Middle School Math Quiz: Create And Use Equivalent Ratio Tables
20 questions · exam conditions
0:00
Create And Use Equivalent Ratio TablesQuestion 1 of 20

A recipe uses a ratio of 22 cups of flour for every 55 cups of milk. Complete the equivalent ratio table. What is the missing value ?? in the last row?

Flour (cups): 2, 4, 6, ?2,\ 4,\ 6,\ ?
Milk (cups): 5, 10, 15, 205,\ 10,\ 15,\ 20

?=12?=12
?=10?=10
?=7?=7
?=8?=8
← Back to quizzes

Middle School Math Quiz

Middle School Math Quiz: Create And Use Equivalent Ratio Tables

Practice Create And Use Equivalent Ratio Tables in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Create And Use Equivalent Ratio Tables, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A recipe uses a ratio of 22 cups of flour for every 55 cups of milk. Complete the equivalent ratio table. What is the missing value ?? in the last row?

Flour (cups): 2, 4, 6, ?2,\ 4,\ 6,\ ?
Milk (cups): 5, 10, 15, 205,\ 10,\ 15,\ 20

  1. ?=12?=12
  2. ?=10?=10
  3. ?=7?=7
  4. ?=8?=8 (correct answer)
Explanation: This problem is all about equivalent ratios, which are ratios that keep the same relationship even when the numbers grow. The recipe uses 22 cups of flour for every 55 cups of milk. Look at how the milk grows down the table: 5, 10, 15, 205,\ 10,\ 15,\ 20. Each step adds another batch of the recipe. By the last row, the milk is 2020 cups, which is 44 batches because 5×4=205 \times 4 = 20. So the flour must also be 44 batches: 2×4=82 \times 4 = 8. That makes the missing value ?=8? = 8. Think of it like making lemonade. If one pitcher needs 22 scoops of mix and 55 cups of water, then 44 pitchers need 44 times as much of each ingredient. Both grow together! Try this at home: Pick a snack recipe and double or triple every ingredient. Check that each one multiplies by the same number.

Question 2

Two snack mixes compare nuts to raisins.

Mix A ratio (nuts:raisins) is 2:32:3.
Mix B ratio (nuts:raisins) is 3:53:5.

Using equivalent ratio tables or unit rates, which mix has the greater number of nuts per 1 raisin?

  1. They are equal
  2. Not enough information
  3. Mix B
  4. Mix A (correct answer)
Explanation: This question tests comparing ratios using equivalent ratio tables or unit rates to determine which mix has more nuts per raisin. Equivalent ratios are formed by multiplying both parts by the same number, but here we compare unit rates: for Mix A 2:3, nuts per raisin is 2/3 ≈0.67, for Mix B 3:5 is 3/5=0.6. Tables can organize scaled versions, like for A: nuts 2,4,6 and raisins 3,6,9; for B: 3,6,9 and 5,10,15, to see rates. To compare, calculate unit rates (nuts/raisins) and see A's 0.67 > B's 0.6, so A has more nuts per raisin. The correct answer is Mix A, as it has the greater unit rate. Common errors include comparing totals without rates, like just looking at numerators, or inverting the ratios. For comparison, find unit rates by dividing; if scaling to same denominator (e.g., A to 10 raisins: nuts ≈6.67, B to 10: nuts=6), A is greater, with mistakes from not using a common basis or arithmetic errors.

Question 3

Two different juice mixtures are being compared. Mixture A uses 6 cups of apple juice to 4 cups of cranberry juice. Mixture B uses 9 cups of apple juice to 5 cups of cranberry juice. To determine which mixture has a stronger apple flavor, Sarah needs to compare the ratios. What can she conclude?

