lesson #47
1. study the equation ( 5(3 + 7)=15 + 35 ). because of the distributive each term is multiplied by 5. we can use the distributive property to an equivalent expression that includes variables: ( 5(7 + m)=35 + 5m ) distributive property to write an equivalent expression for ( 9(3n + 7) ).
2. thomas finds 29 ants, 20 bees, and 4 spiders in his garden. write the bees to spiders.
3. find the quotient of ( \frac{1}{3}div\frac{2}{3} ). check your answer by multiplying.
4. ( 78.9 - 12.76 =? )
5. study dot plot d (appendix). what is the range?
6. a freezer is 5 feet high, 2 feet deep and 3 feet wide. how much space (volume) does the freezer have?
7. ( 4 imes(24div6)=? )
8. candice cut a rectangular piece of paper into two congruent triangles, each with a base of 9 inches and a height of 12 inches. what was the area of the rectangle?
9. evaluate the expression. ( (1.3 - 0.3) imes3^{4} )
10. ( 840div50 =? )
11. might maids cleaning service cleans 4 rooms in 2 hours. give the unit rate rooms per hour.
12. locate table l in the appendix. give the mean, median, mode and range of bronze medal data.
13. compare the ratio of frogs to toads. if the ratio stays the same and there are total number amphibians, how many are toads and how many are frogs?
14. find the prime factorization of 48.
15. identify the terms in the expression ( 3u^{3}-4w ).

Question

lesson #47
1. study the equation ( 5(3 + 7)=15 + 35 ). because of the distributive each term is multiplied by 5. we can use the distributive property to an equivalent expression that includes variables: ( 5(7 + m)=35 + 5m ) distributive property to write an equivalent expression for ( 9(3n + 7) ).
2. thomas finds 29 ants, 20 bees, and 4 spiders in his garden. write the bees to spiders.
3. find the quotient of ( \frac{1}{3}div\frac{2}{3} ). check your answer by multiplying.
4. ( 78.9 - 12.76 =? )
5. study dot plot d (appendix). what is the range?
6. a freezer is 5 feet high, 2 feet deep and 3 feet wide. how much space (volume) does the freezer have?
7. ( 4	imes(24div6)=? )
8. candice cut a rectangular piece of paper into two congruent triangles, each with a base of 9 inches and a height of 12 inches. what was the area of the rectangle?
9. evaluate the expression. ( (1.3 - 0.3)	imes3^{4} )
10. ( 840div50 =? )
11. might maids cleaning service cleans 4 rooms in 2 hours. give the unit rate rooms per hour.
12. locate table l in the appendix. give the mean, median, mode and range of bronze medal data.
13. compare the ratio of frogs to toads. if the ratio stays the same and there are total number amphibians, how many are toads and how many are frogs?
14. find the prime factorization of 48.
15. identify the terms in the expression ( 3u^{3}-4w ).

Accepted Answer

### Problem 1:
# Explanation:
## Step1: Recall distributive property
The distributive property is $a(b + c)=ab+ac$. Here, $a = 9$, $b=3n$, $c = 7$.
## Step2: Apply distributive property
$9(3n + 7)=9\times3n+9\times7 = 27n+63$
# Answer: $27n + 63$

### Problem 2:
# Explanation:
## Step1: Identify the numbers
Number of bees $= 20$, number of spiders $= 4$.
## Step2: Write the ratio
The ratio of bees to spiders is $\frac{20}{4}=5:1$ (simplified by dividing numerator and denominator by 4).
# Answer: $20:4$ (or $5:1$)

### Problem 3:
# Explanation:
## Step1: Recall division of fractions
Dividing by a fraction is multiplying by its reciprocal. So, $\frac{1}{3}\div\frac{2}{3}=\frac{1}{3}\times\frac{3}{2}$
## Step2: Multiply the fractions
$\frac{1\times3}{3\times2}=\frac{3}{6}=\frac{1}{2}$
## Step3: Check by multiplying
Multiply the quotient $\frac{1}{2}$ by the divisor $\frac{2}{3}$: $\frac{1}{2}\times\frac{2}{3}=\frac{2}{6}=\frac{1}{3}$ (which is the dividend, so correct).
# Answer: $\frac{1}{2}$

### Problem 4:
# Explanation:
## Step1: Align the decimals
$78.90- 12.76$ (add a zero to 78.9 to make it 78.90 for subtraction)
## Step2: Subtract
$78.90-12.76 = 66.14$
# Answer: $66.14$

### Problem 5:
(Note: Since Dot Plot D is in the Appendix which is not provided, we can't solve this without the dot plot. But the general method for range is maximum value - minimum value from the data in the dot plot.)

