Guided Practice

Compare the ratios 2 : 3 and 4 : 5. Is 2 : 3 greater than, less than, or equal to 4 : 5?

You can compare ratios by first finding equivalent ratios.

10/15 is less than 12/15, so the ratio 2 : 3 is less than the ratio 4 : 5.

2 : 3 < 4 : 5

Suppose the tables show the number of words two people typed over a number of minutes. Which person typed faster? How do you know?

person a | |
---|---|

Words | Min. |

165 | 3 |

330 | 6 |

495 | 9 |

person b | |
---|---|

Words | Min. |

160 | 4 |

200 | 5 |

240 | 6 |

Person A typed faster, because 330 : 6 > 240 : 6.

In 6 minutes, Person A typed 330 words. But Person B typed only 240 words in 6 minutes.
Use >, <, or = to compare the ratios of squares to triangles.

1 : 1 3 : 1

Use >, <, or = to compare the ratios of circles to rectangles.

2 : 3 4 : 6

Use >, <, or = to compare the ratios of triangles to circles.

1 : 3 1 : 4

Use >, <, or = to compare the ratios of squares to triangles.

1 : 2 3 : 5

Complete the sentences about each person's typing speed.

Person A typed words every minute.

Person B typed words every minute.

Which person typed faster?

person x | |
---|---|

Words | Min. |

25 | 1 |

50 | 2 |

100 | 4 |

person y | |
---|---|

Words | Min. |

36 | 3 |

144 | 12 |

180 | 15 |

Person typed faster.

Person X typed words every minute.

Person Y typed words every minute.

Which person typed faster?

person x | |
---|---|

Words | Min. |

30 | 2 |

45 | 3 |

60 | 4 |

person y | |
---|---|

Words | Min. |

36 | 3 |

144 | 12 |

180 | 15 |

Person typed faster.

Person X typed words every minute.

Person Y typed words every minute.

Which toy costs less?

toy a | |
---|---|

$ | Number |

20 | 5 |

28 | 7 |

toy b | |
---|---|

$ | Number |

14 | 7 |

20 | 10 |

Toy costs less.

Toy A costs $.

Toy B costs $.

Which recipe is sweeter?

recipe a | |
---|---|

Batches | Sugar |

3 | 3 c |

6 | 6 c |

9 | 9 c |

recipe b | |
---|---|

Batches | Sugar |

4 | 8 c |

5 | 10 c |

6 | 12 c |

Recipe is sweeter.

Recipe A uses cup(s) of sugar for every batch.

Recipe B uses cup(s) of sugar for every batch.

Which recipe is sweeter?

recipe a | |
---|---|

Batches | Sugar |

3 | 9 c |

1 | 3 c |

0 | 0 c |

recipe b | |
---|---|

Batches | Sugar |

5 | 10 c |

6 | 12 c |

7 | 14 c |

Recipe is sweeter.

Recipe A uses cup(s) of sugar for every batch.

Recipe B uses cup(s) of sugar for every batch.

Increase or decrease the numerator or denominator of the ratio to make the statement true.

3 : < 3 : 4

For a hot cocoa mix, the directions say to use 3 spoons of cocoa for every 4 ounces of hot water. Change the denominator of the ratio of cocoa to water so that the cocoa is less chocolatey than this.

The ratio 3 spoons of cocoa to ounces of water would be less chocolatey.

For a hot cocoa mix, the directions say to use 6 spoons of cocoa for every 8 ounces of hot water. Change the denominator of the ratio of cocoa to water so that the cocoa is more chocolatey than this.

The ratio 6 spoons of cocoa to ounces of water would be more chocolatey.

Increase or decrease the numerator or denominator of the ratio to make the statement true.

1 : > 1 : 6

One brand of green paint uses 1 part blue paint to 6 parts yellow paint. Change the denominator of the ratio of blue to yellow so that the paint is more blue than this.

The ratio 1 blue to yellow is more blue than 1 blue to 6 yellow.

One brand of green paint uses 5 parts blue paint to 6 parts yellow paint. Change the denominator of the ratio of blue to yellow so that the paint is less blue than this.

The ratio 5 blue to yellow is more blue than 5 blue to 6 yellow.

Increase or decrease the numerator or denominator of the ratio to make the statement true.

8 : 3 > : 3

At Mark's grocery store, $8 is what 3 boxes of crackers cost. Change the numerator of the ratio of boxes to dollars to make the crackers cheaper.

The crackers would be cheaper if you could spend $ for 3 boxes instead of $8 for 3 boxes.

Increase or decrease the numerator or denominator of the ratio to make the statement true.

: 7 > 5 : 7

For every 5 laps that Kirk runs around the track, Bridget runs 7 laps. Change the numerator of the ratio of Kirk's laps to Bridget's laps so that Kirk runs faster than he does now.

If Kirk ran laps for every 7 of Bridget's laps, he would be faster than he is now.

For every 5 laps that Kirk runs around the track, Bridget runs 7 laps. Change the numerator of the ratio of Kirk's laps to Bridget's laps so that Kirk runs slower than he does now.

If Kirk ran laps for every 7 of Bridget's laps, he would be slower than he is now.

Enter a numerator or denominator of the ratio to make each statement true.

10 : < 10 : 12

10 : 12 > : 12

10 : 12 < 10 :

10 : 12 < : 12

Enter a numerator or denominator of the ratio to make each statement true.

3 : < 3 : 3

3 : 3 > : 3

3 : 3 < 3 :

3 : 3 < : 3

Enter a numerator or denominator of the ratio to make each statement true.

25 : < 25 : 2

25 : 2 > : 2

25 : 2 < 25 :

25 : 2 < : 2

Enter a numerator or denominator of the ratio to make each statement true.