  1. Mixture A has a stronger apple flavor because 6:4 reduces to 3:2, while 9:5 cannot be reduced further
  2. Mixture A has a stronger apple flavor because it uses fewer total cups, making the apple concentration higher
  3. Both mixtures have equally strong apple flavor because they both use more apple juice than cranberry juice
  4. Mixture B has a stronger apple flavor because 9:5 equals 1.8:1, while 6:4 equals 1.5:1 in apple-to-cranberry ratio (correct answer)
Explanation: When comparing ratios to determine which mixture has a stronger flavor, you need to find out how much of one ingredient there is for every unit of the other. The key is converting each ratio to see which has more apple juice per cup of cranberry juice. For Mixture A (6 cups apple to 4 cups cranberry), divide both numbers by 4: 6÷4=1.56 ÷ 4 = 1.5 and 4÷4=14 ÷ 4 = 1. This gives you 1.5:1, meaning 1.5 cups of apple juice for every 1 cup of cranberry juice. For Mixture B (9 cups apple to 5 cups cranberry), divide both by 5: 9÷5=1.89 ÷ 5 = 1.8 and 5÷5=15 ÷ 5 = 1. This gives you 1.8:1, meaning 1.8 cups of apple juice for every 1 cup of cranberry juice. Since 1.8 > 1.5, Mixture B has more apple juice per cup of cranberry juice, making it stronger in apple flavor. Answer D correctly identifies this reasoning. Answer A incorrectly focuses on whether ratios can be simplified rather than comparing their actual values. Answer B makes the mistake of thinking fewer total cups means stronger concentration—but concentration depends on the ratio, not the total amount. Answer C incorrectly assumes that any mixture with more apple than cranberry has equal apple strength, ignoring the specific proportions. Remember: when comparing ratios, convert them to the same format (like "something to 1") so you can easily see which is larger. This makes ratio comparisons much clearer.

Question 4

A school is planning field trips using the ratio of 2 teachers to 15 students. The principal creates an equivalent ratio table but accidentally leaves some values blank. If one row shows 8 teachers, and another row shows 75 students, what is the sum of the missing values in these two rows?

  1. The sum of missing values is 70 because 60 students and 10 teachers are needed (correct answer)
  2. The sum of missing values is 68 because 60 students and 8 teachers are needed
  3. The sum of missing values is 70 because 50 students and 20 teachers are needed
  4. The sum of missing values is 75 because 65 students and 10 teachers are needed
Explanation: Using ratio 2:15 (teachers:students). For 8 teachers: 8÷2=4, so 4×15=60 students needed. For 75 students: 75÷15=5, so 5×2=10 teachers needed. Missing values: 60 students + 10 teachers = 70 total. Choice B miscalculates the teachers needed for 75 students. Choice C uses wrong student calculation. Choice D uses incorrect calculations for both scenarios.

Question 5

A recipe calls for ingredients in the ratio of 5 parts vegetables to 3 parts meat. If a chef wants to prepare meals with 25, 40, and 45 parts vegetables, and the missing values in the equivalent ratio table are represented by xx, yy, and zz respectively, what is the value of x+y+zx + y + z?

  1. x+y+z=63x + y + z = 63 parts of meat total
  2. x+y+z=66x + y + z = 66 parts of meat total (correct answer)
  3. x+y+z=69x + y + z = 69 parts of meat total
  4. x+y+z=72x + y + z = 72 parts of meat total
Explanation: Using ratio 5:3 (vegetables:meat), find meat portions: For 25 vegetables: 25÷5=5, so 5×3=15 meat (x=15). For 40 vegetables: 40÷5=8, so 8×3=24 meat (y=24). For 45 vegetables: 45÷5=9, so 9×3=27 meat (z=27). Therefore x+y+z = 15+24+27 = 66. Choice A uses incorrect calculations. Choice C adds an extra 3 to the total. Choice D miscalculates one or more ratios.

Question 6

Two buses travel at constant rates.

Bus A travels 99 miles in 33 hours. Bus B travels 1212 miles in 55 hours.

Using ratio tables (miles per hour), which bus has the greater speed?

