This problem requires dividing a unit fraction by a whole number: $$\frac{1}{3} \div 4$$. To solve this, we multiply $$\frac{1}{3}$$ by $$\frac{1}{4}$$, which gives us $$\frac{1}{12}$$. The information about buying 2 more pizzas is extra information meant to distract. Choice B represents dividing by 7 (4+3) instead of 4. Choice C incorrectly multiplies $$\frac{1}{3}$$ by 4. Choice D represents the reciprocal of the division.

Fraction division solves sharing or measuring problems by calculating how many servings fit into a total volume. The coach has 2 gallons of drink, and each player needs 1/4 gallon, so we find how many players can be served. We count the number of 1/4-gallon unit fractions in 2 gallons, which totals 8. Imagine 2 whole gallons, each divided into 4 quarters, so there are 8 quarters overall. A misconception is believing division by a fraction less than 1 decreases the result, but here it increases it because we're counting small units. In general, fraction division addresses problems like allocating drinks in sports. It helps determine the maximum number of equal portions from a supply.

First, find the remaining board length: 6 - 2 = 4 feet. Then divide 4 by $$\frac{1}{4}$$: $$4 \div \frac{1}{4} = 4 \times 4 = 16$$ pieces. Choice B uses the original 6-foot length ($$6 \div \frac{1}{4} = 24$$). Choice C incorrectly divides 4 by 2 instead of using the unit fraction division. Choice D represents $$\frac{1}{4} \times 16$$ instead of division.

When you see a word problem involving fractions and "complete pieces," you need to find the usable material first, then divide by the piece size.

Start with what happened to the ribbon. The factory had 8 yards total, but $$\frac{3}{7}$$ yard was wasted. To find the usable ribbon, subtract: $$8 - \frac{3}{7}$$. Convert 8 to sevenths: $$8 = \frac{56}{7}$$. So you have $$\frac{56}{7} - \frac{3}{7} = \frac{53}{7}$$ yards of usable ribbon.

Now divide the usable ribbon by the size of each piece. Each piece is $$\frac{1}{7}$$ yard, so you need: $$\frac{53}{7} \÷ \frac{1}{7}$$. When dividing fractions, multiply by the reciprocal: $$\frac{53}{7} \times \frac{7}{1} = 53$$ complete pieces.

Looking at the wrong answers: Answer A (21) likely comes from incorrectly calculating $$3 \times 7 = 21$$ instead of properly handling the subtraction. Answer B (56) represents the total yards converted to sevenths before subtracting the waste—this ignores the defective material entirely. Answer D (45) might result from calculation errors in the fraction arithmetic.

The correct answer is C: 53 complete pieces.

Remember this strategy: in multi-step fraction problems, work systematically. First find what you actually have to work with (subtract any waste or unusable amounts), then perform the division to find how many complete units you can make. Always convert to common denominators when adding or subtracting fractions.

When you see a word problem involving fractions and division, you need to carefully track what's happening step by step. This problem involves dividing a fraction equally among multiple groups.

Sarah doubled the recipe, so she has $$\frac{1}{4}$$ cup of vanilla extract that needs to be divided equally among 3 batches. To find how much goes in each batch, you divide $$\frac{1}{4} \div 3$$. When dividing by a whole number, multiply the fraction by the reciprocal: $$\frac{1}{4} \times \frac{1}{3} = \frac{1}{12}$$. Each batch gets $$\frac{1}{12}$$ cup of vanilla extract.

Choice A ($$\frac{1}{6}$$) represents a common error where students might divide the original $$\frac{1}{8}$$ by 3 incorrectly, getting confused about which amount to use. Choice B ($$\frac{1}{24}$$) likely comes from incorrectly dividing the original $$\frac{1}{8}$$ by 3: $$\frac{1}{8} \times \frac{1}{3} = \frac{1}{24}$$, but this ignores that Sarah doubled the recipe. Choice C ($$\frac{3}{4}$$) is way too large and might result from multiplying instead of dividing, or confusing the fractions entirely.

