Number and Operations>Applying Operations with Rational Numbers to Solve Problems(TEKS.Math.7.3.B)
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Texas 7th Grade Math › Number and Operations>Applying Operations with Rational Numbers to Solve Problems(TEKS.Math.7.3.B)
The temperature at sunrise was 18.4°F. It dropped 2.6°F each hour for 3.5 hours, then rose 4.75°F around noon. A cold front then decreased the temperature by 1.2°F. What is the final temperature with correct units?
What is the final temperature?
12.85°F
33.45°F
14.05°F
9.30°F
Explanation
Model the situation with signed numbers and a rate: $18.4 - 2.6 \times 3.5 + 4.75 - 1.2$. Compute: $2.6 \times 3.5 = 9.1$, so $18.4 - 9.1 = 9.3$, $9.3 + 4.75 = 14.05$, and $14.05 - 1.2 = 12.85$. Final temperature: 12.85°F, which makes sense because overall there was more cooling than warming.
A recipe that serves 6 people uses 2 2/3 cups of flour. How much flour is needed for 4 people, and how much extra flour would be used if you accidentally made enough for 9 people instead of 4?
What are the two amounts (for 4 people; and the extra if making for 9)?
$1 \tfrac{1}{3}$ cups; extra $1 \tfrac{2}{3}$ cups
$1 \tfrac{7}{9}$ cups; extra $2 \tfrac{2}{9}$ cups
$1 \tfrac{5}{9}$ cups; extra $2 \tfrac{4}{9}$ cups
$1 \tfrac{7}{9}$ cups; extra $4$ cups
Explanation
Total flour for 6 is $2\tfrac{2}{3}=\tfrac{8}{3}$ cups. Per person: $\tfrac{8}{3}\div 6=\tfrac{8}{18}=\tfrac{4}{9}$ cup. For 4 people: $4\cdot \tfrac{4}{9}=\tfrac{16}{9}=1\tfrac{7}{9}$ cups. For 9 people: $9\cdot \tfrac{4}{9}=4$ cups. Extra compared to the 4-person amount: $4-\tfrac{16}{9}=\tfrac{20}{9}=2\tfrac{2}{9}$ cups. These values are proportional to servings, so they are reasonable.
Mia's bank account is at a negative balance of \$18.75. She deposits \$32.40, then makes 3 purchases of \$5.25 each, and later receives a \$4.50 refund. What is her final balance?
What is the final balance?
-7
21
2
-2
Explanation
Use signed operations: starting at $-18.75$, add deposit, subtract purchases, add refund: $-18.75 + 32.40 - 3(5.25) + 4.50$. Compute $3(5.25)=15.75$. Then $-18.75 + 32.40 = 13.65$, $13.65 - 15.75 = -2.10$, and $-2.10 + 4.50 = 2.40$. The small positive balance $\$2.40$ makes sense after covering the overdraft.
A hiker starts at an elevation of 150 feet. She descends 65.5 feet, climbs 28.75 feet, then takes a detour that descends at 12.5 feet per minute for 2.4 minutes. What is her final elevation?
What is the final elevation with correct units?
113.25 ft
143.25 ft
214.25 ft
83.25 ft
Explanation
Translate each change into signed operations. The detour descent is $12.5\times 2.4=30$ feet. Compute: $150 - 65.5 + 28.75 - 30 = 83.25$ ft. This is below the start, which fits the overall net descent.