  1. Cannot be determined
  2. Bus B
  3. They have the same speed
  4. Bus A (correct answer)
Explanation: This question tests comparing ratios using tables or unit rates to find which bus has greater speed in miles per hour. Equivalent ratios are formed by multiplying, but here we find unit rates: Bus A 9:3 =3 mph, Bus B 12:5=2.4 mph. Tables can scale to compare, like A: miles 9,18,27 and hours 3,6,9 (3 mph); B: 12,24,36 and 5,10,15 (2.4 mph). To compare, calculate rates (miles/hours), showing A's 3 > B's 2.4. The bus with greater speed is Bus A. Common errors include comparing totals without dividing, like thinking more miles means faster without time. For comparison, compute unit rates; scaling to same hours (e.g., A in 5 hours: 15 miles, B 12 miles) shows A faster, with mistakes from not using rates or arithmetic errors.

Question 7

Are the ratios 6:86:8 and 9:129:12 equivalent?

  1. No, because 6+8≠9+126+8 \ne 9+12.
  2. No, because 6×12≠8×96 \times 12 \ne 8 \times 9.
  3. Yes, because 6:86:8 is larger than 9:129:12.
  4. Yes, because both simplify to 3:43:4. (correct answer)
Explanation: This question tests determining if ratios are equivalent by simplifying or cross-multiplying, which helps compare without tables. Equivalent ratios simplify to the same value; 6:8 simplifies to 3:4 (divide by 2), and 9:12 to 3:4 (divide by 3), or cross-products 6×12=72 and 8×9=72 are equal. A table for 3:4 would include 6:8, 9:12, confirming equivalence. Yes, they are equivalent because both simplify to 3:4. Errors include using addition (choice B) or misapplying cross-multiplication (choice C, though products are equal). To check: simplify both or compare cross-products. Avoid comparing sizes directly without simplifying, as in choice D.

Question 8

Two smoothie recipes are compared.

Recipe A: 55 strawberries for every 22 cups of yogurt
Recipe B: 66 strawberries for every 33 cups of yogurt

Using equivalent ratios or unit rates, which recipe uses more strawberries per 1 cup of yogurt?

  1. They use the same amount
  2. Recipe A (correct answer)
  3. Recipe B
  4. Cannot be compared without a graph
Explanation: This question tests creating equivalent ratio tables by scaling both quantities by the same factor, finding missing values, plotting on coordinate planes through the origin, and comparing ratios. Equivalent ratios are formed by multiplying both parts of the ratio by the same number to preserve the relationship, such as 3:4 scaled by ×2 gives 6:8, by ×3 gives 9:12, all equal to the ratio 3/4; a table organizes these scaled versions, like for ratio 2:3 with batches 1,2,3,4 and cups 2,4,6,8 where each row is equivalent to 2:3; finding missing values involves identifying the scale, like if 3:4=9:?, the scale from 3 to 9 is ×3, so 4×3=12; plotting pairs like (1,2), (2,4), (3,6) on a plane forms a line through the origin indicating proportionality; comparing ratios uses unit rates, like 2:3 is 2/3≈0.67 and 3:5 is 0.6, so the first is greater. For example, with ratio 3:4, a table could be 3,6,9,12 | 4,8,12,16 (×1,×2,×3,×4), missing: if 3:4=?:12, find 3×3=9; plot (3,4), (6,8), (9,12) line through (0,0). The correct answer is choice A: Recipe A uses more strawberries per yogurt, with unit rate 5/2=2.5 vs B's 6/3=2. Common errors include thinking they are equal since both simplify to similar but actually different rates, or comparing without units. To compare, calculate unit rates: strawberries per yogurt 5/2 > 6/3. Mistakes involve comparison without common basis, like totaling instead of per unit, or suggesting a graph is needed when rates suffice.

Question 9

A video game gives coins and gems in a ratio of 3:43:4 (coins:gems). If a player earns 2020 gems, how many coins did they earn at the same rate?

