Question

1. a student jumps $40\frac{5}{12}$ inches for the high jump. on his second try, he jumps $1\frac{8}{12}$ inches higher. he can tie the school record if he raises the bar another $3\frac{10}{12}$ inches and successfully jumps over it. what is the school record for the high jump?

Explanation:

Step1: Add the first two jumps

First, we need to add the initial jump height \( 40\frac{5}{12} \) inches and the additional height from the second try \( 1\frac{8}{12} \) inches. To add mixed numbers, we add the whole numbers and the fractions separately.

The whole numbers: \( 40 + 1 = 41 \)

The fractions: \( \frac{5}{12} + \frac{8}{12} = \frac{5 + 8}{12} = \frac{13}{12} = 1\frac{1}{12} \)

Now, add the results from the whole numbers and the fractions: \( 41 + 1\frac{1}{12} = 42\frac{1}{12} \) inches. This is the height after the second try.

Step2: Add the final increment

Next, we need to add the additional height \( 3\frac{10}{12} \) inches to the height after the second try \( 42\frac{1}{12} \) inches to get the school record.

Again, add the whole numbers and the fractions separately.

The whole numbers: \( 42 + 3 = 45 \)

The fractions: \( \frac{1}{12} + \frac{10}{12} = \frac{1 + 10}{12} = \frac{11}{12} \)

Now, combine the whole number and the fraction: \( 45 + \frac{11}{12} = 45\frac{11}{12} \) inches.

Answer:

The school record for the high jump is \( 45\frac{11}{12} \) inches.