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Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 18.6 Volume of a Solid existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 18.6 Volume of a Solid

Exercises
SOLVE

Question 1.
What is the volume of a cube with sides of 10 inches?

Answer:
Volume of the cube = 1,000 cubic inches.

Explanation:
Sides of the cube = 10 inches.
Volume of the cube = Sides of the cube × Sides of the cube × Sides of the cube
= 10 × 10 × 10
= 100 × 10
= 1,000 cubic inches.

Question 2.
A shoe box has dimensions of 12 inches by 8 inches by 6 inches. How many cubic feet is it?
Answer:
Volume of the show box = 0.33 cubic feet.

Explanation:
Length of the show box = 12 inches.
Width of the show box = 8 inches.
Height of the show box = 6 inches.
Volume of the show box = Length of the show box × Width of the show box × Height of the show box
= 12 × 8 × 6
= 96 × 6
= 576 cubic inches.
Conversion:
1 cubic feet = 1728 cubic inches
?? cubic feet = 576 cubic inches
=> 1 × 576 = 1728 × ??
=> 576 ÷ 1728 = ??
=> 0.33 cubic feet = ??

Question 3.
A rectangular solid with sides of 9 ft by 5 ft by 13 ft has what volume?
Answer:
Volume of the rectangular solid = 585 cubic feet.

Explanation:
Length of the rectangular solid = 13 ft.
Width of the rectangular solid = 9 ft.
Height of the rectangular solid = 5 ft.
Volume of the rectangular solid = Length of the rectangular solid × Width of the rectangular solid × Height of the rectangular solid
= 13 × 9 × 5
= 117 × 5
= 585 cubic feet.

Question 4.
A cube that has sides of 120 inches has how many cubic yards of volume?
Answer:
Volume of the cube = 37.037 cubic yards.

Explanation:
Side of the cube = 120 inches.
Volume of the cube = Side of the cube × Side of the cube × Side of the cube
= 120 × 120 × 120
= 14400 × 120
= 17,28,000 cubic inches.
Conversion:
1 cubic yard = 46,656 cubic inches.
?? cubic yard = 17,28,000 cubic inches.
=> 1 × 17,28,000 = 46,656 × ??
=> 17,28,000 ÷ 46,656 = ??
=> 37.037 cubic yards = ??

Question 5.
A storage container in the form of a rectangular solid has dimensions of 12 inches by 30 inches by 16 inches. If a pound of sugar takes up \(\frac{1}{4}\) sq ft, how many pounds of sugar can you put in the container?
Answer:
Number of pounds of sugar can be put in the container = 23,040.

Explanation:
Length of the rectangular solid = 30 inches.
Width of the rectangular solid = 16 inches.
Height of the rectangular solid = 12 inches.
Volume of the rectangular solid = Length of the rectangular solid × Width of the rectangular solid × Height of the rectangular solid
= 30 × 16 × 12
= 480 × 12
= 5,760 cubic inches.
Area of the pound of sugar = \(\frac{1}{4}\) sq ft.
Number of pounds of sugar can be put in the container = Volume of the rectangular solid ÷ Area of the pound of sugar
= 5,760 ÷ \(\frac{1}{4}\)
= 5,760 × \(\frac{4}{1}\)
= 23,040.

Question 6.
A parking lot measures 420 ft long and 162 ft wide. If a construction company is told that it needs to have 3 feet of asphalt under the parking lot for proper drainage, how many cubic yards do they need to order?
Answer:
Volume of the asphalt under the parking lot for proper drainage required = 7,560 cubic yards.

Explanation:
Length of the parking lot = 420 ft.
Width of the parking lot = 162 ft.
Area of the parking lot = Length of the parking lot × Width of the parking lot
= 420 × 162
= 68,040 square feet.
Length of the asphalt under the parking lot for proper drainage = 3 feet.
Volume of the asphalt under the parking lot for proper drainage required = Area of the parking lot × Length of the asphalt under the parking lot for proper drainage
= 68,040 × 3
= 204,120 cubic feet.
Conversion:
1 cubic yard  = 27 cubic feet.
?? cubic yards = 2,04,120 cubic feet.
=> 1 × 2,04,120  = 27 ÷ ??
=> 2,04,120 ÷ 27 = ??
=> 7,560 cubic yards = ??

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 18.5 Area existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 18.5 Area

Exercises
SOLVE
Question 1.
How many people can you allow on a beach if the lifeguards want to have 20 sq ft per person and the beach is 1,000 ft long and 200 ft wide? Round to a whole number.
Answer:
Number of people can be allow on a beach = 10,000.