  1. 24
  2. 12
  3. 15 (correct answer)
  4. 18
Explanation: This question tests using equivalent ratios to find a missing value, like coins for 20 gems in ratio 3:4, by scaling to match the given amount. Equivalent ratios are formed by multiplying both by the same number, like finding the factor for gems 4 to 20 (×5), then coins 3×5=15. A table can organize this: coins 3,6,9,12,15 and gems 4,8,12,16,20, showing the fifth row matches. For example, if 3:4 = ?:20, scale by ×5 to get 15:20. The correct number is 15 coins. Common errors include inverting the ratio or using addition, like adding 3 repeatedly. To solve, identify the scale factor from gems (4 to 20 is ×5), apply to coins; mistakes often involve wrong factors or not preserving the ratio.

Question 10

A science club mixes vinegar and baking soda in a ratio of 3:23:2. They made a table of equivalent ratios and want to plot the ordered pairs (vinegar, baking soda)(\text{vinegar},\ \text{baking soda}) on a coordinate plane.

Which set of points is correct for 1–4 batches?

  1. (2,3), (4,6), (6,9), (8,12)(2,3),\ (4,6),\ (6,9),\ (8,12)
  2. (3,2), (6,5), (9,8), (12,11)(3,2),\ (6,5),\ (9,8),\ (12,11)
  3. (3,2), (5,4), (7,6), (9,8)(3,2),\ (5,4),\ (7,6),\ (9,8)
  4. (3,2), (6,4), (9,6), (12,8)(3,2),\ (6,4),\ (9,6),\ (12,8) (correct answer)
Explanation: This question tests using equivalent ratio tables by scaling to generate ordered pairs for plotting on a coordinate plane, ensuring the points form a line through the origin for proportional relationships. Equivalent ratios are formed by multiplying both parts of the original ratio 3:2 (vinegar to baking soda) by the same number, like ×2 giving 6:4, ×3 giving 9:6, all preserving the ratio of 3/2. A table organizes these scaled versions, for example, vinegar 3,6,9,12 and baking soda 2,4,6,8, where each row is equivalent. For plotting, use pairs like (3,2), (6,4), (9,6), (12,8), which lie on a line through the origin since they are proportional. The correct set of points is option A, representing 1 to 4 batches accurately. Common errors include points that don't scale both by the same factor, like in option B with inconsistent increases, or option D with additive patterns. To plot, list the scaled pairs as coordinates and connect them; the line should pass through (0,0) for proportionality, with mistakes often from not verifying the scale factor or plotting non-equivalent ratios.

Question 11

A trail map uses a scale where 33 cm on the map represents 44 km in real life. If a trail measures 1515 cm on the map, how many kilometers is the trail in real life?

  1. 12 km
  2. 16 km
  3. 18 km
  4. 20 km (correct answer)
Explanation: This question tests finding missing values using equivalent ratios from a scale, by identifying and applying the scale factor. Equivalent ratios preserve the proportion; for 3 cm:4 km, scaling by ×2 gives 6:8, by ×3 gives 9:12, all with unit rate 4/3 km per cm. For 15 cm, the factor is 15÷3=5, so km=4×5=20. The correct distance is 20 km, matching the proportion. Common mistakes include wrong operations, like adding instead of multiplying, leading to 12 or 18. Solve by: (1) find factor (15÷3=5), (2) apply to km (4×5=20). Confirm by checking ratios: 15:20 simplifies to 3:4.

Question 12

A science club mixes salt and water in a ratio of 33 teaspoons of salt to 44 cups of water. Which ordered pairs (x,y)(x,y) should be plotted to represent this proportional relationship if xx is cups of water and yy is teaspoons of salt?

