## Math Expressions Common Core Grade 5 Unit 8 Lesson 4 Answer Key Customary Units of Length

**Math Expressions Grade 5 Unit 8 Lesson 4 Homework**

**Complete.**

Question 1.

36in. = _____ ft

Answer:

36in. = 3ft.

Explanation:

Here, 1in. = \(\frac{1}{12}\) ft,

So 36in. = \(\frac{1}{12}\) × 36

= 3 ft.

Question 2.

12ft = _______ yd

Answer:

12ft = 4 yd.

Explanation:

Here, 1ft. = \(\frac{1}{3}\) yd,

So 12ft. = \(\frac{1}{3}\) × 12

= 4 yd.

Question 3.

36in. = _______ yd

Answer:

36in. = 1 yd.

Explanation:

Here, 36in. = 1 yd.

Question 4.

_____ in. = 4ft

Answer:

48in. = 4ft.

Explanation:

Here, 1ft = 12in,

so 4ft = 12×4

= 48in.

Question 5.

______ ft = 2 yd

Answer:

6 ft = 2 yd.

Explanation:

Here, 1 yd = 3 ft,

so 2 yd = 2 × 3

= 6 ft.

Question 6.

______ in. = 3 yd

Answer:

108 in = 3 yd.

Explanation:

Here, 1 yd = 36 in,

so 3 yd = 36 × 3

= 108 in.

Question 7.

_____ ft = 90 in.

Answer:

7\(\frac{1}{2}\) ft = 90 in.

Explanation:

Here, 1 in = \(\frac{1}{12}\) ft,

so 90 in = \(\frac{1}{12}\) × 90

= 7 \(\frac{6}{12}\)

= 7\(\frac{1}{2}\) ft.

Question 8.

______ in. = 5\(\frac{1}{2}\) ft

Answer:

66 in. = 5\(\frac{1}{2}\) ft.

Explanation:

Here, 1 ft = 12 inch,

so 5\(\frac{1}{2}\) ft = 12 × 5\(\frac{1}{2}\) ft

= 12 × \(\frac{11}{2}\)

= 6 × 11

= 66 in.

Question 9.

6yd = ________ in.

Answer:

6yd = 216 in.

Explanation:

Here, 1 yd = 36 in,

so 6 yd = 36 × 6

= 216 in.

Question 10.

______ yd = 432 in.

Answer:

12 yd = 432 in.

Explanation:

Here, 36 in. = 1yd,

so 432 in. = 432 ÷ 36

= 12 yd.

Question 11.

1\(\frac{1}{4}\) yd = ______ ft

Answer:

1\(\frac{1}{4}\) yd = 3\(\frac{3}{4}\) ft.

Explanation:

Here, 1 yd = 3 ft,

so 1\(\frac{1}{4}\) yd = 1\(\frac{1}{4}\) × 3

= \(\frac{5}{4}\) × 3

= \(\frac{15}{4}\)

= 3\(\frac{3}{4}\) ft.

Question 12.

90 ft = ________ yd

Answer:

90 ft = 30 yds.

Explanation:

Here, 3ft = 1 yd,

so 90ft = 90 ÷ 3

= 30 yds.

**Find the perimeter of each figure in feet.**

Question 13.

P = __________

Answer:

P = 8ft.

Explanation:

Given length and breadth of the figure is 36 in which is 3 ft and 1 ft,

So the perimeter of the figure is 2(L+B)

= 2(3+1)

= 2(4)

= 8ft.

Question 14.

P = __________

Answer:

Perimeter = 9 ft.

Explanation:

Given the measurements of a figure are 48 in which is 4 ft, 3 yd which is 9 ft, 5 ft, 1 yd which is 3 ft and 9 ft. So the perimeter of the figure is 4 ft + 9 ft + 5 ft + 3 ft + 9 ft = 30 ft.

Find the perimeter of each figure in yards.

Question 15.

P = __________

Answer:

The perimeter of the figure is 14 yd.

Explanation:

Given the measurements of a figure are 1 yd, 12 ft which is 4 yd, 9 ft which is 3 yd, and 36 inches which is 1 yd. So the perimeter of the figure is 1 + 4 + 3 + 1 + 5 = 14 yd.

Question 16.

P = __________

Answer:

The perimeter is 22 yd.

Explanation:5

Given the measurements of a figure are 6 yd, 15 ft which is 5 yd, 6 yds, and 5 yds. So the perimeter of the figure is 6 + 5 + 6 + 5 = 22 yd.

**Math Expressions Grade 5 Unit 8 Lesson 4 Remembering**

**Write an expression for the words.**

Question 1.

Multiply 12 by the sum of 8 and t. ___________

Answer:

The expression is 12(8+t).

Explanation:

The expression for Multiply 12 by the sum of 8 and t is 12(8+t).

Question 2.

Divide 10 by 4 and then subtract 6.2. __________

Answer:

The expression is 6.2 is 10 ÷ 4 – 6.2.