Explanation:
Length of the beach = 1,000 ft.
Width of the beach = 200 ft.
Area of the beach =  Length of the beach × Width of the beach
= 1,000 × 200
= 2,00,000 square feet.
Number of square feet each person wants = 20 square feet.
Number of people can be allow on a beach = Area of the beach ÷ Number of square feet each person wants
= 2,00,000 ÷ 20
= 10,000.

Question 2.
A square that has sides of 25 ft is split in half down the middle. What is the area of each of the pieces?
Answer:
Area of each of the piece = 312.5 square feet.

Explanation:
Side of the square = 25 ft.
A square that has sides of 25 ft is split in half down the middle.
Area of each of the piece = \(\frac{1}{2}\) × Side of the square × Side of the square
= \(\frac{1}{2}\) × 25 × 25
= \(\frac{1}{2}\) × 625
= 312.5 square feet.

Question 3.
A right triangle has a base of 24 feet and a height of 7 feet. What is its area?

Answer:
Area of the right triangle = 84 square feet.

Explanation:
Base of the right triangle = 24 feet.
Height of the right triangle = 7 feet.
Area of the right triangle = \(\frac{1}{2}\) × Base of the right triangle × Height of the right triangle
= \(\frac{1}{2}\) × 24 × 7
= \(\frac{1}{1}\) × 12 × 7
= 84 square feet.

Question 4.
Which has a larger area, a triangle with a base of 15 ft and a height of 25 ft or a square with sides of 14 ft?

Answer:
Square has a larger area than a triangle with a base of 15 ft and a height of 25 ft.

Explanation:
Base of the triangle = 15 feet.
Height of the triangle = 25 feet.
Area of the triangle = \(\frac{1}{2}\) × Base of the triangle × Height of the triangle
= \(\frac{1}{2}\) × 15 × 25
= \(\frac{1}{2}\) × 375
= 187.5 square feet.
Side of the square = 14 feet.
Area of the square = Side of the square × Side of the square
= 14 × 14
= 196 square feet.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 18.4 Perimeter existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 18.4 Perimeter

Exercises
SOLVE
Question 1.
Which has a longer perimeter, a triangle with sides of 26 feet or a hexagon with sides of 18 feet?
Answer:
Hexagon has a longer perimeter than a triangle with sides of 26 feet.

Explanation:
Side of triangle = 26 feet.
Perimeter of triangle = Side of triangle + Side of triangle+ Side of triangle
=26 + 26 + 26
= 52 + 26
= 78 feet.
Side of hexagon = 18 feet.
Perimeter of hexagon = 6 × Side of hexagon
= 6 × 18
= 108 feet.

Question 2.
If Trent walks east for 25 feet, then north for 30 feet, then west for 25 feet, how long would he have to walk to get to his starting point and how long did he walk in total?
Answer:
Total number of feet Trent walks in all = 110.

Explanation:
Number of feet Trent walks east = 25.
Number of feet Trent walks north = 30
Number of feet Trent walks west = 25.
Number of feet Trent walks south = 30.
Total number of feet Trent walks in all = Number of feet Trent walks east + Number of feet Trent walks west + Number of feet Trent walks north + Number of feet Trent walks south
= 25 + 30 + 25 + 30
= 55 + 25 + 30
= 80 + 30
= 110.

Question 3.
If you have a 120-foot piece of fencing wire, how long would each side of a square-shaped corral be if all the fencing is used?
Answer:
Each side of square- shaped corral would be 30 feet if all the fencing is used.

Explanation:
Number of feet is the piece of fencing wire = 120.
Perimeter of square-shaped corral = 4 × side of square- shaped corral
=> 120 = 4 × side of square- shaped corral
=> 120 ÷ 4 = side of square- shaped corral
=> 30 = side of square- shaped corral

Question 4.
If you want to put a ribbon around a rectangular box with sides of 5 and 10 inches, how much ribbon would you need?
Answer:
Perimeter of the rectangular box = 30 inches.

Explanation:
Length of the rectangular box = 10 inches.
Width of the rectangular box = 5 inches.
Perimeter of the rectangular box = 2 (Length of the rectangular box + Width of the rectangular box)
= 2 (10 + 5)
= 2 × 15
= 30.

Question 5.
What is the perimeter of the figure shown?

Answer:
Perimeter of the given figure = 72 feet.

Explanation:
Length of first side of the given figure = 20 feet.
Length of second side of the given figure = 15 feet.
Length of third side of the given figure = 22 feet.
Length of fourth side of the given figure = 15 feet.
Perimeter of the given figure = Length of first side of the given figure + Length of second side of the given figure + Length of third side of the given figure + Length of fourth side of the given figure
= 20 + 15 + 22 + 15
= 35 + 22 + 15
= 57 + 15
= 72 feet.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 18.3 Customary Units of Weight existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 18.3 Customary Units of Weight

Exercises
CALCULATE
Question 1.
20 pounds is how many ounces?
Answer:
20 pounds is equal to 320 ounces.