  1. (4,3),(8,6),(12,9),(16,12)(4,3), (8,6), (12,9), (16,12) (correct answer)
  2. (3,4),(6,8),(9,12),(12,16)(3,4), (6,8), (9,12), (12,16)
  3. (4,3),(8,5),(12,7),(16,9)(4,3), (8,5), (12,7), (16,9)
  4. (0,3),(4,6),(8,9),(12,12)(0,3), (4,6), (8,9), (12,12)
Explanation: This question tests plotting ordered pairs from equivalent ratios on a coordinate plane, where the points should form a straight line through the origin representing the proportional relationship. Equivalent ratios are formed by scaling both quantities; for salt to water 3:4, pairs are (water, salt) like (4,3), (8,6), (12,9), since x is water and y is salt, all with slope 3/4. Plotting these shows points (4,3), (8,6), (12,9), (16,12), lying on a line through (0,0). The correct set is (4,3), (8,6), (12,9), (16,12), as it matches the ratio with proper variable assignment. Common errors include swapping x and y, as in choice B, or non-proportional scaling like in C and D, where points don't align. To plot: generate pairs by scaling (e.g., ×1: (4,3), ×2: (8,6)), plot on the plane, and ensure the line passes through origin. Compare by calculating the constant ratio y/x = 3/4 for each point to verify proportionality.

Question 13

Examine the ratio table showing the relationship between time spent studying and practice problems completed. If this pattern continues, which row contains an error in the equivalent ratios?

  1. Row showing 4 hours and 28 problems contains the error in equivalent ratios
  2. Row showing 6 hours and 42 problems contains the error in equivalent ratios
  3. Row showing 8 hours and 54 problems contains the error in equivalent ratios (correct answer)
  4. Row showing 10 hours and 70 problems contains the error in equivalent ratios
Explanation: From the first row (2 hours, 14 problems), the ratio is 2:14 = 1:7. Each hour corresponds to 7 problems. Check: 4 hours = 4×7 = 28 problems ✓. 6 hours = 6×7 = 42 problems ✓. 8 hours = 8×7 = 56 problems, not 54 ✗. 10 hours = 10×7 = 70 problems ✓. Choice A, B, and D all show correct equivalent ratios following the 1:7 pattern.

Question 14

Using the table shown, which statement correctly compares the ratios of red marbles to blue marbles across different containers?

  1. Container A has the highest ratio, and Container C has the lowest ratio of red to blue marbles
  2. Container B has the highest ratio, and Container A has the lowest ratio of red to blue marbles
  3. Container C has the highest ratio, and Container A has the lowest ratio of red to blue marbles (correct answer)
  4. Container A has the highest ratio, and Container B has the lowest ratio of red to blue marbles
Explanation: Calculate each ratio: Container A: 6:9 = 2:3 ≈ 0.67, Container B: 8:10 = 4:5 = 0.8, Container C: 12:8 = 3:2 = 1.5. Container C has the highest ratio (1.5) and Container A has the lowest (0.67). Choice A reverses the comparison. Choice B incorrectly identifies Container B as highest. Choice D incorrectly identifies Container B as lowest.

Question 15

Two students are comparing reading rates using ratios.

  • Student A reads 22 pages in 33 minutes.
  • Student B reads 33 pages in 55 minutes.

Using equivalent ratio tables or unit rates, which student reads at a greater rate (pages per minute)?

  1. Student A (correct answer)
  2. They read at the same rate.
  3. Not enough information to compare.
  4. Student B
Explanation: This question tests comparing ratios using unit rates or equivalent tables to determine which has a greater rate, such as pages per minute. Equivalent ratios maintain the relationship by scaling; for Student A (2:3 pages to minutes), unit rate is 2/3 ≈0.67 ppm, and for B (3:5), it's 3/5=0.6 ppm. Tables would show A's rates like 2:3, 4:6, 6:9, and B's 3:5, 6:10, 9:15; comparing unit rates shows 2/3 > 3/5. Thus, Student A reads at a greater rate. Mistakes include comparing totals without rates or inverting ratios, leading to wrong conclusions like them being equal. To compare: calculate unit rates (pages ÷ minutes), then compare numerically (0.67 > 0.6). Avoid errors by ensuring a common basis, like per minute, rather than total pages.

Question 16

Based on the coordinate plane shown, which equivalent ratio table correctly represents the plotted points?

