change ^{4}⁄_{6} to ^{2}⁄_{3}, divide both the numerator and the denominator by 2. |

More examples of equivalent fractions:

^{3} ⁄_{4} = ^{9} ⁄_{12} (Multiplied by 3)

^{5} ⁄_{6} = ^{20} ⁄_{24} (Multiplied by 4)

^{30} ⁄_{36} = ^{5} ⁄_{6} (Divided by 6)

^{20} ⁄_{30} = ^{2} ⁄_{3} (Divided by 10)

## Questions

What is the missing number, X?

**Q1.** ^{1} ⁄_{2} = ^{X} ⁄_{10}
**Q2.** ^{1} ⁄_{3} = ^{X} ⁄_{12}
**Q3.** ^{1} ⁄_{2} = ^{10} ⁄_{X}
**Q4.** ^{2} ⁄_{3} = ^{X} ⁄_{18}
**Q5.** ^{25} ⁄_{100} = ^{X} ⁄_{4}

**Answers**
**A1.** 5
**A2.** 4
**A3.** 20
**A4.** 12
**A5.** 1

## Changing a Mixed Number to an Improper Fraction

A **mixed number** is a mixture of a whole number and a fraction. An example of a mixed number is 2^{1}⁄_{2}
When a mixed number is converted to a fraction only, it is called an **improper fraction**. An example of an improper fraction is ^{5} ⁄_{2}

1^{3}⁄_{4} = ^{7}⁄_{4} |

To change the mixed number of 1^{3}⁄_{4} to the improper fraction of ^{7}⁄_{4},multiply the whole number 1 by the denominator 4, and then add on the numerator 3. |

## Changing an Improper Fraction Back to a Mixed Number

1^{2}⁄_{3} = ^{5}⁄_{3} |

To change the mixed number of 1^{2}⁄_{3} to the improper fraction of ^{5}⁄_{3},multiply the whole number 1 by the denominator 3, and then add on the numerator 2. |