Sure! Let's answer each question one by one.
26. Vocabulary
A rational number can be written as the ratio of one integer to another and can be represented by a repeating or terminating decimal.
27. Problem Solving
To determine which boy is taller, we need the heights of Marcus and Ben in feet. If Marcus is "X" feet tall and Ben is "Y" feet tall, then we can justify that if X > Y, Marcus is taller, and if Y > X, Ben is taller. If X = Y, both boys are the same height. Without specific heights, we cannot identify who is taller.
28. Represent Real-World Problems
Let's say Store A sells a certain fraction of a bushel of apples for $9, and Store B sells another fraction for $9. To determine which store has the better deal, you need to find out how much apples you get per dollar at each store.
For example:
- If Store A is selling 1/2 of a bushel of apples for $9, then you’re paying $9 for 0.5 bushel, so that’s $18 per bushel.
- If Store B is selling 1/3 of a bushel of apples for $9, then you’re paying $9 for approximately 0.333 bushel, which is $27 per bushel.
Based on this hypothetical example, Store A is a better deal. Please plug in the actual fractions to make a comparison.
29. Analyze Relationships
If a fraction is in simplest form and results in a repeating decimal, then the denominator must have prime factors other than 2 and 5. The numbers from 1 to 10 that could be the denominator are:
- 3 (which gives 0.333...)
- 6 (which gives 0.166...)
- 7 (which gives 0.142857...)
- 8 (which is terminating but does not apply)
- 9 (which gives 0.111...)
- 10 (which is terminating but does not apply)
Thus, the possible denominators from 1 to 10 that result in a repeating decimal are 3, 6, 7, and 9.
30. Communicate Mathematical Ideas
To compare Julie's scores, we need to convert the correct answers into fractions:
- Math: 21 out of 23, which is \( \frac{21}{23} \approx 0.913 \)
- Science: 29 out of 32, which is \( \frac{29}{32} \approx 0.90625 \)
From the calculations above, since \( 0.913 > 0.90625 \), Julie scored higher on her math test than her science test. You can compare the fractions directly as above, or cross-multiply to avoid decimals:
- \( 21 \times 32 = 672 \)
- \( 29 \times 23 = 667 \)
Since 672 > 667,math test > science test.
31. Look for a Pattern
The decimal 0.121122111222... does not appear to be a repeating decimal. Instead, it follows a pattern where the number of 1s increases after each whole number, meaning it doesn’t settle into a fixed repeating section. Therefore, it is classified as a non-repeating (non-terminating) decimal.
If you have any further questions or need clarification on any points, feel free to ask!