Explanation:
Conversion:
1 pound = 16 ounces.
20 pounds = ?? ounces
=> 1 × ?? = 16 × 20
=> ?? = 320 ounces.

Question 2.
5.2 tons is how many pounds?
Answer:
5.2 tons is equal to 10,400 pounds.

Explanation:
Conversion:
1 ton = 2,000 pounds.
5.2 tons = ?? pounds
=> 1 × ?? = 2,000 × 5.2
=> ?? = 10,400 pounds.

Question 3.
4 tons is how many ounces?
Answer:
4 tons is equal to 1,28,000 ounces.

Explanation:
Conversion:
1 ton = 32,000 ounces.
4 tons = ?? ounces.
=> 1 × ?? = 32,000 × 4
=> ?? = 1,28,000 ounces.

Question 4.
196 ounces is how many pounds?
Answer:
196 ounces is equal to 3,136 ounces.

Explanation:
Conversion:
1 pound = 16 ounces.
196 ounces = ?? ounces.
=> 1 × ?? = 16 × 196
=> ?? = 3,136 ounces.

Question 5.
3.5 tons is how many pounds?
Answer:
3.5 tons is equal to 7,000 pounds.

Explanation:
Conversion:
1 ton = 2,000 pounds.
3.5 tons = ?? pounds.
=> 1 × ?? = 2,000 × 3.5
=> ?? = 7,000 pounds.

Question 6.
1,600 pounds is how many tons?
Answer:
1,600 pounds is equal to 0.8 tons.

Explanation:
Conversion:
1 ton = 2,000 pounds.
?? tons = 1,600 pounds
=> 1 × 1,600 = 2,000 × ??
=> 1,600 ÷ 2,000 = ??
=> 0.8 tons = ??

Question 7.
1.5 tons is how many ounces?
Answer:
1.5 tons is equal to 48,000 ounces.

Explanation:
Conversion:
1 ton = 32,000 ounces.
1.5 tons = ?? ounces.
=> 1 × ?? = 32,000 × 1.5
=> ?? = 48,000 ounces.

Question 8.
680 ounces is how many pounds?
Answer:
680 ounces is equal to 42.5 ounces.

Explanation:
Conversion:
1 pound = 16 ounces.
?? pounds = 680 ounces
=> 1 × 680 = 16 × ??
=> 680 ÷ 16 = ??
=> 42.5 ounces = ??

Question 9.
3.2 tons is how many pounds?
Answer:
3.2 tons is equal to 6,400 pounds.

Explanation:
Conversion:
1 ton = 2,000 pounds.
3.2 tons  = ?? pounds.
=> 1 × ?? = 2,000 × 3.2
=> ?? = 6,400 pounds.

Question 10.
48,000 ounces is how many tons?
Answer:
48,000 ounces is equal to

Explanation:
Conversion:
1 ton = 32,000 ounces
?? tons = 48,000 ounces
=> 1 × 48,000 = 32,000 × ??
=> 48,000 ÷ 32,000 = ??
=> 1.5 tons = ??

Question 11.
65.2 lbs is how many ounces?
Answer:
65.2 lbs is equal to 1,043.2 pounds.

Explanation:
Conversion:
1 pound = 16 ounces.
65.2 lbs = ?? pounds
=> 1 × ?? = 16 × 65.2
=> ?? = 1,043.2 pounds.

Question 12.
80,000 ounces is how many tons?
Answer:
80,000 ounces is equal to 2.5 tons.

Explanation:
Conversion:
1 ton = 32,000 ounces.
?? tons = 80,000 ounces
=> 1 × 80,000 = 32,000 × ??
=>  80,000 ÷ 32,000  = ??
=> 2.5 tons = ??

Question 13.
Three 200-pound men weigh how many tons?
Answer:
Three 200-pound men weigh is equals to 1.6 tons.

Explanation:
Conversion:
1 ton = 2,000 pounds.
?? tons = 3,200 pound men
=> 1 × 3,200 = 2,000 × ??
=> 3,200 ÷ 2,000 = ??
=> 1.6 tons = ??

Question 14.
A 13.5-ton elephant weighs how many pounds?
Answer:
A 13.5-ton elephant weighs equal to 27,000 pounds.

Explanation:
Conversion:
1 ton = 2,000 pounds.
13.5-ton elephant = ?? pounds
=> 1 × ?? = 2,000 × 13.5
=> ?? = 27,000 pounds.

Question 15.
A 1\(\frac{3}{4}\) ton truck can carry 1 \(\frac{3}{4}\) of a ton of materials in its bed. How many pounds is that?
Answer:
Number of tons of materials in its bed truck can carry = 3,500 pounds.

