Chapter 1 Use Positive Rational Numbers
Mid Topic
Page 25 Exercise 1 Answer
Find the closest whole number to the given decimal number which can be divided by given whole number. That is the required compatible number. Dividing that compatible number by the given whole number gives us the estimate.
Result
The required compatible number is the closest whole number to the given decimal number. Divide that number by the given whole number to get an estimate.
Page 25 Exercise 2 Answer
Keaton is building a rectangular tabletop and wnats to put a metal border around the edge. The length of the tabletop is 1.83 meters and the width is 0.74 meter. Use the formula P = 2l + 2w to find the perimeter of the tabletop.
P = 2l + 2w = 2 x 1.83 + 2 x 0.74
P = 2 x 1.83 + 2 x 0.74 = 1.48 + 3.66
P = 1.48 + 3.66 = 5.14
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Result
The perimeter of the tabletop is 5.14 meters.
Page 25 Exercise 3 Answer
Norbert’s Nursery is having a sale. Flats of flowers are priced as follows: petunias 5.25 per flat, daisy 7.65 per flat, and begonia 8.40 per flat. Jake buys 2 flats of petunias, 3 flats of daisies, and 1 flat of begonias. If he pays with a 50 bill, how much change should Jake receive?
First, we must calculate the exact price of the flowers.
2 x 5.25 + 3 x 7.65 + 1 x 8.40 = ?
2 x 5.25 + 3 x 7.65 + 1 x 8.40 = 10.50 + 22.95 + 8.40
10.50 + 22.95 + 8.40 = 41.85
The exact price Jake must pay is 41.85.
Jake paid with a 50 bill, and he received change which is the difference between 50 and 41.85.
Result
Jake received $8.15 of change.
Page 25 Exercise 4 Answer
It is given that \(\frac{1}{4}\) page in the book costs $ 15.50 and we need to complete the table to find the cost for \(\frac{2}{4}\) page, \(\frac{3}{4}\) page, and \(\frac{4}{4}\) page.
Since \(\frac{2}{4}=2 \times \frac{1}{4}\), we can multiply the cost for \(\frac{1}{4}\) page by 2 to get the cost for \(\frac{2}{4}\) page:
Similarly, we can find the costs for \(\frac{3}{4}\) page and \(\frac{4}{4}\) page by multiplying the cost for \(\frac{1}{4}\) page by 3 and 4:
The table is then completed as:
Now we need to determine which of the given expressions can be used to find the cost for \(\frac{3}{4}\) page:
3 x $15.50 was teh expression we used to find the cost for the table, so the expression 3 x $15.50 is correct.
$1.50 + $15.50 + $15.50 is the repeated addition form of 3 x $15.50. The expression $1.50 + $15.50 + $15.50 is then also correct.
We know that \(\frac{3}{4} \times \$ 15.50 \neq 3 \times \$ 15.50\) so the expression \(\frac{3}{4}\) x $15.50 is not correct.
Using the Distributive Property gives:
(4 x $15.50) – $15.50 = (4 – 1) x $15.50 = 3 x $15.50
The expression (4 x $15.50) – $15.50 is then also correct.
3 + $15.50 is not correct since we know the total cost needs to be 3 times $15.50, not 3 plus $15.50.
Result
3 x $15.50, $15.50 + $15.50 + $15.50, and (4 x $15.50) – $15.50
Page 25 Exercise 5 Answer
Latisha hired 4 babysitters in the last month, paid a total of $170 in babysitting fees, each babysitter worked a total of 5 hours and is paid the same amount. We need to find how much each babysitter earns per hour.
Each babysitter is then paid $42.50 in total.
Each babysitter is then paid $8.50 per hour.
Result
Each babysitter is paid $8.50 per hour.
Page 25 Exercise 6 Answer
It is given that Lucia walks \(2 \frac{3}{4}\) miles on Monday and walks \(1 \frac{1}{2}\) times farther on Tuesday.
To find how far she walked on Tuesday, we must multiply \(2 \frac{3}{4}\) and \(1 \frac{1}{2}\).
To multiply two mixed numbers, rewrite each mixed number as an improper fraction. Then multiply the numerators and multiply the denominators. Reduce the fraction and rewrite as a mixed number if necessary:
\(2 \frac{3}{4} \times 1 \frac{1}{2}=\frac{11}{4} \times \frac{3}{2}=\frac{11 \times 3}{4 \times 2}=\frac{33}{8}=4 \frac{1}{8}\)Lucia then walked \(4 \frac{1}{8}\) miles on Tuesday.
Result
\(4 \frac{1}{8}\) miles
Page 26 Exercise 1a Answer
Team members Eric and Natalia secure a grant for $75.00 and need to buy 3 beams and 6 channels. We need to determine if the grant will cover the cost, and if so, how much of the grant will remain.
A beam costs $5.95 and a channel costs $8.50.
The cost is $68.85 so the grant will cover the cost.
After they buy beams and channels, there will be left $6.15 of the grant.
Result
The grant will cover the cost and $6.15 will remain.
Page 26 Exercise 1b Answer
We know 3 teams members will equally share the cost of 2 motor controllers and 4 wheels.
From the table, the cost of 1 motor controller is $99.75 and the cost of 1 wheel is $18.90. The cost of 2 controllers and the cost of 4 wheels are then:
The total cost of the 2 controllers and 4 wheels is then:
Since they share the total cost evenly, we can divide the total cost by 3 to find how much each person pays:
Each person then contributed $91.70.
Result
$91.70
Page 26 Exercise 1c Answer
Nyan Robotics has a budget of $99 to buy sprockets, axles, and gears and they spend \(\frac{2}{3}\) of the budget on sprockets. We need to find how much money from the budget remains to buy axles and gears.
If they spent \(\frac{2}{3}\) on sprockets, it means they spent \(\frac{2}{3}\) of $99 on sprockets, and the rest was left to be spent on axles and gears.
\(\frac{2}{3} \times 99=\frac{2}{3} \times \frac{99}{1}=\frac{2 \times 99}{3 \times 1}=\frac{198}{3}=66\)$66 was spent on sprockets.
99 – 66 = 33
$33 remains to buy axles and gears.
Result
$33 remains to buy axles and gears.