Convert $$\frac{4}{10}$$ to $$\frac{40}{100}$$, then add: $$\frac{40}{100} + \frac{35}{100} = \frac{75}{100}$$. Choice A incorrectly adds denominators. Choice C fails to convert tenths to hundredths. Choice D incorrectly converts the second fraction to tenths instead of the first to hundredths.

Convert $$\frac{6}{10} = \frac{60}{100}$$. Add: $$\frac{60}{100} + \frac{28}{100} = \frac{88}{100}$$. Compare to $$\frac{9}{10} = \frac{90}{100}$$. Since $$\frac{88}{100} < \frac{90}{100}$$, the requirement is met. Choice B has the wrong inequality direction. Choices C and D incorrectly add 6 + 28 = 34 without converting.

First, convert $$\frac{7}{10}$$ to hundredths: $$\frac{7}{10} = \frac{70}{100}$$. Then add: $$\frac{70}{100} + \frac{25}{100} = \frac{95}{100}$$. Choice A incorrectly adds numerators without converting (7 + 25 = 32). Choices C and D incorrectly add denominators (10 + 100 = 110).

Convert $$\frac{1}{10} = \frac{10}{100}$$. Add known costs: $$\frac{10}{100} + \frac{42}{100} = \frac{52}{100}$$. Subtract from total budget: $$\frac{100}{100} - \frac{52}{100} = \frac{48}{100}$$. Choice A adds 1 + 42 = 43 without converting. Choice C shows the combined cost of ribbon and beads. Choice D incorrectly adds all three materials as 10 + 42 + 5 = 57.

Convert sugar to hundredths: $$\frac{3}{10} = \frac{30}{100}$$. Find the difference: $$\frac{45}{100} - \frac{30}{100} = \frac{15}{100}$$. Choice B subtracts incorrectly (45 - 3 = 42). Choice C adds instead of subtracting (45 + 3 = 48). Choice D adds the total amount (45 + 30 = 75).

When you see a problem about parts of a whole, remember that all the parts must add up to 1 (or 100%). Here, you need to find what fraction is left after accounting for chocolate chip and oatmeal cookies.

First, convert both fractions to the same denominator so you can work with them. The chocolate chip cookies are $$\frac{8}{10}$$ of all cookies, which equals $$\frac{80}{100}$$ when you multiply both numerator and denominator by 10. The oatmeal cookies are already $$\frac{15}{100}$$.

Now add these known portions: $$\frac{80}{100} + \frac{15}{100} = \frac{95}{100}$$. This means chocolate chip and oatmeal cookies together make up $$\frac{95}{100}$$ of all cookies sold.

Since all cookies must equal $$\frac{100}{100}$$, subtract to find the remaining portion: $$\frac{100}{100} - \frac{95}{100} = \frac{5}{100}$$. This represents all other cookie types combined.

Looking at the wrong answers: Choice A gives $$\frac{95}{100}$$, which is actually the total of chocolate chip and oatmeal cookies, not the remaining portion. Choice B shows $$\frac{23}{100}$$, which you might get if you incorrectly subtracted $$\frac{15}{100} - \frac{8}{100}$$ instead of finding the remainder. Choice C gives $$\frac{77}{100}$$, which appears if you only subtracted the oatmeal cookies from the total, forgetting about the chocolate chip cookies.

Remember: when finding a missing part, convert fractions to common denominators first, then subtract the sum of known parts from the whole.

When you need to find how much more one fraction is than another, you're looking for the difference between them. This means you need to subtract the smaller fraction from the larger one.

First, you need to compare $$\frac{9}{10}$$ and $$\frac{55}{100}$$. To subtract fractions, they must have the same denominator. Since $$\frac{9}{10} = \frac{90}{100}$$, you can now see that athlete A ran $$\frac{90}{100}$$ of the course while athlete B ran $$\frac{55}{100}$$.

To find how much more athlete A ran, subtract: $$\frac{90}{100} - \frac{55}{100} = \frac{35}{100}$$. This makes C the correct answer.

Let's examine why the other answers are wrong. Choice A ($$\frac{54}{100}$$) likely comes from subtracting $$\frac{55}{100} - \frac{9}{100}$$ instead of converting $$\frac{9}{10}$$ to hundredths first. Choice B ($$\frac{46}{100}$$) might result from incorrectly converting $$\frac{9}{10}$$ or making an arithmetic error during subtraction. Choice D ($$\frac{145}{100}$$) comes from adding the fractions instead of subtracting them ($$\frac{90}{100} + \frac{55}{100} = \frac{145}{100}$$).

Remember: When comparing fractions, always convert them to the same denominator first. Look for key words like "how much more" or "difference" – these signal subtraction problems. Take your time converting fractions and double-check that you're performing the right operation.

When you see a problem asking about leftover portions, you need to find what remains after subtracting all the parts that were used. This is a fraction subtraction problem, but first you'll need to work with equivalent fractions.