Explanation:
Number of tons truck = 1\(\frac{3}{4}\)
Number of tons of materials in its bed truck can carry = 1 \(\frac{3}{4}\)
Conversion:
1 ton = 2,000 pounds.
1 \(\frac{3}{4}\)  tons = ?? pounds
=> 1 × ?? = 2,000 × 1 \(\frac{3}{4}\)
=> ?? = 2,000 × {[(1× 4) + 3] ÷ 4}
=> ?? = 2,000 × [(4 + 3) ÷ 4]
=> ?? = 2,000 × \(\frac{7}{4}\)
=> ?? = 500 × \(\frac{7}{1}\)
=> ?? = 3,500 pounds.

Question 16.
If there are 1,050 students at school and each eats 3 ounces of turkey burger for lunch, how many pounds of turkey burger is that?
Answer:
Total quantity of pounds of turkey burger for lunch all students ate = 196.875.

Explanation:
Number of students at school = 1,050.
Quantity of ounces of turkey burger for lunch each eats = 3.
Total quantity of ounces of turkey burger for lunch all students ate = Number of students at school × Quantity of ounces of turkey burger for lunch each eats
= 1,050 × 3
= 3,150.
Conversion:
Total quantity of pounds of turkey burger for lunch all students ate =
1 pound = 16 ounces.
?? pounds = 3,150 ounces.
=> 1 × 3,150 = 16 × ??
=> 3,150 ÷ 16 = ??
=> 196.875 pounds = ??

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 18.2 Customary Units of Liquid Volume existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 18.2 Customary Units of Liquid Volume

Exercises
CALCULATE
Question 1.
4 gallons is how many pints?
Answer:
4 gallons is equal to 32 pints.

Explanation:
Conversion:
1 gallon = 8 pints.
4 gallons = ?? pints.
=> 1 × ?? = 8 × 4
=> ?? = 32 pints.

Question 2.
A 33-gallon gas tank has how many quarts?
Answer:
A 33-gallon gas tank has 132 quarts.

Explanation:
Conversion:
1 gallon = 4 quarts.
33 gallon = ?? quarts
=> 1 × ?? = 4 × 33
=> ?? = 132 quarts.

Question 3.
64 quarts is how many gallons?
Answer:
64 quarts is equal to 16 gallons.

Explanation:
Conversion:
1 gallon = 4 quarts.
?? gallons = 64 quarts.
=> 1 × 64 = 4 × ??
=> 64 ÷ 4 = ??
=> 16 gallons = ??

Question 4.
36 pints is how many gallons?
Answer:
36 pints is  equal to 4.5 gallons.

Explanation:
Conversion:
1 gallon = 8 pints.
?? gallons = 36 pints
=> 1 × 36 = 8 × ??
=> 36 ÷ 8 = ??
=> 4.5 gallons = ??

Question 5.
2,000 cups is how many quarts?
Answer:
2,000 cups is equal to 500 quarts.

Explanation:
Conversion:
1 quart = 4 cups.
?? quarts = 2,000 cups
=> 1 × 2,000 = 4 × ??
=> 2,000 ÷ 4 = ??
=> 500 quarts = ??

Question 6.
300 pints is how many cups?
Answer:
300 pints is equal to 600 cups.

Explanation:
Conversion:
1 pint = 2 cups.
300 pints = ?? cups.
=> 1 × ?? = 2 × 300
=> ?? = 600 cups.

Question 7.
64 gallons is how many pints?
Answer:
64 gallons is equal to 512 pints.

Explanation:
Conversion:
1 gallon = 8 pints.
64 gallons = ?? pints.
=> 1 × ?? = 8 × 64
=> ?? = 512 pints.

Question 8.
42 quarts is how many cups?
Answer:
42 quarts is equal to 168 cups.

Explanation:
Conversion:
1 quart = 4 cups.
42 quarts = ?? cups
=> 1 × ?? = 4 × 42
=> ?? = 168 cups.

Question 9.
64 pints is how many gallons?
Answer:
64 pints is equal to 32 gallons.

Explanation:
Conversion:
1 gallon = 2 pints.
?? gallon = 64 pints
=> 1 × 64 = 2 × ??
=> 64 ÷ 2 = ??
=> 32 gallons = ??

Question 10.
132 pints is how many quarts?
Answer:
132 pints is equal to 66 gallons.

Explanation:
Conversion:
1 gallon = 2 pints.
?? gallons = 132 pints
=> 1 × 132 = 2 × ??
=> 132 ÷ 2 = ??
=> 66 gallons = ??

Question 11.
250 cups is how many pints?
Answer:
250 cups is equal to 125 pints.

Explanation:
Conversion:
1 pint = 2 cups.
?? pints = 250 cups
=. 1 × 250 = 2 × ??
=> 250 ÷ 2 = ??
=> 125 pints = ??

