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Sagot :
Sure, let's go through each of the questions one by one and solve them step by step.
Question 1:
Which answer expresses the ratio 10 feet to 12 feet as a fraction in lowest terms?
- The fraction is [tex]\(\frac{10}{12}\)[/tex]. To reduce it to lowest terms, we divide both the numerator and the denominator by their greatest common divisor (GCD).
- The GCD of 10 and 12 is 2.
- [tex]\(\frac{10 \div 2}{12 \div 2} = \frac{5}{6}\)[/tex].
The correct answer is:
C. [tex]\(\frac{5}{6}\)[/tex].
Question 2:
Write the ratio 21 students to 28 students as a fraction in lowest terms.
- The fraction is [tex]\(\frac{21}{28}\)[/tex]. To reduce it to lowest terms, we divide both the numerator and the denominator by their GCD.
- The GCD of 21 and 28 is 7.
- [tex]\(\frac{21 \div 7}{28 \div 7} = \frac{3}{4}\)[/tex].
The answer is:
[tex]\(\frac{3}{4}\)[/tex].
Question 3:
Which answer expresses the rate 24 miles per 36 minutes as a fraction in lowest terms?
- The fraction is [tex]\(\frac{24}{36}\)[/tex]. To reduce it to lowest terms, we divide both the numerator and the denominator by their GCD.
- The GCD of 24 and 36 is 12.
- [tex]\(\frac{24 \div 12}{36 \div 12} = \frac{2}{3}\)[/tex].
The correct answer is:
B. [tex]\(\frac{2}{3}\)[/tex].
Question 5:
Which answer expresses the rate 200 miles per 4 hours as a unit rate?
- The unit rate is calculated by dividing 200 miles by 4 hours.
- [tex]\(\frac{200 \text{ miles}}{4 \text{ hours}} = 50 \frac{\text{miles}}{\text{hour}}\)[/tex].
The correct answer is:
B. [tex]\(50 \frac{\text{miles}}{\text{hour}}\)[/tex].
Question 6:
Write the rate 42 ounces per 5 mugs as a unit rate. Write your answer as a decimal number.
- The unit rate is calculated by dividing 42 ounces by 5 mugs.
- [tex]\( \frac{42 \text{ ounces}}{5 \text{ mugs}} = 8.4 \frac{\text{ounces}}{\text{mug}}\)[/tex].
The answer is:
8.4.
Question 7:
In the first paragraph of an essay, Carmen wrote 70 words in 6 sentences. Which answer expresses this as a unit rate?
- The unit rate is calculated by dividing 70 words by 6 sentences.
- [tex]\(\frac{70 \text{ words}}{6 \text{ sentences}} \approx 11.6667 \frac{\text{words}}{\text{sentence}}\)[/tex].
- As a mixed number, this is [tex]\(11 \frac{2}{3} \frac{\text{words}}{\text{sentence}}\)[/tex].
The correct answer is:
A. [tex]\(11 \frac{2}{3} \frac{\text{words}}{\text{sentence}}\)[/tex].
Question 1:
Which answer expresses the ratio 10 feet to 12 feet as a fraction in lowest terms?
- The fraction is [tex]\(\frac{10}{12}\)[/tex]. To reduce it to lowest terms, we divide both the numerator and the denominator by their greatest common divisor (GCD).
- The GCD of 10 and 12 is 2.
- [tex]\(\frac{10 \div 2}{12 \div 2} = \frac{5}{6}\)[/tex].
The correct answer is:
C. [tex]\(\frac{5}{6}\)[/tex].
Question 2:
Write the ratio 21 students to 28 students as a fraction in lowest terms.
- The fraction is [tex]\(\frac{21}{28}\)[/tex]. To reduce it to lowest terms, we divide both the numerator and the denominator by their GCD.
- The GCD of 21 and 28 is 7.
- [tex]\(\frac{21 \div 7}{28 \div 7} = \frac{3}{4}\)[/tex].
The answer is:
[tex]\(\frac{3}{4}\)[/tex].
Question 3:
Which answer expresses the rate 24 miles per 36 minutes as a fraction in lowest terms?
- The fraction is [tex]\(\frac{24}{36}\)[/tex]. To reduce it to lowest terms, we divide both the numerator and the denominator by their GCD.
- The GCD of 24 and 36 is 12.
- [tex]\(\frac{24 \div 12}{36 \div 12} = \frac{2}{3}\)[/tex].
The correct answer is:
B. [tex]\(\frac{2}{3}\)[/tex].
Question 5:
Which answer expresses the rate 200 miles per 4 hours as a unit rate?
- The unit rate is calculated by dividing 200 miles by 4 hours.
- [tex]\(\frac{200 \text{ miles}}{4 \text{ hours}} = 50 \frac{\text{miles}}{\text{hour}}\)[/tex].
The correct answer is:
B. [tex]\(50 \frac{\text{miles}}{\text{hour}}\)[/tex].
Question 6:
Write the rate 42 ounces per 5 mugs as a unit rate. Write your answer as a decimal number.
- The unit rate is calculated by dividing 42 ounces by 5 mugs.
- [tex]\( \frac{42 \text{ ounces}}{5 \text{ mugs}} = 8.4 \frac{\text{ounces}}{\text{mug}}\)[/tex].
The answer is:
8.4.
Question 7:
In the first paragraph of an essay, Carmen wrote 70 words in 6 sentences. Which answer expresses this as a unit rate?
- The unit rate is calculated by dividing 70 words by 6 sentences.
- [tex]\(\frac{70 \text{ words}}{6 \text{ sentences}} \approx 11.6667 \frac{\text{words}}{\text{sentence}}\)[/tex].
- As a mixed number, this is [tex]\(11 \frac{2}{3} \frac{\text{words}}{\text{sentence}}\)[/tex].
The correct answer is:
A. [tex]\(11 \frac{2}{3} \frac{\text{words}}{\text{sentence}}\)[/tex].
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