  1. A table with x-values 2, 4, 6, 8 and corresponding y-values 3, 6, 9, 12
  2. A table with x-values 1, 2, 3, 4 and corresponding y-values 2, 4, 6, 8
  3. A table with x-values 3, 6, 9, 12 and corresponding y-values 2, 4, 6, 8 (correct answer)
  4. A table with x-values 2, 4, 6, 8 and corresponding y-values 1, 2, 3, 4
Explanation: Reading the plotted points from the coordinate plane: (3,2), (6,4), (9,6), (12,8). This creates the ratio 3:2 and its equivalent ratios. The x-values are 3, 6, 9, 12 and y-values are 2, 4, 6, 8. Choice A reverses x and y values. Choice B uses a 1:2 ratio instead of 3:2. Choice D also reverses the coordinates.

Question 17

A bakery uses a ratio of 3 cups of flour to 2 cups of sugar in their cookie recipe. If they want to make batches that use 18, 24, and 30 cups of flour, what is the total amount of sugar needed for all three batches combined?

  1. 36 cups of sugar
  2. 48 cups of sugar (correct answer)
  3. 54 cups of sugar
  4. 72 cups of sugar
Explanation: First, find the sugar needed for each batch using the ratio 3:2 (flour:sugar). For 18 cups flour: 18÷3=6, so 6×2=12 cups sugar. For 24 cups flour: 24÷3=8, so 8×2=16 cups sugar. For 30 cups flour: 30÷3=10, so 10×2=20 cups sugar. Total sugar = 12+16+20 = 48 cups. Choice A incorrectly uses 2:1 ratio. Choice C adds the flour amounts instead of calculating sugar properly. Choice D incorrectly uses 1:1 ratio.

Question 18

Three stores sell trail mix using different ratios of nuts to dried fruit. Store A uses 8:3, Store B uses 12:5, and Store C uses 16:6. A customer wants to buy the trail mix with the highest ratio of nuts to dried fruit. Which analysis correctly determines the best choice?

  1. Store A has the highest ratio at 2.67, followed by Store C at 2.67, then Store B at 2.40
  2. Store A has the highest ratio at 2.67, followed by Store B at 2.40, then Store C at 2.67
  3. Store C has the highest ratio at 2.67, followed by Store A at 2.67, then Store B at 2.40 (correct answer)
  4. Store B has the highest ratio at 2.40, followed by Store A at 2.67, then Store C at 2.67
Explanation: When comparing ratios, you need to convert each ratio to a decimal or fraction to see which is actually largest. The ratio "nuts to dried fruit" means nuts ÷ dried fruit. Let's calculate each store's ratio:
  • Store A: 8÷3=2.678 ÷ 3 = 2.67
  • Store B: 12÷5=2.4012 ÷ 5 = 2.40
  • Store C: 16÷6=2.6716 ÷ 6 = 2.67
Store C has the highest ratio at 2.67, meaning it has 2.67 parts nuts for every 1 part dried fruit. Store A ties for second place with the same ratio of 2.67, while Store B has the lowest ratio at 2.40. Choice A incorrectly lists Store A as having the highest ratio when it actually ties with Store C. More importantly, it shows Store C at 2.67 in second place when Store C should be first. Choice B makes similar ranking errors and incorrectly places Store B in the middle position. Choice D completely reverses the order, putting Store B (the lowest ratio) first and showing the two tied stores as if they have different rankings. The key trap here is thinking that larger numbers in the original ratio automatically mean a higher ratio. Store B uses 12:5, which might look "bigger" than 8:3, but when you do the division, 12÷5 = 2.40 is actually smaller than 8÷3 = 2.67. Always convert ratios to decimals when comparing them. Don't be fooled by which numbers look larger in the original ratio format.

Question 19

Two paint mixtures are compared using tables.

Mixture A has ratio 22 cups yellow : 33 cups blue. Mixture B has ratio 33 cups yellow : 55 cups blue.

Which mixture has the greater amount of yellow per 1 cup of blue?