Question 12.
175 pints is how many cups?
Answer:
175 pints is equal to 350 cups.

Explanation:
Conversion:
1 pint = 2 cups.
175 pints = ?? cups
=> 1 × ?? = 2 × 175
=> ?? = 350 cups.

Question 13.
88 gallons is how many quarts?
Answer:
88 gallons is equal to 352 quarts.

Explanation:
Conversion:
1 gallon = 4 quarts.
88 gallons = ?? quarts
=> 1 × ?? = 4 × 88
=> ?? = 352 quarts.

Question 14.
42 pints is how many gallons?
Answer:
42 pints is equal to 5.25 gallons.

Explanation:
Conversion:
1 gallon = 8 pints.
?? gallons = 42 pints
=> 1 × 42 = 8 × ??
=> 42 ÷ 8 = ??
=> 5.25 gallons = ??

Question 15.
384 quarts is how many gallons?
Answer:
384 quarts is equal to 96 gallons.

Explanation:
Conversion:
1 gallon = 4 quarts.
?? gallons = 384 quarts
=> 1 × 384 = 4 × ??
=> 384 ÷ 4 = ??
=> 96 gallons = ??

Question 16.
225 cups is how many pints?
Answer:
225 cups is equal to 112.5 pints.

Explanation:
Conversion:
1 pint = 2 cups
?? pints = 225 cups
=> 1 × 225 = 2 × ??
=> 225 ÷ 2 = ??
=> 112.5 pints = ??

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 18.1 Customary Units of Length existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 18.1 Customary Units of Length

Exercises
CALCULATE
Question 1.
12.5 feet is how many yards?
Answer:
12.5 feet is equal to 4.16 yards.

Explanation:
Conversion:
1 yard = 3 feet.
?? yards = 12.5 feet
=> 12.5 × 1 = 3 × ??
=> 12.5 ÷ 3 = ??
=> 4.16 yards.

Question 2.
1 mile is how many feet?
Answer:
1 mile is equal to 5280 feet.

Explanation:
Conversion:
1 mile = 5280 feet.
1 mile = ?? feet
=> 1 × ?? = 5280 × 1
=> ?? = 5280 feet.

Question 3.
144 inches is how many yards?
Answer:
144 inches is equal tp 4 yards.

Explanation:
Conversion:
1 yard = 36 inches.
?? yards = 144 inches.
=> 144 × 1 = 36 × ??
=> 144 ÷ 36 = ??
=> 4 yards.

Question 4.
3 miles is how many yards?
Answer:
3 miles is equal to 5,280 yards.

Explanation:
Conversion:
1 mile = 1760 yards.
3 miles = ?? yards.
=> 1 × ?? = 1760 × 3
=> ?? = 5,280 yards.

Question 5.
128 inches is how many feet?
Answer:
128 inches is equal to 10.66 feet.

Explanation:
Conversion:
1 feet = 12 inches.
?? feet = 128 inches.
=> 1 × 128 = 12 × ??
=> 128 ÷ 12 = ??
=> ?? = 10.66 feet.

Question 6.
10,560 yards is how many miles?
Answer:
10,560 yards is equal to  6 miles.

Explanation:
Conversion:
1 mile = 1,760 yards.
?? miles = 10,560 yards
=> 1 × 10,560 = 1760 × ??
=> 10,560  ÷ 1,760 = ??
=> 6 miles = ??

Question 7.
15.5 yards is how many feet?
Answer:
15.5 yards is equal to 46.5 feet.

Explanation:
Conversion:
1 yard = 3 feet.
15.5 yards = ?? feet
=> 1 × ?? = 3 × 15.5
=> ?? = 46.5 feet.

Question 8.
3.25 miles is how many inches?
Answer:
3.25 miles is equal to 2,05,920 inches.

Explanation:
Conversion:
1 miles = 63360 inches.
3.25 miles = ?? inches.
=> 1 × ?? = 63360 × 3.25
=> ?? = 2,05,920 inches.

Question 9.
31.5 yards is how many inches?
Answer:
31.5 yards is equal to 1,134 inches.

Explanation:
Conversion:
1 yard = 36 inches.
31.5 yards = ?? inches.
=> 1 × ?? = 36 × 31.5
=> ?? = 1,134 inches.

Question 10.
25 miles is how many yards?
Answer:
25 miles is equal to 44,000 miles.

Explanation:
Conversion:
1 mile = 1760 yards.
25 miles = ?? yards.
=> 1 × ?? = 1760 × 25
=> ?? = 44,000 miles.

Question 11.
42,931 feet is how many miles?
Answer:
42,931 feet is equal to 8.13 miles.