Explanation:

The expression for divide 10 by 4 and then subtract 6.2 is 10 ÷ 4 – 6.2.

Question 3.

Add the product of 7 and 10 to 80. ___________

Answer:

The expression is 80 + 7 × 10.

Explanation:

The expression for add the product of 7 and 10 to 80 is 80 + 7 × 10.

Question 4.

Subtract \(\frac{1}{8}\) from \(\frac{5}{6}\) ____________

Answer:

The expression is \(\frac{5}{6}\) – \(\frac{1}{8}\).

Explanation:

The expression for subtract \(\frac{1}{8}\) from \(\frac{5}{6}\) is \(\frac{5}{6}\) – \(\frac{1}{8}\).

**Simplify. Follow the Order of Operations.**

Question 5.

12 – 7 + 9 – 2

Answer:

12 – 7 + 9 – 2 = 12.

Explanation:

The solution of the expression 12 – 7 + 9 – 2 is

= 5 + 7

= 12.

Question 6.

15 + 0.3 + 6 ÷ 0.02

Answer:

15 + 0.3 + 6 ÷ 0.02 = 315.3.

Explanation:

The solution of the expression 15 + 0.3 + 6 ÷ 0.02 is

= 15 + 0.3 + 300

= 315.3.

Question 7.

(2\(\frac{3}{8}\) – \(\frac{1}{4}\)) × \(\frac{1}{5}\)

Answer:

(2\(\frac{3}{8}\) – \(\frac{1}{4}\)) × \(\frac{1}{5}\) = \(\frac{17}{40}\).

Explanation:

The solution of the expression (2\(\frac{3}{8}\) – \(\frac{1}{4}\)) × \(\frac{1}{5}\) is

= (\(\frac{19}{8}\) – \(\frac{1}{4}\)) × \(\frac{1}{5}\)

= (\(\frac{19 – 2}{8}\) × \(\frac{1}{5}\)

= \(\frac{17}{8}\) × \(\frac{1}{5}\)

= \(\frac{17}{40}\).

Question 8.

\(\frac{1}{6}\) • \(\frac{1}{6}\) ÷ \(\frac{1}{6}\)

Answer:

\(\frac{1}{6}\) • \(\frac{1}{6}\) ÷ \(\frac{1}{6}\) = \(\frac{1}{6}\).

Explanation:

The solution of the expression \(\frac{1}{6}\) • \(\frac{1}{6}\) ÷ \(\frac{1}{6}\) is

= \(\frac{1}{6}\) • 1

= \(\frac{1}{6}\).

Question 9.

(7.2 – 3.3) • (0.5 + 0.5)

Answer:

(7.2 – 3.3) • (0.5 + 0.5) = 3.9.

Explanation:

The solution of the expression (7.2 – 3.3) • (0.5 + 0.5) is

= (3.9) • (1)

= 3.9.

Question 10.

36 ÷ (6.6 + 2.4) • 4

Answer:

36 ÷ (6.6 + 2.4) • 4 = 16.

Explanation:

The solution of the expression 36 ÷ (6.6 + 2.4) • 4 is

= 36 ÷ 9 • 4

= 4 • 4

= 16.

**Complete.**

Question 11.

5 mg = __________ g

Answer:

5 mg = 0.005 g.

Explanation:

As 1 mg = 0.001 g,

so 5 mg = 0.001 × 5

= 0.005 g.

Question 12.

13.45 kg = __________ g

Answer:

13.45 kg = 13,450 g.

Explanation:

As 1 kg = 1000 g,

so 13.45 kg = 13.45 × 1000

= 13,450 g.

Question 13.

66 g = 0.066 __________

Answer:

66 g = 0.066 kg.

Explanation:

As 1 g = 0.001 kg,

so 66 g = 66 × 0.001

= 0.066 kg.

Question 14.

0.02 1 g = 21 __________

Answer:

0.02 1 g = 21 mg.

Explanation:

As 1 g = 1000 mg,

so 0.021g = 0.021 × 1000

= 21 mg.

Question 15.

5.003 kg = __________ mg

Answer:

5.003 kg = 5003000 mg.

Explanation:

As 1kg = 1000000 mg,

so 5.003 kg = 5.003 × 1000000

= 5003000 mg.

Question 16.

782 mg = 0.782 __________

Answer:

782 mg = 0.782 g.

Explanation:

As 1mg = 0.001 g,

so 782 mg = 782 × 0.001

= 0.782 g.

Question 17.

**Stretch Your Thinking** Draw a figure composed of three different rectangles that has a perimeter of 140 yards. Use measurements in yards and feet to label the sides of your figure.

Answer:

The measurements of the figure are 30 feet, 23 yards, 90 feet, 8 yards, 60 feet, 25 yards, 17 yards.

Explanation:

The figure the represents three different rectangles that have a perimeter of 140 yards is