This requires multiple steps: Jake started with 7/10, added 2/10 to get 9/10, then subtracted 1/10 to get 8/10. The operations are: 7/10 + 2/10 - 1/10 = 8/10. Choice A subtracts both amounts from the original. Choice C only accounts for the addition, not the subtraction. Choice D adds all amounts together.

Subtraction of fractions represents separating or removing parts from a whole. Sarah needs 3/5 total and has already added 1/5, so she's finding what remains: 3/5 - 1/5 = 2/5. Choice B describes addition, not subtraction. Choice C describes division. Choice D also describes addition rather than finding the difference.

Emma read 1/4 on Monday, then 2/4 on Tuesday for a total of 3/4. However, 1/4 of Tuesday's reading was double-counted, so she must subtract 1/4: 1/4 + 2/4 - 1/4 = 2/4. Choice B ignores the double-counting correction. Choice C adds all amounts without considering the overlap. Choice D only counts Monday's reading.

When you see fraction problems involving multiple steps and changes over time, you need to carefully track what gets added and what gets removed from the total.

Let's work through this step by step. Start with the garden sections that get planted: On Saturday, $$\frac{4}{9}$$ was planted with vegetables. On Sunday, $$\frac{2}{9}$$ more was planted with flowers. At this point, you have $$\frac{4}{9} + \frac{2}{9} = \frac{6}{9}$$ of the garden planted.

But here's the key detail: On Monday, $$\frac{1}{9}$$ of the flower section was moved to a different garden entirely. This means $$\frac{1}{9}$$ of the original garden is no longer planted at all. So you need to subtract: $$\frac{6}{9} - \frac{1}{9} = \frac{5}{9}$$.

Answer choice A ($$\frac{4}{9}$$) only counts the vegetables and ignores the flowers completely. Answer choice B ($$\frac{6}{9}$$) represents the amount planted before Monday's change—this is the trap for students who forget about the flowers being moved. Answer choice C ($$\frac{7}{9}$$) incorrectly adds all three fractions without recognizing that the moved flowers should be subtracted, not added.

The correct answer is D: $$\frac{5}{9}$$ of the original garden remains planted.

Remember: In multi-step fraction problems, pay close attention to words like "moved," "removed," or "taken away"—these signal subtraction, even when they appear after addition steps. Always read through the entire problem before calculating.

Initially: Art (4/12) + Writing (3/12) = 7/12 used, leaving 5/12 for photos. After reducing writing to 1/12: Art (4/12) + Writing (1/12) = 5/12 used, leaving 7/12 for photos. Choice A represents the original photo space. Choice B would result from miscalculating the art section. Choice D incorrectly assumes only 4/12 total is used.

When adding fractions with the same denominator, we add the numerators and keep the same denominator. Since both fractions refer to parts of the same whole pizza (eighths), we add 2 + 3 = 5 eighths. Choice A incorrectly adds denominators. Choice C multiplies instead of adding. Choice D subtracts denominators, creating division by zero.

When you see a word problem with fractions that have the same denominator, you're adding and subtracting parts of a whole. Think of this pizza as being divided into 8 equal slices, and you need to track what happens to each slice.

Let's work through what happened to the pizza step by step. Alex ate $$\frac{2}{8}$$ and Jordan ate $$\frac{3}{8}$$, so together they ate $$\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$$ of the pizza. Then they set aside $$\frac{1}{8}$$ to save for later. The total pizza that's either been eaten or saved is $$\frac{5}{8} + \frac{1}{8} = \frac{6}{8}$$.

Since the whole pizza equals $$\frac{8}{8}$$, the amount left that they could still eat right now is $$\frac{8}{8} - \frac{6}{8} = \frac{2}{8}$$. This makes D correct.

