Guided Practice

Why can you write more than one ratio to describe this picture?

You can write both 2 : 3 and 4 : 6 to describe this picture, because the ratios 2 : 3 and 4 : 6 are equivalent ratios.

The ratios 3 : 2 and 6 : 4 are also equivalent ratios.

What ratios are equivalent to 5 : 10?

To determine an equivalent ratio, you can multiply or divide both values in the ratio by the same number.

The ratios 5 : 10 and 1 : 2 are equivalent ratios.

The ratios 5 : 10 and 10 : 20 are equivalent ratios.

Fill in the table, and then complete the sentence.

Circles | Squares |
---|---|

For every 1 circle, there are squares.

Fill in the table, and then complete the sentence.

Triangles | Squares |
---|---|

For every 2 triangles, there are squares.

Complete the sentences.

For every 2 rectangles, there are diamonds.

For every 4 rectangles, there are diamonds.

Complete the table for the picture of rectangles and diamonds.

Rectangles | Diamonds |
---|---|

3 | |

4 |

Complete the ratio table.

Triangles | Circles |
---|---|

4 | |

2 |

Complete the ratio table.

Triangles | Squares |
---|---|

1 | |

2 |

For every 2 dollars, there are 8 quarters. Complete the table to show ratios equivalent to 2 : 8.

Dollars | Quarters |
---|---|

1 | |

2 | |

10 |

For every 2 dollars, there are 20 dimes. Complete the table to show ratios equivalent to 2 : 20.

Dollars | Dimes |
---|---|

1 | |

3 | |

7.5 |

Suppose that every 1 hour you drive, you go 60 miles. Complete the table to show ratios equivalent to 60 : 1.

Miles | Hours |
---|---|

1 | |

2 | |

3 | |

4 |

Suppose that every 1 hour you drive, you go 68.5 miles. Complete the table.

Miles | Hours |
---|---|

1 | |

2 | |

3 | |

4 |

For every 28 days, there are 4 weeks. Complete the table to show ratios equivalent to 28 : 4.

Days | Weeks |
---|---|

7 | |

21 | |

4 | |

5 |

A double number line can be used to show a rate and a unit rate.

The top number line counts hamburgers, and the bottom number line counts dollars. The double number line shows that 5 hamburgers cost $15.

You can use the double number line to determine the cost per hamburger.

Write the speed of the car as a unit rate.

ft : s = ft per s

A car travels 220 feet in 2 seconds. Write the speed of the car as a unit rate.

ft : s = ft per s

A car travels 165 miles in 3 hours. Write the speed of the car as a unit rate.

mi : h = mi per h

In four hours a train goes 420 miles. Write the speed of the train as a unit rate.

mi : h = mi per h

A car travels 80 miles in 1 hour. Write the speed of the car as a unit rate.

mi : h = mi per h

A tortoise travels 2 miles in 6 hours. Write the speed of the tortoise as a unit rate.

mi : h = mi per h

Write a unit rate to show how much hamburger you get per dollar.

hamburger(s) per dollar

At Bob's Burger, 15 hamburgers cost $26.25. Write a unit rate to show the price per hamburger at Bob's Burger.

$ per hamburger

Tricia's car can travel 654 miles on a full tank of gas. A full tank in Tricia's car is 21.8 gallons.

Write a decimal unit rate to show the number of gallons Tricia's car uses per mile. Round to the nearest hundredth.

gallon per mile

When Mitsu was born, she was 18 inches long. After 12 years, she is now 5 feet tall.

Write a decimal unit rate to show the average number of inches Mitsu grew each year.

inches per year

When Joey was born, he was 9.5 pounds. On his 13th birthday, he was 100.5 pounds.

Write a unit rate to show the average amount Joey gained each year.

pounds per year

Suppose that in 2012 the population of Kansas was approximately 2,880,000. Kansas has an area of approximately 80,000 square miles.

Write a fractional unit rate to show the number of square miles there were for each person in Kansas in 2012.

square mile per person

Suppose that in 2017 the population of New Hampshire was approximately 1,343,000. New Hampshire has an area of approximately 9349 square miles.

Write a decimal unit rate to the nearest thousandth to show the number of square miles there were for each person in New Hampshire in 2017.

square mile per person

Use the double number line shown in the example. What is the cost per hamburger?

Each hamburger costs $.

Use the double number line shown in the example. What is the cost of 9 hamburgers?

Nine hamburgers cost $.

Determine the cost of 27 hamburgers.

Twenty-seven hamburgers cost $.

Use the double number line shown in the example. How many hamburgers can you get for $21?

You can get hamburgers for $21.

Explain how you can change any rate into

a unit rate.

Estimate the product.

3.02 × 1.98 ≈

Estimate the product.

6.89 × 0.51 ≈

Estimate the product.

10.48 × 2.13 ≈

Estimate the product.

12.91 × 0.48 ≈

Estimate the product.

4 × 3.11 ≈

Estimate the product.

22.06 × 0.99 ≈

Complete the ratio table.

4 | 12 | 20 | |||

5 | 10 | 20 | 50 |

Complete the ratio table. Use whole numbers and decimals.

5 | 6 | 11 | 55 | ||

3 | 6 | 9 |

Complete the ratio table. Use whole numbers and decimals.

1 | 5 | 10 | |||

8 | 32 | 4 | 1 |

Complete the ratio table. Use whole numbers and decimals.

3 | 7.5 | 9 | |||

2 | 5 | 1 | 6 |

Complete the ratio table. Use whole numbers and decimals.

16 | 24 | 40 | |||

1 | 0.5 | 3 | 4 |

Complete the ratio table. Use whole numbers and decimals.

1 | 2 | 2.5 | 3 | ||

15 | 45 | 90 |

Complete the ratio table. Use whole numbers and decimals.

1 | 9 | 10 | 16 | ||

5 | 8 | 12 |

Complete the ratio table. Use whole numbers and decimals.

0.1 | 1 | 7 | 8 | ||

4 | 6 | 7 |

Complete the ratio table. Use whole numbers and decimals.

0.6 | 2.4 | 3 | 15 | ||

0.5 | 1 | 10 |

Explain how you can use division to create an equivalent ratio.

Pick any ratio. Can you construct a tower that represents your ratio using 2, 3, 4, . . . any number of blocks? (Use the shelves to stack blocks more than 2 high.)

Can you build only symmetrical towers?

What is the smallest tower you can build to represent a certain ratio? What is the largest?

Take screenshots of your constructions, tell us about them, and share them with us: qanda@guzintamath.com.

Can you build only symmetrical towers?

What is the smallest tower you can build to represent a certain ratio? What is the largest?

Take screenshots of your constructions, tell us about them, and share them with us: qanda@guzintamath.com.

= 0.4 | = 1 |

= 2 | = 3 |

= 4 | = 10 |