Explanation:
Conversion:
1 mile = 5,280 feet.
?? miles = 42,931 feet.
=> 1 × 42,931 = 5,280 × ??
=> 42,931 ÷ 5,280 = ??
=> 8.13 miles = ??

Question 12.
52 feet is how many inches?
Answer:
52 feet is equal to 624 inches.

Explanation:
Conversion:
1 feet = 12 inches.
52 feet = ?? inches.
=> 1 × ?? = 12 × 52
=> ?? = 624 inches.

Question 13.
345 yards is how many feet?
Answer:
345 yards is equal to 1,035 feet.

Explanation:
Conversion:
1 yard = 3 feet.
345 yards = ?? feet.
=> 1 × ?? = 3 × 345
=> ?? = 1,035 feet.

Question 14.
63,360 inches is how many miles?
Answer:
63,360 inches is equal to 1 mile.

Explanation:
Conversion:
1 mile = 63360 inches.
?? miles = 63360 inches.
=> 1 × 63360 = ?? × 63360
=> 63360 ÷ 63360 = ??
=> 1 mile = ??

Question 15.
31,680 inches is how many miles?
Answer:
31,680 inches is equal to 0.5 miles.

Explanation:
Conversion:
1 mile = 63,360 inches.
?? miles = 31,680 inches
=> 1 × 31,680 = 63,360 × ??
=> 31,680 ÷ 63,360 = ??
=> 0.5 miles = ??

Question 16.
7,000 yards is how many inches?
Answer:
7,000 yards is equal to 2,52,000 inches.

Explanation:
Conversion:
1 yard = 36 inches.
7,000 yards = ?? inches
=> 1 × ?? = 36 × 7,000
=> ?? = 2,52,000 inches.

Question 17.
1,590 feet is how many yards?
Answer:
1,590 feet is equal to 530 yards.

Explanation:
Conversion:
1 yard = 3 feet.
?? yards = 1,590 feet.
=> 1 × 1590 = 3 × ??
=> 1590 ÷ 3 = ??
=> 530 yards = ??

Question 18.
500 miles is how many yards?
Answer:
500 miles is equal to 8,80,000 yards.

Explanation:
Conversion:
1 mile = 1,760 yards.
500 miles = ?? yards
=> 1 × ?? = 1,760 × 500
=> ?? = 8,80,000 yards.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 17.4 Solving Equations and Inequalities by Multiplication and Division existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 17.4 Solving Equations and Inequalities by Multiplication and Division

Exercises

SOLVE

Question 1.
2y + 15 = 25
Answer:
Given equation is 2y + 15 = 25
Subtract 15 from both sides of the equation.
2y + 15 – 15 = 25 – 15
2y = 10
To solve above multiplication equation we need to divide both sides of the equation by 2 to find y.
2y/2 = 10/2
y = 5
The value of y is equal to 5.

Question 2.
5 + 5p < 70
Answer:
Given inequality is 5 + 5p < 70
Subtract 5 from both sides of the inequality.
5 + 5p – 5 < 70 – 5
5p < 65
To solve above multiplication inequality we need to divide both sides of the inequality by 5 to find p.
5p/5 < 65/5
p < 13
The value of p is less than 13.

Question 3.
8c + 8 > 224
Answer:
Given inequality is 8c + 8 > 224
Subtract 8 from both sides of the inequality.
8c + 8 – 8 > 224 – 8
8c > 216
To solve above multiplication inequality we need to divide both sides of the inequality by 8 to find c.
8c/8 > 216/8
c > 27
The value of c is greater than 27.

Question 4.
17 + \(\frac{w}{3}\) = 45
Answer:
Given equation is 17 + \(\frac{w}{3}\) = 45
Subtract 17 from both sides of the equation.
17 + \(\frac{w}{3}\) – 17= 45 – 17
\(\frac{w}{3}\) = 28
To solve above division equation we need to multiply both sides of the equation by 3 to find w.
\(\frac{w}{3}\) x 3 = 28 x 3
w = 84
The value of w is equal to 84.

Question 5.
34 = 10 + 4q
Answer:
Given equation is 34 = 10 + 4q
Subtract 10 from both sides of the equation.
34 – 10 = 10 + 4q -10
24 = 4q
To solve above multiplication equation we need to divide both sides of the equation by 4 to find q.
24/4 = 4q/4
6 = q
The value of q is equal to 6.

Question 6.
42 = 7 + \(\frac{z}{5}\)
Answer:
Given equation is 42 = 7 + \(\frac{z}{5}\)
Subtract 7 from both sides of the equation.
42 – 7 = 7 + \(\frac{z}{5}\) – 7
35 = \(\frac{z}{5}\)
To solve above division equation we need to multiply both sides of the equation by 5 to find z.
35 x 5= \(\frac{z}{5}\) x 5
175 = z
The value of z is equal to 175.

