RATIOS |

**Ratios, Fractions, Lowest Terms**

Classy mathematicians call **fractions** by another name. They call them **ratio**nal numbers because as we can see in the first 5 letters of the word -- they are ratios or fractions. Not all ratios can be expressed as fractions however. Only **2-term ratios can be written as fractions**.

Say our favourite hockey team has won 6, lost 3 and tied 1 of the last 10 games they played. We say that the ratio of wins to losses is 6 to 3 or, in reduced form -- 2 to 1. We use the colon (:) to replace the word "to" so these ratios are 6 : 3 and 2 : 1

As a fraction, we write this ratio

The ratio of losses to wins is 3 : 6 or 1 : 2. As a fraction, we write this ratio

Write these ratios in reduced form, first as ratios then as fractions.

a) ratio of squares to circles ratio = 3 : 4, fraction = ¾ |
b) ratio of circles to triangles ratio = 4: 6 = 2: 3, fraction = |
c) squares to triangles. ratio = 3: 6 = 1: 2, fraction =½ |

We always write the fraction representation for a ratio in lowest terms. So when we have numbers in a ratio with a common factor, we must divide by that factor.

Example: The ratio 8 : 6, is when written as a fraction, since both 8 and 6 are divisible by 2.

Example: Write the ratio 10 to 25 in two other ways:

10 to 25 is the same as 10: 25 and as a fraction it is since both 10 and 25 are divisible by 5.

**Note:** the quantities of a ratio must be in the same units, so to express the ratio of 5 centimeters to 3 meters, we must first change the 3 meters to centimeters. The ratio is 5:300 or 1/60.

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**Practice**

Express each ratio in lowest terms:

1) Use the diagram to express each ratio in 3 different ways. ("to", (:) , and fraction)

a) yellow to blue circles | b) blue to yellow circles | c) green to all circles |

d) all to yellow circles. | e) blue to all circles | f) blue to non-blue circles. |

2) Write each ratio in 2 other ways.

a) 9 to 5 | b) | c) 6 : 1 |

d) | e) 2: 19 | f) 4 to 52 |

3) 2) Write each ratio in lowest terms.

a) 8 to 4 | b) | c) 10 : 8 |

d) | e) 12: 15 | f) 10 to 30 |

4) For every 70 kg of iron found within the Earth, there are 60 kg. of oxygen and 30 kg. of silicon, from which computer chips are made. Express these ratios in lowest terms.

a) mass of oxygen to silicon | b) mass of iron to oxygen | c) mass of silicon to iron. |

5) Express these quantities in the same units, then write the ratio in lowest terms.

a) 5 cm to 2 m | b) 3 days to 2 weeks | c) 50 m to 2.5 km |

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**Solutions**

1) Use the diagram to express each ratio in 3 different ways. ("to", (:) , and fraction)

a) yellow to blue circles 4 to 3; 4 : 3 and . |
b) blue to yellow circles 3 to 4; 3 : 4 and . |
c) green to all circles 1 to 8; 1 : 8 and . |

d) all to yellow circles. 2 to 1; 2 : 1 and . |
e) blue to all circles 3 to 8; 3 : 8 and . |
f) blue to non-blue circles. 3 to 5; 3 : 5 and . |

2) Write each ratio in 2 other ways.

a) 9 to 5; 9 : 5, and | b) ; 2 to 3, and 2 : 3 | c) 6 : 1; 6 to 1 and |

d) ; 8 to 7, and 8 : 7 | e) 2: 19; 2 to 19 and | f) 4 to 52; 4 : 52 and . |

3) Write each ratio in lowest terms.

a) 8 to 4 = 2 to 1 | b) | c) 10 : 8 = 5 : 4 |

d) | e) 12: 15 = 4 : 5 | f) 10 to 30 = 1 to 3 |

4) For every **70 kg** of iron found within the Earth, there are **60 kg**. of oxygen and **30 kg**. of silicon, from which computer chips are made. Express these ratios in lowest terms.

a) mass of oxygen to silicon = 60 : 30 = 2 : 1 |
b) mass of iron to oxygen 70 : 60 = 7 : 6 |
c) mass of silicon to iron. 30 : 70 = 3 : 7 |

5) Express these quantities in the same units, then write the ratio in lowest terms.

a) 5 cm to 2 m 2 m = 200 cm; ratio = 1 : 40 |
b) 3 days to 2 weeks 2 weeks = 14 days; ratio = 3 : 14 |
c) 50 m to 2.5 km 2.5 km = 2500 m ratio = 1 : 50 |