Unit 5, Lesson 9
Multiplying Rational Numbers (Part 2)
Grade 7
Practice
Problem 1
Complete each equation with the number that makes it true.
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\(\text-2 \boldcdot (\text-4.5) = {?}\)
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\((\text-8.7) \boldcdot (\text-10) = {?}\)
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\(\text-7 \boldcdot {?} = 14\)
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\({?} \boldcdot (\text-10) = 90\)
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Problem 2
A weather station on the top of a mountain reports that the temperature is currently \(0^\circ\text{C}\) and has been falling at a constant rate of \(3^\circ\text{C}\) per hour. If it continues to fall at this rate, find each indicated temperature. Explain or show your reasoning.
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What will the temperature be in 2 hours?
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What will the temperature be in 5 hours?
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What will the temperature be in \(\frac12\) hour?
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What was the temperature 1 hour ago?
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What was the temperature 3 hours ago?
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What was the temperature 4.5 hours ago?
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Problem 3
Find the value of each expression.
- \(\frac14 \boldcdot (\text-12)\)
- \(\text{-}\frac {1}{3} \boldcdot 39\)
- \((\text{-}\frac {4}{5}) \boldcdot (\text-75)\)
- \(\text{-}\frac {2}{5} \boldcdot (\text{-}\frac {3}{4})\)
- \(\frac83 \boldcdot \text-42\)
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Problem 4
George Washington Carver was a scientist who experimented with natural ways that farmers could improve their soil and grow more crops.
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In 1897 he spent about \$16 on his experiment, and his crops earned about \$10. How much profit was made?
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After improving the soil for 5 years, in 1902 he spent \$12 on his experiment, and his crops earned \$50. How much profit was made?
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How much greater was the profit in 1902 than in 1897?
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- Here are the vertices of rectangle \(FROG\): \((\text-2,5), (\text-2,1), (6,5), (6,1)\). Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane.
- Find the area of the rectangle \(FROG\).
- Here are the coordinates of rectangle \(PLAY\): \((\text-11, 20), (\text-11, \text-3), (\text-1, 20), (\text-1, \text-3)\). Find the perimeter and area of this rectangle. See if you can figure out its side lengths without plotting the points.
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Problem 6
To make a specific hair dye, a hair stylist uses a ratio of \(1\frac18\) oz of red tone, \(\frac 34\) oz of gray tone, and \(\frac58\) oz of brown tone.
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If the stylist needs to make 20 oz of dye, how much of each dye color is needed?
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If the stylist needs to make 100 oz of dye, how much of each dye color is needed?
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