Sarah ate $$\frac{3}{10}$$ and Mike ate $$\frac{24}{100}$$ of the pizza. To add these fractions, you need a common denominator. Since $$\frac{3}{10} = \frac{30}{100}$$, you can rewrite Sarah's portion as $$\frac{30}{100}$$. Now add: $$\frac{30}{100} + \frac{24}{100} = \frac{54}{100}$$ of the pizza was eaten.

Since the whole pizza equals $$\frac{100}{100}$$, subtract the eaten portion: $$\frac{100}{100} - \frac{54}{100} = \frac{46}{100}$$. This confirms answer choice C is correct.

Looking at the wrong answers: Choice A gives $$\frac{27}{100}$$, which you'd get if you incorrectly subtracted $$\frac{3}{10}$$ from the whole without converting to hundredths first. Choice B gives $$\frac{54}{100}$$, which is actually the amount eaten, not the amount left over - a common mistake when students calculate correctly but answer the wrong question. Choice D gives $$\frac{73}{100}$$, which results from incorrectly adding $$\frac{3}{10} + \frac{24}{100}$$ as $$\frac{27}{100}$$ without proper conversion.

Remember: when working with fraction word problems, always convert to a common denominator first, double-check what the question is actually asking for (eaten vs. remaining), and verify your final answer makes sense.

When you see a problem about parts of a whole, remember that all the parts must add up to exactly 1 whole (or $$\frac{100}{100}$$). Here, you need to find what fraction of the garden is grass by subtracting the known sections from the total.

First, convert both fractions to the same denominator so you can work with them. The vegetable section is $$\frac{5}{10}$$, which equals $$\frac{50}{100}$$ when you multiply both the numerator and denominator by 10. The flower section is already $$\frac{18}{100}$$.

Now add the vegetable and flower sections: $$\frac{50}{100} + \frac{18}{100} = \frac{68}{100}$$. This means the vegetable and flower sections together cover $$\frac{68}{100}$$ of the garden.

Since the whole garden equals $$\frac{100}{100}$$, subtract to find the grass area: $$\frac{100}{100} - \frac{68}{100} = \frac{32}{100}$$. The grass covers $$\frac{32}{100}$$ of the garden.

Looking at the wrong answers: Choice A gives $$\frac{23}{100}$$, which is the result if you incorrectly subtracted $$\frac{18}{100} - \frac{5}{10}$$. Choice B gives $$\frac{68}{100}$$, which is the combined area of vegetables and flowers, not the grass. Choice C gives $$\frac{77}{100}$$, which comes from incorrectly adding without proper conversion.

Always convert fractions to common denominators before adding or subtracting, and remember that in "parts of a whole" problems, your final answer plus all given parts should equal exactly 1.

This question tests 4th grade ability to express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (CCSS.4.NF.5). To add fractions with denominators 10 and 100, we must first convert to a common denominator—$100 = 10 \times 10$. The key relationship: $\frac{1}{10} = \frac{10}{100}$ (one tenth equals ten hundredths), so any fraction $\frac{a}{10} = \frac{10a}{100}$ by multiplying numerator and denominator by 10. Once both fractions have denominator 100, add the numerators and keep the denominator: $\frac{10a}{100} + \frac{b}{100} = \frac{10a + b}{100}$. Convert $8/10$ to hundredths and add $9/100$: $\frac{8}{10} = \frac{8 \times 10}{100} = \frac{80}{100}$. Then add: $\frac{80}{100} + \frac{9}{100} = \frac{80 + 9}{100} = \frac{89}{100}$. Choice A is correct because converting $8/10$: multiply numerator $8 \times 10 = 80$, denominator $10 \times 10 = 100$, giving $\frac{80}{100}$; then adding: $\frac{80}{100} + \frac{9}{100}$, add numerators: $80 + 9 = 89$, keep denominator 100: $\frac{89}{100}$. This demonstrates understanding that tenths must be expressed as hundredths before adding. Choice B represents adding without converting (added $8+9=17$ directly), which happens when students don't recognize need for common denominator. To help students: Visualize with hundredths grid ($10\times10$ squares)—each COLUMN is $\frac{1}{10} = 10$ squares, each SQUARE is $\frac{1}{100}$. To convert tenths to hundredths, multiply numerator by 10: $\frac{8}{10} = \frac{8\times10}{100} = \frac{80}{100}$. Check: count squares ($80$ squares for 8 columns). Then add: $\frac{80}{100} + \frac{9}{100} = \frac{89}{100}$ ($80 + 9 = 89$ squares total). Connect to decimals: $\frac{8}{10} = 0.8$, $\frac{9}{100} = 0.09$, $0.8 + 0.09 = 0.89 = \frac{89}{100}$. Use money: 8 dimes ($\frac{8}{10}$ dollar) = 80 pennies ($\frac{80}{100}$ dollar), plus 9 pennies = 89 pennies = $\frac{89}{100}$ dollar. Pattern: $\frac{1}{10}=\frac{10}{100}$, $\frac{2}{10}=\frac{20}{100}$, $\frac{8}{10}=\frac{80}{100}$ (multiply numerator by 10). Watch for: not converting tenths to hundredths before adding, multiplying by wrong number, arithmetic errors, and adding denominators.