Question

40 which equation can be represented by the model below?
options:

• $\frac{3}{4} - \frac{3}{5} = \frac{3}{20}$
• $\frac{7}{12} - \frac{1}{4} = \frac{1}{3}$
• $\frac{6}{7} - \frac{2}{3} = \frac{4}{21}$
• $\frac{7}{12} - \frac{1}{3} = \frac{1}{4}$

Explanation:

Step1: Analyze the model (assuming the model has 10 equal parts, 6 shaded initially, then 4 unshaded? Wait, maybe the model is a bar with 10 parts, 6 shaded, then we remove some. Wait, let's check the fractions. Let's convert to tenths or twelfths? Wait, the options have fractions like 7/12, 1/3, 1/4, etc. Let's find a common denominator. Let's take the second option: 7/12 - 1/3. Convert 1/3 to 4/12. Then 7/12 - 4/12 = 3/12 = 1/4. Wait, let's check each option:

Option 1: 1/4 - 1/5. Common denominator 20: 5/20 - 4/20 = 1/20. Not matching.

Option 2: 7/12 - 1/3. 1/3 = 4/12. 7/12 - 4/12 = 3/12 = 1/4. Let's see the model: if the bar is divided into 12 parts? Wait, maybe the model has 12 parts, 7 shaded, then we remove 4 (1/3 of 12 is 4). So 7 - 4 = 3, which is 3/12 = 1/4. That matches.

Option 3: 4/7 - 3/7 = 1/7. Not related to 12 or 4.

Option 4: 7/12 - 4/7. Common denominator 84: 49/84 - 48/84 = 1/84. Not matching.

So the correct option is the second one: 7/12 - 1/3 = 1/4. Wait, but let's check the original model. If the model has 10 parts, but maybe I misread. Wait, the user's image: the model is a bar with, say, 10 parts? No, the options have 12, 7, etc. Wait, the second option: 7/12 - 1/3. Let's compute: 7/12 - 4/12 = 3/12 = 1/4. That makes sense. So the equation represented is 7/12 - 1/3 = 1/4, which is the second option (assuming the options are labeled, maybe the second option is 7/12 - 1/3 = 1/4? Wait, the user's options: let's re-express:

Looking at the options:

1. 1/4 - 1/5 =...

1. 7/12 - 1/3 = 1/4

1. 4/7 - 3/7 = 1/7

1. 7/12 - 4/7 = 1/4? No, 7/12 - 4/7 is (49 - 48)/84 = 1/84.

Wait, maybe the model is a bar with 12 units, 7 shaded, then we take away 1/3 (which is 4 units, since 12*(1/3)=4). So 7 - 4 = 3, which is 3/12 = 1/4. So the equation is 7/12 - 1/3 = 1/4, which is the second option.

Step2: Confirm each option's calculation:

Option 1: 1/4 - 1/5 = (5 - 4)/20 = 1/20. Not matching.

Option 2: 7/12 - 1/3 = 7/12 - 4/12 = 3/12 = 1/4. Correct.

Option 3: 4/7 - 3/7 = 1/7. Incorrect.

Option 4: 7/12 - 4/7 = (49 - 48)/84 = 1/84. Incorrect.

Answer:

B. $\frac{7}{12} - \frac{1}{3} = \frac{1}{4}$ (assuming the second option is labeled B, but based on the calculation, the correct equation is $\frac{7}{12} - \frac{1}{3} = \frac{1}{4}$)