  1. Not enough information
  2. Mixture B
  3. Mixture A (correct answer)
  4. They are equal
Explanation: This question tests creating equivalent ratio tables by scaling both quantities by the same factor, finding missing values, plotting on coordinate planes through the origin, and comparing ratios. Equivalent ratios are formed by multiplying both parts of the ratio by the same number to preserve the relationship, such as 3:4 scaled by ×2 gives 6:8, by ×3 gives 9:12, all equal to the ratio 3/4; a table organizes these scaled versions, like for ratio 2:3 with batches 1,2,3,4 and cups 2,4,6,8 where each row is equivalent to 2:3; finding missing values involves identifying the scale, like if 3:4=9:?, the scale from 3 to 9 is ×3, so 4×3=12; plotting pairs like (1,2), (2,4), (3,6) on a plane forms a line through the origin indicating proportionality; comparing ratios uses unit rates, like 2:3 is 2/3≈0.67 and 3:5 is 0.6, so the first is greater. For example, with ratio 3:4, a table could be 3,6,9,12 | 4,8,12,16 (×1,×2,×3,×4), missing: if 3:4=?:12, find 3×3=9; plot (3,4), (6,8), (9,12) line through (0,0). The correct answer is choice A: Mixture A has greater yellow per blue, since unit rate for A is 2/3≈0.67 and for B is 3/5=0.6. Common errors include comparing without unit rates, like thinking larger numbers mean greater without normalizing, leading to wrong conclusions. To compare, calculate unit rates by dividing yellow by blue for each, then compare numerically: 2/3 > 3/5. Mistakes involve comparison without a common basis, like directly comparing totals instead of per unit, or arithmetic errors in rates.

Question 20

A school club makes bracelets using 44 blue beads for every 33 red beads. Which ordered pairs (red,blue)(\text{red},\text{blue}) should be plotted to represent the equivalent ratios for 1–4 groups of the basic ratio?

  1. (3,4), (6,8), (9,12), (12,16)(3,4),\ (6,8),\ (9,12),\ (12,16) (correct answer)
  2. (4,3), (8,6), (12,9), (16,12)(4,3),\ (8,6),\ (12,9),\ (16,12)
  3. (3,4), (6,7), (9,10), (12,13)(3,4),\ (6,7),\ (9,10),\ (12,13)
  4. (3,4), (5,8), (7,12), (9,16)(3,4),\ (5,8),\ (7,12),\ (9,16)
Explanation: This question tests creating equivalent ratio tables by scaling both quantities by the same factor, finding missing values, plotting on coordinate planes through the origin, and comparing ratios. Equivalent ratios are formed by multiplying both parts of the ratio by the same number to preserve the relationship, such as 3:4 scaled by ×2 gives 6:8, by ×3 gives 9:12, all equal to the ratio 3/4; a table organizes these scaled versions, like for ratio 2:3 with batches 1,2,3,4 and cups 2,4,6,8 where each row is equivalent to 2:3; finding missing values involves identifying the scale, like if 3:4=9:?, the scale from 3 to 9 is ×3, so 4×3=12; plotting pairs like (1,2), (2,4), (3,6) on a plane forms a line through the origin indicating proportionality; comparing ratios uses unit rates, like 2:3 is 2/3≈0.67 and 3:5 is 0.6, so the first is greater. For example, with ratio 3:4, a table could be 3,6,9,12 | 4,8,12,16 (×1,×2,×3,×4), missing: if 3:4=?:12, find 3×3=9; plot (3,4), (6,8), (9,12) line through (0,0). The correct ordered pairs are in choice A: (3,4), (6,8), (9,12), (12,16), representing red:blue as 3:4 scaled by ×1 to ×4. Common errors include switching the order like in B to (4,3) etc., or not scaling properly like in C with additive increases. For plotting, use the pairs as coordinates, ensuring they form a line through the origin in proportional y=kx form. Mistakes involve plot errors like not passing through origin or incorrect scaling, such as in D with non-equivalent ratios.