TEKS 6.4D Worksheets — Grade 6 Give examples of ratios as multiplicative comparisons

Carlos wants to buy a new skateboard that costs $120. He has saved $45 so far. What fraction of the total cost of the skateboard has Carlos saved?

1. 3/8 ✓
2. 1/3
3. 3/5
4. 2/5

Why: To find the fraction of the total cost that Carlos has saved, divide the amount he has saved by the total cost. Carlos has saved $45 and the skateboard costs $120. So, the fraction is 45/120. Simplifying this fraction, both 45 and 120 can be divided by 15, giving us 3/8. Therefore, Carlos has saved 3/8 of the total cost.

Emma is planning a school field trip to Big Bend National Park. The bus can hold 60 students. If 24 students have signed up so far, what is the ratio of students signed up to the total bus capacity? Which of the following ratios best represents this situation?

1. 2/5 ✓
2. 3/5
3. 4/5
4. 1/2

Why: To find the ratio of students signed up to the total bus capacity, we first identify the number of students signed up (24) and the total capacity of the bus (60). The ratio can be expressed as 24/60. Simplifying this fraction, we divide both the numerator and the denominator by 12, which gives us 2/5. Thus, the correct answer is 2/5.

Tomas and his family are visiting the Edwards Plateau in Texas for a hiking trip. They want to bring enough snacks for the hike. If they pack 3 bags of trail mix and each bag contains 2/5 of a pound of trail mix, how many pounds of trail mix did they pack in total?

1. 3/5
2. 1 1/5 ✓
3. 1/2
4. 2/5

Why: To find the total weight of trail mix, multiply the number of bags by the weight per bag. Tomas has 3 bags, each with 2/5 of a pound of trail mix. So, the calculation is 3 * (2/5) = 6/5 or 1 1/5 pounds. Therefore, the best answer is 1 1/5.

Adriana is helping her family on their ranch near Amarillo, Texas. They have 160 acres of grazing land for their cattle. For every 4 acres, they can sustain 3 cows. How many cows can Adriana's family sustain on their total grazing land?

1. 120 ✓
2. 160
3. 80
4. 60

Why: To find out how many cows can be sustained, first determine the number of groups of 4 acres in 160 acres. Divide 160 by 4, which gives you 40 groups. Since each group of 4 acres can sustain 3 cows, multiply 40 by 3. Therefore, 40 × 3 = 120. Thus, Adriana's family can sustain 120 cows on their land.

Olivia is making a batch of enchiladas for her family's picnic in Fort Worth. The recipe calls for a ratio of 2 cups of cheese for every 3 cups of beans. If she wants to use 9 cups of beans, how many cups of cheese does she need to maintain the same ratio?

1. 6 ✓
2. 4
3. 3
4. 5

Why: To find the amount of cheese needed, set up the ratio based on the recipe: 2 cups of cheese / 3 cups of beans. If Olivia uses 9 cups of beans, calculate the cheese using the proportional relationship. The equation is 2/3 = x/9. Cross-multiplying gives 3x = 18. Thus, x = 18 / 3, which means x = 6. Therefore, Olivia needs 6 cups of cheese.

Karim is making a batch of Tex-Mex salsa for a family gathering. The recipe requires 2 1/2 cups of tomatoes for every 1 1/4 cups of onions. If he wants to use 10 cups of tomatoes, how many cups of onions will he need?

1. 5 ✓
2. 4
3. 3
4. 2

Why: To find out how many cups of onions Karim needs, first establish the ratio of tomatoes to onions from the recipe: 2 1/2 cups of tomatoes to 1 1/4 cups of onions. This can be expressed as the fraction 2.5 / 1.25, which simplifies to 2.5 ÷ 1.25 = 2. The ratio of tomatoes to onions is 2:1. If Karim uses 10 cups of tomatoes, we can set up a proportion: 10 / x = 2 / 1. Cross-multiplying gives us 2x = 10, so x = 10 / 2, which simplifies to 5. Therefore, Karim needs 5 cups of onions.

Onyx and her family went to a food festival in Austin, Texas, where they enjoyed both tacos and tamales. The ratio of tacos to tamales they bought is 3:2. If they purchased a total of 50 items, how many tacos did they buy?

1. 30 ✓
2. 20
3. 25
4. 15

Why: To find out how many tacos Onyx bought, we first need to understand the ratio of tacos to tamales, which is 3:2. This means for every 5 items (3 tacos + 2 tamales), 3 are tacos. To find out how many groups of 5 fit into the total of 50 items, we divide 50 by 5, which equals 10 groups. Since there are 3 tacos in each group, we multiply 10 groups by 3 tacos per group: 10 * 3 = 30 tacos. Therefore, Onyx bought 30 tacos.

During a field trip to the Palo Duro Canyon, Nia noticed that the height of the canyon walls was represented by a ratio. If the height of the south wall is 120 feet and the height of the north wall is 80 feet, which of the following ratios represents the height of the south wall compared to the height of the north wall?

1. 3/2 ✓
2. 2/3
3. 4/3
4. 3/4

Why: To find the ratio of the height of the south wall to the height of the north wall, we set up the ratio as 120/80. This simplifies to 3/2 since both numbers can be divided by 40. Therefore, the correct answer is 3/2, which shows that the south wall is 1.5 times the height of the north wall.