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Common Core Math Grade 6 - Ratios & Proportional Relationships: Standards3 chapters | 15 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you'll find out how to solve ratio problems in three different ways. For example, you'll learn how to use a table, a tape diagram and a double number line while deciding which method for solving a ratio problem is right for you.

A **ratio problem** is a math problem that involves solving **ratios**, or how two values are related to each other. For example, a toy car model may have a ratio of 12:1 to its real-world counterpart. This means that 12 inches in the real-life version is equal to one inch in the toy version.

Real-life ratios can also be found in phone plans. For instance, if you pay 40 cents per minute to call someone, then you have a cents-to-minutes ratio of 40:1. Let's say that Sarah spends six minutes talking to her mom and 12 minutes talking to her brother. How much money do the calls cost Sarah if her cents-to-minutes ratio is 40:1? To solve this ratio problem, we can use a table, tape diagram and double number line.

To solve this ratio with a table, we'll need to create one using the information provided in the problem. The first column refers to the number of minutes used to make the call, while the second column totals the cost of the call. To calculate the cost of the call, we multiply the number of minutes by 40 cents. The problem tells us that Sarah spent six minutes on the phone with her mom and 12 minutes on the phone with her brother for a total of 18 minutes. According to our table, those 18 minutes on the phone cost Sarah 720 cents, or $7.20.

Minutes | Cents |
---|---|

1 | 40 |

2 | 80 |

3 | 120 |

4 | 160 |

5 | 200 |

6 | 240 |

7 | 280 |

8 | 320 |

9 | 360 |

10 | 400 |

11 | 440 |

12 | 480 |

13 | 520 |

14 | 560 |

15 | 600 |

16 | 640 |

17 | 680 |

18 | 720 |

Now, let's take a look at solving the same problem but with a tape diagram. The first row of blocks represents the six minutes Sarah spends on the phone with her mom, while the second row of blocks represents her 12-minute call to her brother.

If we add both rows of blocks, we end up with a total of 18 blocks. We know that each block represents 40 cents. So, multiplying the 18 blocks by 40 cents gives us 18 * 40 = 720 cents. So Sarah spends 720 cents, or $7.20, for 18 minutes of phone time.

Now, let's look at solving this problem by using a double number line. A **double number line** consists of two lines with matching tick marks and corresponding values. In our problem, each tick mark in the minutes line represents one minute of call time, while each tick mark on the cents line represents 40 cents.

To find our answer, we need to locate the 18th tick mark on the minute's line, or the total of Sarah's call time. Now, we need to locate its equivalent in the cents line. So, our answer then is the equivalent value of that tick mark on the cents line: Sarah's two phone calls for a total of 18 minutes will cost her 720 cents, or $7.20.

A **ratio problem** involves finding out how two values are related to each other. In this lesson, we learned three different ways to solve these kinds of problems. We can solve a ratio problem by using a **table**, where we write out each set of values that apply to our ratio. We can also solve a ratio problem using a **tape diagram**, where each block represents countable items. Finally, **double number lines** allow us to solve problems by finding the matching values on each line.

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Common Core Math Grade 6 - Ratios & Proportional Relationships: Standards3 chapters | 15 lessons

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