Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of serving drinks, with 5 gallons and each serving 1/5 gallon, 5 ÷ 1/5 finds the number of servings. You count the fractional units by observing that each gallon contains 5 units of 1/5 gallon, so 5 gallons contain 5 × 5 = 25 units. A model could be 5 circles each divided into 5 equal parts, showing 25 total fifths. A common misconception is thinking this is like dividing by a whole number, but multiplying by the reciprocal gives the correct count. In general, smaller denominators in unit fractions lead to smaller quotients, but larger denominators increase them. For instance, 5 ÷ 1/2 = 10, smaller than 5 ÷ 1/5 = 25.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of baking, with 3 cups of flour and each batch needing 1/4 cup, 3 ÷ 1/4 calculates the number of batches possible. You count the fractional units by seeing that each cup holds 4 units of 1/4 cup, so 3 cups hold 3 × 4 = 12 units. A bar model can represent this, with 3 bars each split into 4 quarters, totaling 12 quarters. A common misconception is that division always produces a quotient smaller than the dividend, but here 12 is larger than 3, making claim D incorrect. In general, dividing by smaller unit fractions results in larger quotients because more tiny units fit. For example, 3 ÷ 1/5 = 15, which is larger than 3 ÷ 1/4 = 12.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of marking a trail, with 3 miles marked every 1/6 mile, 3 ÷ 1/6 finds the number of intervals. You count the fractional units by seeing each mile has 6 units of 1/6 mile, so 3 miles have 3 × 6 = 18 units. A number line from 0 to 3 with ticks every 1/6 mile demonstrates 18 intervals. A common misconception is counting the marks instead of intervals, but it accurately shows 18. In general, smaller unit fractions lead to more units fitting, thus larger quotients. For example, 3 ÷ 1/3 = 9, but 3 ÷ 1/6 = 18, illustrating the inverse relationship.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of measuring string, with 2 yards divided into 1/6-yard lengths, 2 ÷ 1/6 determines the number of segments. You count the fractional units by noting each yard has 6 units of 1/6 yard, so 2 yards have 2 × 6 = 12 units. The best model is a number line from 0 to 2 split into 12 equal parts, each representing 1/6 yard. A common misconception is miscounting the splits, like thinking it divides into fewer parts, but accurate scaling shows 12. In general, unit fractions with larger denominators produce bigger quotients as more small units fit. For example, 2 ÷ 1/3 = 6, but 2 ÷ 1/6 = 12, doubling the quotient.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of painting projects, with 6 quarts and each using 1/2 quart, 6 ÷ 1/2 determines the number of projects. You count the fractional units by noting each quart holds 2 units of 1/2 quart, so 6 quarts hold 6 × 2 = 12 units. A bar diagram with 6 bars each split in half visualizes 12 halves. A common misconception is inverting the operation wrongly, but multiplying by the reciprocal ensures accuracy. In general, larger unit fractions (like 1/2) yield smaller quotients than smaller ones (like 1/4). For example, 6 ÷ 1/2 = 12, but 6 ÷ 1/3 ≈ 18, increasing as the fraction shrinks.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of distributing water, if a teacher has 6 liters and each bottle holds 1/3 liter, the division 6 ÷ 1/3 determines the number of bottles that can be filled. You count the fractional units by recognizing that each liter contains 3 units of 1/3 liter, so 6 liters contain 6 × 3 = 18 units. A helpful model is to draw 6 rectangles each divided into 3 equal parts, showing 18 total thirds for the bottles. A common misconception is that dividing by a fraction should yield a small result, but here the quotient 18 is larger than 6 because the divisor is less than 1. In general, smaller unit fractions allow more units to fit into the whole, resulting in a larger quotient. For instance, dividing by 1/4 would yield an even larger quotient than dividing by 1/3 for the same whole number.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of cutting border, with 8 feet into 1/4-foot pieces, 8 ÷ 1/4 finds the number of pieces. You count the fractional units by seeing each foot has 4 units of 1/4 foot, so 8 feet have 8 × 4 = 32 units. A ruler model from 0 to 8 marked every 1/4 foot shows 32 marks. A common misconception is that division reduces the value below the dividend, but 32 > 8, making statement B incorrect. In general, as unit fractions decrease in size, the quotient increases proportionally. For example, 8 ÷ 1/2 = 16, smaller than 8 ÷ 1/8 = 64.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of marking a hose, with 3 meters sectioned every 1/3 meter, 3 ÷ 1/3 calculates the number of sections. You count the fractional units by realizing each meter includes 3 units of 1/3 meter, so 3 meters include 3 × 3 = 9 units. A tape measure model from 0 to 3 with marks every 1/3 meter illustrates 9 segments. A common misconception is equating this to dividing by 3, but it's actually multiplying by 3. In general, smaller unit fractions mean larger quotients due to fitting more units. For instance, 3 ÷ 1/2 = 6, but 3 ÷ 1/4 = 12, showing the pattern of increase.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of serving lasagna, with 4 pans and each serving 1/8 pan, 4 ÷ 1/8 calculates the servings. You count the fractional units by observing each pan contains 8 units of 1/8 pan, so 4 pans contain 4 × 8 = 32 units. A model of 4 squares each divided into 8 parts shows 32 total eighths. A common misconception is thinking fewer servings from division, but the result is larger. In general, unit fractions with bigger denominators create larger quotients. For instance, 4 ÷ 1/4 = 16, but 4 ÷ 1/8 = 32, doubling as the fraction halves.

Dividing a whole number by a unit fraction measures how many of those fractional units fit into the whole number. In the context of cutting ribbon, if you have 4 meters and cut pieces of 1/2 meter each, 4 ÷ 1/2 finds how many such pieces you get. You count the fractional units by noting that each meter contains 2 units of 1/2 meter, so 4 meters contain 4 × 2 = 8 units. A useful model is a number line from 0 to 4 marked every 1/2 meter, showing 8 segments. A common misconception is confusing this with finding remainders or halves, but it specifically counts the full fractional pieces. In general, as the unit fraction gets smaller, more units fit, increasing the quotient size. For example, dividing 4 by 1/3 yields 12, larger than dividing by 1/2 which gives 8.