The key strategy here is to identify exactly what amount you're working with (the doubled amount of $$\frac{1}{4}$$ cup) and what operation you need (division to split it equally). Always double-check that your answer makes sense—$$\frac{1}{12}$$ cup per batch is reasonable since it's smaller than the total $$\frac{1}{4}$$ cup.

When you encounter multi-step word problems with fractions, break them down into clear steps: identify what you have, what you're using, what remains, and how to divide what's left.

The baker starts with 4 pounds of chocolate chips but saves $$\frac{1}{4}$$ pound for decorating. First, find how much she has for batches: $$4 - \frac{1}{4} = 3\frac{3}{4}$$ pounds. Converting to an improper fraction: $$3\frac{3}{4} = \frac{15}{4}$$ pounds.

Next, divide the remaining chocolate by how much each batch needs. Since each batch uses $$\frac{1}{12}$$ pound, you calculate: $$\frac{15}{4} ÷ \frac{1}{12}$$. Remember that dividing by a fraction means multiplying by its reciprocal: $$\frac{15}{4} × \frac{12}{1} = \frac{180}{4} = 45$$ batches.

Answer B (45 small batches) is correct.

Answer A (48) likely comes from dividing all 4 pounds by $$\frac{1}{12}$$ without subtracting the decorating chocolate first. Answer C (36) might result from incorrectly calculating $$3 × 12$$ instead of properly handling the mixed number $$3\frac{3}{4}$$. Answer D (39) could come from computational errors when converting between mixed numbers and improper fractions.

The key strategy for fraction word problems is to work methodically: handle all addition and subtraction first to find your actual working amount, then perform the division. Always double-check your fraction arithmetic, especially when converting between mixed numbers and improper fractions.

Fraction division solves sharing or measuring problems by calculating how many smaller units are in a whole number of items. The baker has 4 whole pies, with each slice being 1/8 of a pie, using quotative division to count the total slices. We find how many unit fractions of 1/8 are in 4, equaling 32 since each pie yields 8 slices and four pies yield 32. Drawing 4 circles each divided into 8 equal slices clearly shows the 32 pieces. Misconception: some think dividing by a fraction complicates to decimals, but here it simplifies to a whole number. Fraction division like this answers practical questions in food preparation, such as portioning for servings. It generalizes to inventory and distribution, helping in baking or manufacturing contexts.

Fraction division solves sharing or measuring problems by distributing a quantity into equal parts or calculating shares. In this situation, it models splitting one-third kilogram of dough equally among two trays, finding the amount per tray. We split the unit fraction by dividing one-third by two, giving one-sixth kilogram per tray as the equal portion. Imagine a rectangle representing one-third kilogram, divided into two equal parts, each one-sixth. A common misconception is mixing up grouping with sharing, but here it's sharing into equal groups, not counting groups of a certain size. Fraction division applies broadly to cooking and baking, ensuring balanced portions. It helps answer questions about division of limited resources in practical scenarios.

Fraction division solves sharing or measuring problems by determining how many unit fractions fit into a whole number or how to split a fraction equally. In this situation, Mia has 3 cups of yogurt and wants to measure out servings of 1/2 cup each, modeling how many such servings she can get from the total amount. We count how many unit fractions of 1/2 cup are contained within the 3 cups by recognizing that each whole cup holds two 1/2-cup servings. Visually, you can draw three whole circles, each divided into two halves, showing a total of six halves. A common misconception is thinking division by 1/2 halves the number, but actually, it doubles it because you're finding how many halves are there. In general, dividing a whole number by a unit fraction tells us the number of groups we can form. This helps answer real-world questions like portioning food or materials efficiently.

Fraction division solves sharing or measuring problems by calculating the volume per cup when a fraction is poured equally among whole numbers. Here, 1/3 gallon of lemonade is divided into 4 cups, modeling equal pouring. We split the unit fraction 1/3 into 4 equal shares, resulting in 1/12 gallon each. Visually, represent 1/3 as a circle divided into 4 equal wedges, each 1/12. A misconception is thinking division by 4 enlarges the fraction, but it creates smaller portions. This method generalizes to distributing beverages or liquids. It addresses real-world issues like serving drinks at events fairly.