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We constantly compare quantities like length and weight in our everyday lives. Ratios allow us to represent these comparisons mathematically. We connect two quantities using the “:” symbol to show a comparison. Here we will learn how to represent ratios in a tabular format with some examples....Read MoreRead Less

A ratio table is just a table that is used to describe the relationship between two separate quantities. Ratio tables are helpful for visualizing the relationship between two separate quantities. It is a logically organized list of equivalent ratios that aids in understanding the relationship between ratios and numbers. Rates, like your heartbeat, are a type of ratio in which the two numbers being compared have different units.

A ratio table for the multiplication of terms is shown below:

3 | 6 | 9 | 12 |

9 | 18 | 27 | 36 |

In a ratio table, you can find and organize equivalent ratios. In order to complete the ratio table you can use either multiplication or division.

The steps for creating a ratio table are:

Step 1: Draw two columns for the comparison of the given ratio.

Step 2: Label the table and input the values in the first row as that is mentioned in the question.

Step 3: Determine the mathematical operation and fill in the table.

Step 4: Compare the value at the given point and find your answer.

**Example 1:** Write the equivalent ratios by finding the missing values in the ratio table.

(a).

Tables | 1 | 2 | 4 | |

Chairs | 2 | 6 |

(b).

Horses | 3 | 6 | ||

Elephants | 4 | 16 |

(c).

Worms | 1 | 8 | ||

Mosquitoes | 200 | 600 | 1800 |

(d).

Plates | 3 | 2 | ||

Bowls | 2 | 4 |

**Solution:**

Part (a)

We have

Tables | 1 | 2 | 4 | |

Chairs | 2 | 6 |

Because the original ratio is 1 table to 2 chairs, you can repeatedly add 1 to the ﬁrst row and repeatedly add 2 to the second row.

So,

Tables | 1 | 2 | 3 | 4 |

Chairs | 2 | 4 | 6 | 8 |

Part (b)

We have

Horses | 3 | 6 | ||

Elephants | 4 | 32 |

Because the original ratio is 3 horses to 4 elephants, you can repeatedly add 3 to the ﬁrst row and repeatedly add 4 to the second row.

So,

Horses | 3 | 6 | 12 | 24 |

Elephants | 4 | 8 | 16 | 32 |

Part (c)

We have

Worms | 1 | 8 | ||

Mosquitoes | 200 | 600 | 1800 |

Because the original ratio is 1 worm to 200 mosquitoes, you can repeatedly multiply 3 to the ﬁrst row and repeatedly multiply 3 to the second row. In the last column we will subtract 1 from the first row and 200 from the second.

So,

Worms | 1 | 3 | 9 | 8 |

Mosquitoes | 200 | 600 | 1800 | 1600 |

Part (d)

We have

Plates | 3 | 2 | ||

Bowls | 2 | 4 |

Because the original ratio is 3 plates to 2 bowls, you can repeatedly multiply 2 to the ﬁrst and the second column and repeatedly divide by 3 to the third column. In the last column we will add 3 from the first and the second row.

So,

Plates | 3 | 6 | 2 | 5 |

Bowls | 2 | 4 | \( \frac{4}{3} \) | \( \frac{7}{3} \) |

**Example 2:** According to the nutrition label, 12 biscuits contain 75 milligrams of sodium. You consume a total of 18 crackers. How much sodium do you consume on a daily basis?

**Solution: **

We can solve the problem in two different ways:

- Use the incrementing double number number line to represent the sodium and biscuits.

Hence, 112.5 milligrams of sodium is consumed by you in eating 18 biscuits.

- Make use of a ratio table. The sodium content of 12 biscuits is 75 milligrams. With 18 biscuits, find an equivalent ratio.

Sodium (Milligrams) | 75 | 37.5 | 112.5 |

Biscuits | 12 | 6 | 18 |

Hence, 112.5 milligrams of sodium is consumed by you if you eat 18 biscuits.

**Example 3:** You and your teacher are going to make coloured icing. For three drops of pink food colouring, you add four drops of blue food colouring. For every two drops of pink, your teacher adds three drops of blue. Whose frosting has a bluish tint to it?

**Solution:**

The number of drops of food colouring that you and your teacher will use to make frosting is given to you. You must determine who has the more bluish frosting.

Use ratio tables to compare the frostings. Find ratios in which the total number of drops, the number of red drops, and the total number of blue drops is the same. Then you can compare the quantities to see which one is bluish.

Using repeated addition, make ratio tables for 4 : 3 and 3 : 2. Count the total number of drops in each frosting in a separate column.

My Frosting

Drops of Blue | Drops of Pink | Total Drops |
---|---|---|

4 | 3 | 7 |

8 | 6 | 14 |

12 | 9 | 21 |

16 | 12 | 28 |

20 | 15 | 35 |

Teacher’s Frosting

Drops of Blue | Drops of Pink | Total Drops |
---|---|---|

3 | 2 | 5 |

6 | 4 | 10 |

9 | 6 | 15 |

12 | 8 | 20 |

15 | 10 | 25 |

When both frosting will have 6 drops of pink, then the teacher frosting has 9 – 8 = 1 more drops of blue than your frosting.

Hence, teachers’ frosting will be more bluish than yours.

Frequently Asked Questions on Ratio Tables

The general form of expressing a ratio between two quantities, such as ‘a’ and ‘b,’ is a : b, which can be read as ‘a to b.’ This ratio is represented by the fraction \( \frac{a}{b} \).

By dividing two numbers, we can find the ratio used to compare them. If you were comparing one data point (A) to another data point (B), your formula would be \( \frac{A}{B} \). This means you’re dividing data A by data B. For example, if A is six and B is twelve, the ratio is six to twelve.