Here's where the other answers go wrong: Choice A ($$\frac{6}{8}$$) represents the total amount that's been eaten or saved, not what's left to eat. Choice B ($$\frac{3}{8}$$) is just Jordan's portion alone. Choice C ($$\frac{4}{8}$$) might come from incorrectly subtracting only what Alex ate from half the pizza, but this doesn't account for Jordan's portion or the saved slice.

Remember this pattern: when solving fraction word problems, always identify what the question is actually asking for at the end. Here, they wanted the leftover amount available to eat now, not the total consumed or saved portions.

This question tests 4th grade understanding of addition and subtraction of fractions as joining and separating parts referring to the same whole (CCSS.4.NF.3.a). When fractions have the same denominator, they have the same-sized pieces—the denominator tells us the size (eighths, fourths, thirds, etc.). To add fractions with the same denominator, we join the parts by adding the numerators (the count of pieces) and keeping the denominator the same (the size of pieces). The key understanding: we're adding or subtracting the NUMBER of pieces (numerators), not the SIZE of pieces (denominator). Adding 1/5 and 2/5 means joining 1 fifth with 2 fifths, both parts of the same poster, requiring students to add the numerators and keep the denominator. Choice B is correct because adding the numerators 1 + 2 = 3, keeping denominator 5, giving 3/5, which demonstrates understanding that same-denominator fractions represent same-sized pieces, so we add the count of pieces. Choice A represents adding but changing denominator, which happens when students confuse with equivalent fractions or arithmetic errors. To help students: Use visual models like coloring a poster in fifths to show combining parts. Emphasize denominator stays the same for same size pieces, and use contexts like the same poster.

This question tests 4th grade understanding of addition and subtraction of fractions as joining and separating parts referring to the same whole (CCSS.4.NF.3.a). When fractions have the same denominator, they have the same-sized pieces—the denominator tells us the size (eighths, fourths, thirds, etc.). To subtract fractions with the same denominator, we separate parts by subtracting the numerators and keeping the denominator the same. The key understanding: we're adding or subtracting the NUMBER of pieces (numerators), not the SIZE of pieces (denominator). Subtracting 2/10 from 5/10 means starting with 5 tenths and removing 2 tenths from the same bottle, requiring students to subtract the numerators and keep the denominator. Choice A is correct because subtracting numerators 5 - 2 = 3, keeping denominator 10, giving 3/10, which demonstrates understanding that same-denominator fractions represent same-sized pieces, so we subtract the count of pieces. Choice C represents subtracting numerators but changing to a denominator of 20, which happens when students confuse with finding equivalent fractions or make an arithmetic error. To help students: Use visual models like a water bottle divided into tenths to show subtracting 2/10 from 5/10 leaves 3/10—the size (tenths) stays the same. Emphasize saying it aloud: 'five tenths minus two tenths equals three tenths,' and use concrete contexts like drinking from the same bottle to reinforce same whole.

This question tests 4th grade understanding of addition and subtraction of fractions as joining and separating parts referring to the same whole (CCSS.4.NF.3.a). When fractions have the same denominator, they have the same-sized pieces—the denominator tells us the size (eighths, fourths, thirds, etc.). To add fractions with the same denominator, we join the parts by adding the numerators (the count of pieces) and keeping the denominator the same (the size of pieces). To subtract, we separate parts by subtracting the numerators and keeping the denominator the same. The key understanding: we're adding or subtracting the NUMBER of pieces (numerators), not the SIZE of pieces (denominator). Adding 2/8 and 3/8 means joining 2 eighths with chips and 3 eighths with sprinkles from the same tray, requiring students to add the numerators and keep the denominator. Choice B is correct because adding numerators 2 + 3 = 5, keeping denominator 8, gives 5/8, demonstrating understanding that same-denominator fractions represent same-sized pieces, so we add the count of pieces. Choice A represents multiplying or wrong operation, which happens when students don't perform addition correctly. To help students: Use models like cookie trays to combine groups. Say aloud 'two eighths plus three eighths equals five eighths' to reinforce.