Question 7.
232 ≤ 8 + 8x
Answer:
Given inequality is 232 ≤ 8 + 8x
Subtract 8 from both sides of the inequality.
232 – 8 ≤ 8 + 8x – 8
224 ≤ 8x
To solve above multiplication inequality we need to divide both sides of the inequality by 8 to find x.
224/8 ≤ 8x/8
28 ≤ x
The value of x is greater than or equal to 28.

Question 8.
63 = 3 + 4g
Answer:
Given equation is 63 = 3 + 4g
Subtract 3 from both sides of the equation.
63 – 3 = 3 + 4g – 3
60 = 4g
To solve above multiplication equation we need to divide both sides of the equation by 4 to find g.
60/4 = 4g/4
15 = g
The value of g is equal to 15.

Question 9.
12 = \(\frac{g}{9}\)
Answer:
Given equation is 12 = \(\frac{g}{9}\)
To solve above division equation we need to multiply both sides of the equation by 9 to find g.
12 x 9 = \(\frac{g}{9}\) x 9
108 = g
The value of g is equal to 108.

Question 10.
3k + 5 > 56
Answer:
Given inequality is 3k + 5 > 56
Subtract 5 from both sides of the inequality.
3k + 5 – 5 > 56 – 5
3k > 51
To solve above multiplication inequality we need to divide both sides of the inequality by 3 to find k.
3k/3 > 51/3
K > 17
The value of k is greater than 17.

Question 11.
49 ≥ 10 + \(\frac{p}{5}\)
Answer:
Given inequality is 49 ≥ 10 + \(\frac{p}{5}\)
Subtract 10 from both sides of the inequality.
49 – 10 ≥ 10 + \(\frac{p}{5}\) – 10
39 ≥ \(\frac{p}{5}\)
To solve above division equation we need to multiply both sides of the equation by 5 to find p.
39 x 5 ≥ \(\frac{p}{5}\) x 5
195 ≥ p
The value of p is less than or equal to 195.

Question 12.
2y + 5 = 74
Answer:
Given equation is 2y + 5 = 74
Subtract 5 from both sides of the equation.
2y + 5 – 5 = 74 – 5
2y = 69
To solve above multiplication equation we need to divide both sides of the equation by 2 to find y.
2y/2 = 69/2
y = 34.5
The value of y is equal to 34.5.

Question 13.
8d + 130 = 210
Answer:
Given equation is 8d + 130 = 210
Subtract 130 from both sides of the equation.
8d + 130 – 130 = 210 – 130
8d = 80
To solve above multiplication equation we need to divide both sides of the equation by 8 to find d.
8d/8 = 80/8
d = 10
The value of d is equal to 10.

Question 14.
33 + \(\frac{1}{3}\)c ≤ 66
Answer:
Given inequality is 33 + \(\frac{1}{3}\)c ≤ 66
Subtract 33 from both sides of the inequality.
33 + \(\frac{1}{3}\)c – 33 ≤ 66 – 33
\(\frac{1}{3}\)c ≤ 33
To solve above division inequality we need to multiply both sides of the inequality by 3 to find c.
\(\frac{1}{3}\)c x 3 ≤ 33 x 3
c ≤ 99
The value of c is less than or equal to 99.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 17.3 Solving Equations and Inequalities by Addition and Subtraction existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 17.3 Solving Equations and Inequalities by Addition and Subtraction

Exercises

SOLVE

Solve for the variable shown in the expression.

Question 1.
x + 6 = 17
Answer:
Given equation is x + 6 = 17
Subtract 6 from both sides of the equation to find x.
x + 6 – 6 = 17 – 6
x = 11

Question 2.
17 = s + 9
Answer:
Given equation is 17 = s + 9
Subtract 9 from both sides of the equation to find s.
17 – 9 = s + 9 – 9
8 = s

Question 3.
14 + z = 49
Answer:
Given equation is 14 + z = 49
Subtract 14 from both sides of the equation to find z.
14 + z – 14 = 49 – 14
z = 35

Question 4.
17 – f < 14
Answer:
Given inequality is 17 – f < 14
Subtract 14 from 17 to find f.
17 – 14 < f
3 < f

Question 5.
c – 11 > 11
Answer:
Given inequality is c – 11 > 11
Add 11 to both sides of the inequality to find c.
c – 11 + 11 > 11 + 11
c > 22

Question 6.
y + 23 = 25
Answer:
Given equation is y + 23 = 25
Subtract 23 from both sides of the equation to find y.
y + 23 – 23 = 25 – 23
y = 2

Question 7.
107 = 5 + l
Answer:
Given equation is 107 = 5 + I
Subtract 5 from both sides of the equation to find I.
107 – 5 = 5 + I – 5
102 = I

