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 missing value is ?=8 in choice B, since the table shows flour 2,4,6,? and milk 5,10,15,20, scaled by ×1,×2,×3,×4, so 2×4=8 matches 5×4=20. A common error is using additive thinking, like adding 2 repeatedly to get ?=10 in C, instead of multiplying by the scale factor of 4 from 5 to 20. To find missing values, identify the scale factor, such as from 5 to 20 is ×4, then apply to flour: 2×4=8. Mistakes include wrong scale factor, like dividing instead of multiplying, or arithmetic errors leading to ?=7,10, or 12.

This question tests creating equivalent ratio tables by scaling both quantities in the ratio by the same factor, such as for batches of a smoothie recipe, and ensures the tables maintain the proportional relationship without providing missing values or plotting here. Equivalent ratios are formed by multiplying both parts of the original ratio 3:4 (yogurt to fruit) by the same number, like ×2 giving 6:8, ×3 giving 9:12, all preserving the ratio of 3/4. A table organizes these scaled versions, for example, for ratio 3:4 across 1 to 5 batches: yogurt 3,6,9,12,15 and fruit 4,8,12,16,20, where each row is equivalent. For instance, if you have 3:4 and scale to find equivalents, ×4 gives 12:16, fitting the pattern in the table. The correct table is option A, which properly scales both quantities by 1 through 5 for each batch. Common errors include not scaling both parts equally, like in option B where yogurt adds 2 instead of multiplying, or option C where fruit adds 2, breaking the ratio. To create such a table, start with the given ratio 3:4, scale by factors 1 to 5 to get the pairs, and organize in columns for batches, yogurt, and fruit; mistakes often involve additive thinking instead of multiplicative scaling.

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 map length is 20 cm in choice C, since scale 5 cm:2 km, for 8 km the factor is 8/2=4, so 5×4=20 cm. Common errors include wrong scale factor, like multiplying by 8/5 instead, or arithmetic mistakes leading to 16 cm or 40 cm. To find missing values, find scale factor like from 2 km to 8 km is ×4, apply to 5 cm×4=20. Mistakes include additive scaling instead of multiplying, or confusing which quantity to scale.

This question tests creating equivalent ratio tables by scaling both quantities in the ratio by the same factor, such as multiplying by 1 through 5, and identifying the correct table that maintains the proportional relationship. Equivalent ratios are formed by multiplying both parts of the original ratio by the same number, preserving the relationship; for example, the ratio 3:4 scaled by ×2 gives 6:8, which is equivalent, and scaling by ×3 gives 9:12, all equal to the unit rate of 3/4. A table organizes these scaled versions; for the yogurt to fruit ratio of 3:4, the table should show yogurt amounts like 3, 6, 9, 12, 15 and corresponding fruit amounts of 4, 8, 12, 16, 20 for ×1 through ×5, with each row maintaining the 3:4 ratio. In this case, choice B correctly shows yogurt: 3,6,9,12,15 and fruit: 4,8,12,16,20, as each pair is scaled consistently from the original ratio. Common errors include additive scaling instead of multiplicative, like in choice A where fruit increases by +3 each time, or mismatched scaling as in choice C and D, leading to non-equivalent ratios. To create such a table: (1) start with the given ratio (3:4), (2) scale by factors ×1 to ×5 to get pairs like (3,4), (6,8), etc., (3) organize in rows or columns. Always verify equivalence by checking if the ratios simplify to the same value or by cross-multiplying to confirm consistency across rows.

This question tests using equivalent ratios to find missing values by scaling the original ratio to match a given quantity, ensuring the relationship remains proportional. Equivalent ratios preserve the relationship by multiplying both parts by the same factor; for 5:2 blue to white paint, scaling by ×2 gives 10:4, by ×3 gives 15:6, all with the unit rate of 5/2 cups blue per white. To find white paint for 20 cups blue, identify the scale factor (5 to 20 is ×4), then apply to white (2×4=8). The correct answer is 8 cups of white paint, as it maintains the proportion where blue/white = 5/2 consistently. Errors often occur from incorrect scaling, like dividing instead of multiplying, or using additive thinking, resulting in values like 4 or 10. Steps for solving: (1) start with the ratio (5:2), (2) find the factor (20÷5=4), (3) multiply the other quantity (2×4=8). Confirm by checking if the new ratio 20:8 simplifies to 5:2 or by plotting points to see a line through the origin.

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.

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.

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 B: Yes, because both terms are multiplied by 4, since 3×4=12 and 4×4=16. Common errors include checking differences like in A (additive thinking) or cross-products incorrectly like in C. To check equivalence, verify the scale factor is the same, like 12/3=4 and 16/4=4, or cross-multiply 3×16=48 and 4×12=48. Mistakes involve additive checks like adding instead of multiplying, or wrong arithmetic in cross-products.

This question tests understanding equivalent ratios without a full table, by checking if scaling the original 4:7 (flour to water) by a factor like 3 gives 12:21. Equivalent ratios are formed by multiplying both by the same number, preserving the relationship, like 4×3=12 and 7×3=21, both equal to 4/7. While tables can organize multiples, here it's direct: the pairs are equivalent since they scale by 3. For example, a table would show 4:7, 8:14, 12:21, all proportional. The correct answer is yes, because both were multiplied by 3, as in option B. Common errors include checking addition like in A or subtraction in C, instead of multiplication. To verify, find the scale factor (4 to 12 is ×3), apply to the other (7×3=21); mistakes arise from not recognizing multiplicative scaling or confusing with simplification.

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.