Jack spent 15 minutes on his math homework last night and 20 minutes on his reading homework.  What is the ratio of time Jack spent on his math homework to the total amount of time Jack spent on homework last night?

Question 7 options:

3 to 4


7 to 3


3 to 7 


4 to 3

To find the ratio of time Jack spent on his math homework to the total amount of time he spent on homework last night, follow these steps:

### Step 1: Determine the time spent on each activity.
- Time spent on math homework: 15 minutes
- Time spent on reading homework: 20 minutes

### Step 2: Calculate the total time spent on homework.
\[
\text{Total time spent on homework} = 15 \text{ minutes} + 20 \text{ minutes} = 35 \text{ minutes}
\]

### Step 3: Calculate the ratio of time spent on math homework to the total time.
\[
\text{Ratio} = \frac{\text{Time spent on math}}{\text{Total time spent on homework}} = \frac{15}{35}
\]

### Step 4: Simplify the ratio.
To simplify \( \frac{15}{35} \), find the greatest common divisor (GCD) of 15 and 35, which is 5.

\[
\frac{15 \div 5}{35 \div 5} = \frac{3}{7}
\]

So, the ratio is 3 to 7.

Thus, the correct answer is **3 to 7**.

Would you like more details on any step, or do you have any questions? 

Here are 5 related questions you might find interesting:
1. How do you simplify a ratio?
2. What is a proportion, and how does it relate to ratios?
3. How can you express a ratio as a fraction or a decimal?
4. How do you solve word problems involving ratios?
5. Can a ratio be greater than 1?

**Tip:** When solving ratio problems, always simplify the ratio by dividing both terms by their greatest common divisor (GCD).

Learn how to calculate the ratio of time spent on math homework to total homework time with a step-by-step solution. This problem covers key concepts such as ratios, fractions, and the use of GCD in simplification. Suitable for students in Grades 5-7.

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