Question 8.
k + 36 = 64
Answer:
Given equation is k + 36 = 64
Subtract 36 from both sides of the equation to find k.
k + 36 – 36 = 64 – 36
k = 28

Question 9.
15 + u ≤ 43
Answer:
Given inequality is 15 + u ≤ 43
Subtract 15 from both sides of the inequality to find u.
15 + u – 15 ≤ 43 – 15
u ≤ 28

Question 10.
59 – t = 22
Answer:
Given equation is 59 – t = 22
Subtract 59 from both sides of the equation to find the value of t.
59 – t – 59 = 22 – 59
– t = – 37
t = 37

Question 11.
9 – a = 3
Answer:
Given equation is 9 – a = 3
Subtract 9 from both sides of the equation to find the value of a.
9 – a – 9 = 3 – 9
– a = -6
a = 6

Question 12.
75 + b > 101
Answer:
Given inequality is 75 + b > 101
Subtract 75 from both sides of the inequality to find b.
75 + b – 75 > 101 – 75
b > 26

Question 13.
49 – e = 24
Answer:
Given equation is 49 – e = 24
Subtract 49 from both sides of the equation to find the value e.
49 – e – 49 = 24 – 49
– e = – 25
e = 25

Question 14.
16 + d ≥ 39
Answer:
Given inequality is 16 + d ≥ 39
Subtract 16 from both sides of the inequality to find d.
16 + d – 16 ≥ 39 – 16
d ≥ 23

Question 15.
w + 15 ≤ 81
Answer:
Given inequality is w + 15 ≤ 81
Subtract 15 from both sides of the inequality to find w.
w + 15 – 15 ≤ 81 – 15
w ≤ 66

Question 16.
q – 23 = 35
Answer:
Given equation is q – 23 = 35
Add 23 to both sides of the equation to find q.
q – 23 + 23 = 35 + 23
q = 58

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 17.2 Understanding Inequalities existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 17.2 Understanding Inequalities

Exercises

EXPLAIN

Put into words what each expression is describing.

Question 1.
3x < 6
Answer:
The given expression 3x < 6 describes three times a number is less than six.

Question 2.
p – 1 > 5
Answer:
The given expression p – 1 > 5 describes a number minus one is greater than five.

Question 3.
y ≤ 4
Answer:
The given expression y ≤ 4 describes a number is less than or equal to four.

Question 4.
s² ≥ 25
Answer:
The given expression s² ≥ 25 describes a square of a number is greater than or equal to twenty-five.

Question 5.
\(\frac{f}{5}\) < 63
Answer:
The given expression \(\frac{f}{5}\) < 63 describes a number divided by five is less than sixty-three.

Question 6.
w + 9 < 12
Answer:
The given expression w + 9 < 12 describes a number plus nine is less than twelve.

Question 7.
643 < d + g
Answer:
The given expression 643 < d + g describes six hundred forty-three is less than the sum of two numbers.

Question 8.
z + 2 ≤ 15
Answer:
The given expression z + 2 ≤ 15 describes a number plus two is less than or equal to fifteen.

Question 9.
4h > 17
Answer:
The given expression 4h > 17 describes four times a number is greater than seventeen.

Question 10.
1 – n ≥ -63
Answer:
The given expression 1 – n ≥ -63 describes one minus number is greater than or equal to negative sixty-three.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 17.1 Understanding Variable Expressions existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 17.1 Understanding Variable Expressions

Exercises

EXPLAIN

Put into words what each expression is describing.

Question 1.
\(\frac{a}{4}\)
Answer:
The given expression \(\frac{a}{4}\) describes a number is divided by four.

Question 2.
y + 3
Answer:
The given expression y + 3 describes a number plus three.

Question 3.
4b + 8
Answer:
The given expression 4b + 8 describes four times a number plus eight.

Question 4.
.9q – 7
Answer:
The given expression .9q – 7 describes nine tenths of a number minus seven.

Question 5.
\(\frac{(x-3)}{25}\)
Answer:
The given expression \(\frac{(x-3)}{25}\) describes a number minus three, then divided by twenty-five.

Question 6.
8(2g + 6)
Answer:
The given expression 8(2g + 6) describes eight times the sum of two times a number plus six.

Question 7.
2n – 5
Answer:
The given expression 2n – 5 describes two times a number minus five.

Question 8.
12(r – 14)
Answer:
The given expression 12(r – 14) describes twelve times the result of a number minus fourteen.

Question 9.
\(\frac{7}{h}\)
Answer:
The given expression \(\frac{7}{h}\) describes seven is divided by a number.

Question 10.
\(\frac{11+b}{16}\)
Answer:
The given expression \(\frac{11+b}{16}\) describes the sum of eleven plus a number, then divided by sixteen.