1 : < 1 : 100

1 : 100 > : 100

1 : 100 < 1 :

1 : 100 < : 100

Enter a numerator or denominator of the ratio to make each statement true.

6.5 : < 6.5 : 9.5

6.5 : 9.5 > : 9.5

6.5 : 9.5 < 6.5 :

6.5 : 9.5 < : 9.5

To subtract decimals, line up the decimals on the decimal points and subtract the digits in each place from right to left.

We don't have enough hundredths in 94.94 to subtract. So, we take away 1 tenth and make it 10 hundredths.

This gives us 8 tenths and 14 hundredths. What is the final difference?

To multiply decimals, multiply like you would with whole numbers.

The number of decimal places in the product is the total number of decimal places in the factors.

What is the product?

Estimate the sum of 73.66 and 58.85.

Then, determine the exact sum.

Estimate: ---------

73.66 + 58.85 =

Estimate the sum of 25.05 and 34.93.

Then, determine the exact sum.

Estimate: ---------

25.05 + 34.93 =

Estimate the sum of 103.94 and 82.20.

Then, determine the exact sum.

Estimate: -----------

82.20 + 103.94 =

Estimate the sum of 851.5 and 10.19.

Then, determine the exact sum.

Estimate: -------

851.5 + 10.19 =

Estimate the sum of 17.07 and 558.2.

Then, determine the exact sum.

Estimate: --------

558.2 + 17.07 =

Determine the difference.

94.94 – 52.89 =

Determine the difference.

41.95 – 18.82 =

Determine the difference.

84.33 – 29.25 =

Determine the difference.

39.01 – 20.54 =

Determine the difference.

140.08 – 66.59 =

Estimate the difference. Then, determine the exact difference.

Estimate: ---------

90.01 – 56.78 =

Estimate the difference. Then, determine the exact difference.

Estimate: ---------

26.05 – 19.56 =

Estimate the difference. Then, determine the exact difference.

Estimate: --------

60.06 – 44.5 =

Estimate the difference. Then, determine the exact difference.

Estimate: -------

10.99 – 9.03 =

Determine the product.

75.27 × 4.5 =

Determine the product.

64.32 × 20.5 =

Determine the product.

27.53 × 64.08 =

In March, Bob's music store sold 14 guitars and 20 marimbas. In July, they sold 10 guitars and 11 marimbas. During which month did the guitar store sell a greater ratio of guitars to marimbas?

To solve this problem, you can compare ratios.

The ratio 14 : 20 is equal to 0.7, and the ratio 10 : 11 is equal to 0.9090. So, 10 : 11 is greater than 14 : 20.

In July, the store sold a greater ratio of guitars to marimbas.

Soup Station's stew uses 3 pounds of carrots and 6 pounds of potatoes. Souper Soup's stew uses 3 pounds of carrots and 4 pounds of potatoes. Which stew uses a lesser ratio of potatoes to carrots?

's stew uses a lesser ratio of potatoes to carrots.

Soup Station's stew uses 6 pounds of carrots and 3 pounds of potatoes. Souper Soup's stew uses 4 pounds of carrots and 3 pounds of potatoes. Which stew uses a lesser ratio of potatoes to carrots?

's stew uses a lesser ratio of potatoes to carrots.

For a pizza, Josh mixes 2 pounds of Parmesan cheese with 9 pounds of mozzarella. Mike's pizza uses 3 pounds of Parmesan cheese and 20 pounds of mozzarella. Which pizza uses a lesser ratio of Parmesan to mozzarella?

Complete an inequality to represent the problem.

: < :

Fred's school orchestra has 18 violin players and 16 flute players. Vicki's school orchestra has 8 violin players and 6 flute players. Which school orchestra has a greater ratio of violin to flute players?

's orchestra has a greater ratio of violin to flute players.

Fred's school orchestra has 18 violin players and 16 flute players. Vicki's school orchestra has 8 violin players and 6 flute players. Which school orchestra has a greater ratio of flute to violin players?

's orchestra has a greater ratio of flute to violin players.

Complete an inequality to compare the ratios 15/9 and 18/12.

: > :

Complete an inequality to compare the ratios

16 : 20 and 9 : 15.

: < :

Complete an inequality to compare the ratios

5 to 15 and 7 to 10.

: < :

Complete an inequality to compare the ratios

10 : 12 and 19 : 20.

: > :

Complete an inequality to compare the ratios 12/18 and 15/20.

: > :

Complete an inequality to compare the ratios

4 : 2 and 5 : 4.

: < :

A worker at Breads restaurant used 5 loaves of wheat bread and 2 loaves of rye bread to make sandwiches for an event. A worker at Sammich Shop used 7 loaves of wheat bread and 2 loaves of rye bread. Which restaurant used the lesser ratio of rye to wheat bread?

The worker at used a lesser ratio of rye to wheat bread.

Complete an inequality to compare the ratios

40 to 50 and 9 to 10.

: > :

Complete an inequality to compare the ratios

4 : 48 and 6 : 25.

: > :

Complete an inequality to compare the ratios

8/6 and 2/1.

: < :

For every 5 tiles Martin painted blue, he painted 8 red. For every 25 tiles Sara painted blue, she painted 44 red. Which student has the greater ratio of blue to red tiles?

has a greater ratio of blue to red tiles.

Complete an inequality to compare the ratios

1/4 and 16/28.

: < :

Complete an inequality to compare the ratios

5 to 2 and 21 to 13.

: > :

Complete an inequality to compare the ratios

19 : 23 and 36 : 50.

: < :

Complete an inequality to compare the ratios

18 : 5 and 36 : 4.

: < :

Complete an inequality to compare the ratios

16 to 3 and 33 to 7.

: > :

Complete an inequality to compare the ratios 39/40 and 49/50.

: > :

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60

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