### Problem 6:
# Explanation:
## Step1: Recall volume formula for a rectangular prism
Volume $V=l\times w\times h$, where $l = 3$ (width), $w = 2$ (depth), $h = 5$ (height).
## Step2: Calculate volume
$V=3\times2\times5=30$ cubic feet.
# Answer: $30$ cubic feet

### Problem 7:
# Explanation:
## Step1: Solve the parentheses first
$24\div6 = 4$
## Step2: Multiply by 4
$4\times4=16$
# Answer: $16$

### Problem 8:
# Explanation:
## Step1: Recall area of a triangle
Area of a triangle $A=\frac{1}{2}\times base\times height$. For one triangle, $base = 9$, $height=12$, so area of one triangle is $\frac{1}{2}\times9\times12 = 54$ square inches.
## Step2: Area of rectangle
Since the rectangle is cut into two congruent triangles, area of rectangle is $2\times54 = 108$ square inches.
# Answer: $108$ square inches

### Problem 9:
# Explanation:
## Step1: Solve the parentheses
$1.3 - 0.3=1$
## Step2: Calculate $3^4$
$3^4=3\times3\times3\times3 = 81$
## Step3: Multiply the results
$1\times81 = 81$
# Answer: $81$

### Problem 10:
# Explanation:
## Step1: Divide 840 by 50
$840\div50=\frac{840}{50}=\frac{84}{5}=16.8$ (or using long division: 50×16 = 800, 840 - 800 = 40, 40÷50 = 0.8, so 16 + 0.8 = 16.8)
# Answer: $16.8$

### Problem 11:
# Explanation:
## Step1: Calculate unit rate
Unit rate (rooms per hour) $=\frac{4\ rooms}{2\ hours}=2$ rooms per hour.
# Answer: $2$ rooms per hour

### Problem 12:
(Note: Since Table L is in the Appendix which is not provided, we can't solve this without the table. But the general method for mean is sum of data divided by number of data points, median is the middle value (or average of two middle values), mode is the most frequent value, and for range it's max - min.)

### Problem 13:
(Note: The problem statement is incomplete. But the general method for ratio: from the table, for toads $t$ and frogs $f$, find the ratio $\frac{f}{t}$ from the table (e.g., for first row $t = 5$, $f = 8$, ratio $\frac{8}{5}$). Then if total amphibians is $N$, let number of toads be $x$, frogs be $N - x$, then $\frac{N - x}{x}=\frac{8}{5}$ (using first row ratio) and solve for $x$ and $N - x$.)

### Problem 14:
# Explanation:
## Step1: Start dividing by prime numbers
Divide 48 by 2: $48\div2 = 24$
## Step2: Divide 24 by 2: $24\div2 = 12$
## Step3: Divide 12 by 2: $12\div2 = 6$
## Step4: Divide 6 by 2: $6\div2 = 3$
## Step5: 3 is a prime number
So prime factorization of 48 is $2\times2\times2\times2\times3=2^4\times3$
# Answer: $2^4\times3$ (or $2\times2\times2\times2\times3$)

### Problem 15:
# Explanation:
## Step1: Recall terms in an expression
Terms in an expression are separated by plus or minus signs. In $3u^3-4w$, the terms are $3u^3$ and $- 4w$
# Answer: $3u^3$ and $-4w$

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QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Recall distributive property

Step2: Apply distributive property

Step1: Identify the numbers

Step2: Write the ratio

Step1: Recall division of fractions

Step2: Multiply the fractions

Step3: Check by multiplying

Answer:

Problem 2: