When you see a problem asking for a fraction of a recipe, you need to multiply the original amount by the fraction you want to make. This tests your ability to multiply mixed numbers by fractions.

First, convert the mixed number $$2\frac{1}{6}$$ to an improper fraction. Multiply the whole number by the denominator and add the numerator: $$2 \times 6 + 1 = 13$$, so $$2\frac{1}{6} = \frac{13}{6}$$.

Now multiply $$\frac{13}{6} \times \frac{3}{4}$$. Multiply the numerators and denominators: $$\frac{13 \times 3}{6 \times 4} = \frac{39}{24}$$. Simplify by dividing both by 3: $$\frac{39}{24} = \frac{13}{8}$$.

Convert back to a mixed number: $$13 \div 8 = 1$$ remainder $$5$$, so $$\frac{13}{8} = 1\frac{5}{8}$$.

Looking at the wrong answers: Choice A gives $$\frac{13}{8}$$ cups, which is the correct calculation but left as an improper fraction rather than converting to the mixed number form. Choice B shows $$2\frac{11}{12}$$, which would result from incorrectly adding fractions instead of multiplying. Choice D gives $$1\frac{1}{2}$$, which might come from rounding or computational errors during the multiplication process.

Remember this key strategy: when a recipe problem asks for a fraction of the original, always multiply the original amount by that fraction. Convert mixed numbers to improper fractions first to make multiplication easier, then convert your final answer back to a mixed number if needed.

To find the total nuts needed, multiply $$\frac{3}{4} \times 2\frac{1}{3}$$. Convert $$2\frac{1}{3}$$ to $$\frac{7}{3}$$. Then $$\frac{3}{4} \times \frac{7}{3} = \frac{21}{12} = \frac{7}{4} = 1\frac{3}{4}$$ cups. Choice B results from incorrectly adding instead of multiplying. Choice C comes from multiplying $$\frac{3}{4} \times 4\frac{1}{3}$$ (misreading the mixed number). Choice D is the correct answer but not simplified to mixed number form.

When you see a problem asking for a fraction of a whole amount, you need to multiply the fraction by the total capacity. Here, you're finding $$\frac{4}{5}$$ of $$15\frac{1}{4}$$ gallons.

First, convert the mixed number to an improper fraction: $$15\frac{1}{4} = \frac{61}{4}$$. Now multiply: $$\frac{4}{5} \times \frac{61}{4} = \frac{4 \times 61}{5 \times 4} = \frac{244}{20}$$.

Simplify by dividing both numerator and denominator by 4: $$\frac{244}{20} = \frac{61}{5}$$. Convert back to a mixed number: $$61 ÷ 5 = 12$$ with remainder $$1$$, so $$\frac{61}{5} = 12\frac{1}{5}$$ gallons. This confirms answer C is correct.

Answer A ($$11\frac{4}{5}$$) likely comes from incorrectly subtracting $$\frac{4}{5}$$ from the total instead of finding $$\frac{4}{5}$$ of the total. Answer B ($$16\frac{1}{20}$$) suggests adding $$\frac{4}{5}$$ to the tank capacity, which doesn't make sense since the tank can't hold more than its maximum. Answer D ($$12\frac{1}{4}$$) might result from confusing the fraction in the capacity ($$\frac{1}{4}$$) with the answer, or from computational errors during the multiplication.

Remember: "of" in word problems usually means multiplication. When you see "fraction of an amount," multiply the fraction by the total amount. Always double-check that your answer makes logical sense—it should be less than the tank's full capacity.

When you see fraction word problems with multiple steps, break them down one piece at a time and watch your language carefully—especially phrases like "of what someone else ate."

First, find how many slices Tom ate. He ate $$\frac{3}{4}$$ of the 8-slice pizza: $$\frac{3}{4} \times 8 = 6$$ slices.

Next, determine Jerry's portion. The key phrase is "Jerry ate $$\frac{1}{2}$$ of what Tom ate." This means Jerry ate half of Tom's 6 slices, not half of the original pizza. So Jerry ate: $$\frac{1}{2} \times 6 = 3$$ slices.

Answer B (3 slices) is correct.

Here's why the other answers are wrong: Answer A (2 slices) might come from incorrectly calculating $$\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$$ of the pizza, then finding $$\frac{3}{8} \times 8 = 3$$—but making an arithmetic error along the way. Answer C (4 slices) represents $$\frac{1}{2}$$ of the original 8-slice pizza, which misses that Jerry ate half of Tom's portion, not half of the whole pizza. Answer D (1 slice) might result from various calculation errors or misunderstanding the fractions involved.

The trap here is the phrase "of what Tom ate"—this creates a two-step problem where you must first find Tom's amount, then calculate Jerry's portion based on that specific amount. Always identify whose portion you're calculating from when you see "of what [person] ate" in fraction problems.

When you see a problem asking "how many feet can Jake paint each day," you need to find a fraction of the total fence length. This is a fraction multiplication problem: you're finding $$\frac{2}{3}$$ of $$12\frac{3}{4}$$ feet.

