Scott was $63 \frac{3}{8}$ inches tall when he started seventh grade and $65 \frac{1}{4}$ inches tall when he started eighth grade. How many inches did he grow during this time?
A. $2 \frac{5}{8}$
B. $1 \frac{3}{4}$
C. $2 \frac{1}{2}$
D. $1 \frac{7}{8}$
Answer (2)
Convert the mixed numbers to improper fractions: 65 4 1 = 4 261 and 63 8 3 = 8 507 .
Find a common denominator and subtract: 4 261 − 8 507 = 8 522 − 8 507 = 8 15 .
Convert the result back to a mixed number: 8 15 = 1 8 7 .
Scott grew 1 8 7 inches.
Explanation
Understanding the Problem We are given Scott's height at the start of seventh grade ( 63 8 3 inches) and his height at the start of eighth grade ( 65 4 1 inches). We need to find the difference between these two heights to determine how much he grew during this time.
Setting up the Subtraction To find the difference in height, we subtract Scott's height at the start of seventh grade from his height at the start of eighth grade. This can be written as: 65 4 1 − 63 8 3
Converting to Improper Fractions First, let's convert the mixed numbers to improper fractions. 65 4 1 = 4 65 × 4 + 1 = 4 260 + 1 = 4 261 63 8 3 = 8 63 × 8 + 3 = 8 504 + 3 = 8 507
Finding a Common Denominator Now we have the subtraction problem: 4 261 − 8 507 To subtract these fractions, we need a common denominator. The least common denominator for 4 and 8 is 8. So, we convert 4 261 to a fraction with a denominator of 8: 4 261 = 4 × 2 261 × 2 = 8 522
Subtracting the Fractions Now we can subtract the fractions: 8 522 − 8 507 = 8 522 − 507 = 8 15
Converting Back to a Mixed Number Finally, we convert the improper fraction 8 15 back to a mixed number: 8 15 = 1 8 7 So, Scott grew 1 8 7 inches during this time.
Examples
Understanding growth rates is useful in many real-world scenarios. For example, tracking the growth of a plant over time can help determine the effectiveness of different fertilizers. Similarly, monitoring a child's growth can help ensure they are developing healthily. In finance, understanding growth rates is crucial for making informed investment decisions. The ability to calculate and interpret growth rates is a valuable skill in various fields.
Scott grew 1 8 7 inches from the start of seventh grade to the start of eighth grade. This was calculated by converting his heights to improper fractions, finding a common denominator, and then subtracting the two heights. The correct answer is option D: 1 8 7 .
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