First, convert the mixed number to an improper fraction: $$12\frac{3}{4} = \frac{51}{4}$$ (multiply 12 × 4 = 48, then add 3 to get 51). Now multiply: $$\frac{2}{3} \times \frac{51}{4} = \frac{102}{12}$$. Simplify by dividing both numerator and denominator by 6: $$\frac{102}{12} = \frac{17}{2} = 8\frac{1}{2}$$. So Jake paints $$8\frac{1}{2}$$ feet per day.

Answer choice A ($$12\frac{1}{12}$$) comes from incorrectly adding $$\frac{2}{3}$$ to $$12\frac{3}{4}$$ instead of multiplying. Answer choice B ($$19\frac{1}{12}$$) results from adding the fractions incorrectly, getting a number larger than the fence itself, which doesn't make sense. Answer choice C ($$8\frac{1}{6}$$) happens when students make calculation errors during the multiplication or conversion steps, getting close to the right answer but with the wrong fractional part.

The correct answer is D: $$8\frac{1}{2}$$ feet per day.

Remember: when finding "a fraction OF something," you multiply. Always check if your answer makes sense—Jake should paint less than the total fence length each day, and $$8\frac{1}{2}$$ is indeed less than $$12\frac{3}{4}$$.

This problem tests your ability to find a fraction of a mixed number. When you see "fraction of" in a word problem, it signals multiplication.

To find how many miles the crew laid, you need to multiply the total project length by the fraction completed: $$6\frac{2}{3} \times \frac{3}{5}$$.

First, convert the mixed number to an improper fraction. For $$6\frac{2}{3}$$: multiply the whole number by the denominator (6 × 3 = 18), add the numerator (18 + 2 = 20), and place over the original denominator: $$\frac{20}{3}$$.

Now multiply: $$\frac{20}{3} \times \frac{3}{5} = \frac{60}{15} = 4$$. The crew laid exactly 4 miles, making B correct.

Let's examine why the other answers are wrong. Choice A ($$7\frac{4}{15}$$) appears to come from adding $$6\frac{2}{3}$$ and $$\frac{3}{5}$$ instead of multiplying - a common error when students see two fractions together. Choice C ($$3\frac{1}{5}$$) might result from incorrectly converting the mixed number or making arithmetic errors during multiplication. Choice D ($$2\frac{2}{5}$$) could come from multiplying $$6\frac{2}{3}$$ by $$\frac{2}{5}$$ instead of $$\frac{3}{5}$$, mixing up the fraction values.

Remember this key strategy: when a problem asks for "a fraction OF something," always multiply. Convert mixed numbers to improper fractions first to make multiplication easier, then simplify your final answer.

Fraction multiplication represents taking part of a quantity, like an additive amount based on another volume. The gardener mixes $\tfrac{2}{3}$ gallon of water, with fertilizer being $\tfrac{3}{10}$ of that water amount. Multiplying ($\tfrac{3}{10}$) \times ($\tfrac{2}{3}$) gives $\tfrac{1}{5}$ gallon of fertilizer. Envision a gallon jug: $\tfrac{2}{3}$ filled with water; $\tfrac{3}{10}$ of that is like dividing the water into 10 parts and taking 3, equaling $\tfrac{1}{5}$ total. A misconception is using the whole gallon, but it's a fraction of the mixed water. In gardening, it calculates precise mixtures for plant care. It extends to chemistry, mixing solutions in proportional amounts for experiments.

Fraction multiplication represents taking part of a quantity, like determining a portion of a filled amount. In this situation, the bottle is filled to 4/5 liter, and then 1/2 of that filled amount is poured out. The fractions interact by multiplying 1/2 by 4/5 to find the poured-out amount, yielding (1/2) * (4/5) = 2/5 liter. Imagine a number line from 0 to 1 liter: mark 4/5, then half of that segment is 2/5 from the start. One misconception is thinking it means half the bottle regardless, but it's half of the current fill, not the whole. In everyday life, fraction multiplication helps with measurements, such as calculating fuel used from a partially full tank. It extends to science experiments, where you might need to find a fraction of a mixed solution's volume.

Fraction multiplication represents taking part of a quantity. In this lemonade pitcher situation, Aiden is pouring out 3/5 of the full 2-liter capacity. The fractions interact by multiplying 3/5 (the portion poured) by 2 (the full amount), giving the volume removed. Visually, imagine the 2 liters as two whole units; taking 3/5 means 3/5 from each unit, totaling 6/5 liters. A common misconception is treating the whole number as a fraction incorrectly, but here 2 is 2/1, and multiplying yields an improper fraction. In real-world problems, fraction multiplication assists in portioning liquids in recipes or experiments. It also applies to dividing resources like fuel or supplies in travel and logistics.

Fraction multiplication represents taking part of a quantity, such as a portion of an already consumed amount. Here, the class eats 2/3 of the pan, and 3/4 of that eaten amount is consumed at lunch. The fractions interact through multiplication: (3/4) * (2/3) = 1/2 of the whole pan. Picture a pan divided into 12 sections: 2/3 is 8 sections eaten, and 3/4 of 8 is 6 sections, equaling 6/12 or 1/2. A misconception is assuming it's 3/4 of the whole pan, but it's of the eaten part only. This skill applies to resource allocation, like dividing shared supplies in group activities. It also helps in nutrition tracking, calculating portions of meals eaten at different times.