• 19. how many $\frac{1}{3}$s are in $\frac{3}{4}$?
find each unknown number:
20. $0.32w = 32$
21. $x + 3.4 = 5$
• 22. on one roll of a 1–6 number cube, what is the probability that the upturned face will show an even number of dots?
23. arrange these measurements in order from shortest to longest:
1 in., 3 cm, 20 mm
24. larry correctly answered 45% of the questions.
a. explain did larry correctly answer more than or less than half the questions? how do you know?
b. write 45% as a reduced fraction.
25. justify describe how to mentally calculate $\frac{1}{10}$ of $12.50.
26. reduce: $\frac{2 \cdot 5 \cdot 2 \cdot 3 \cdot 3 \cdot 7}{2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 7}$
• 27. analyze what is the sum of the decimal numbers represented by points x and y on this number line?
(number line with 1, 2, 3 marked, x between 1 and 2, y between 2 and 3)
28. model draw a rectangle that is $1\frac{1}{2}$ inches long and $\frac{3}{4}$ inch wide. then draw a segment that divides the rectangle into two triangles.
29. what is the perimeter of the rectangle drawn in problem 28?
• 30. if $a = lw$, and if $l = 1.5$ and $w = 0.75$

Question

• 19. how many $\frac{1}{3}$s are in $\frac{3}{4}$?
find each unknown number:
20. $0.32w = 32$
21. $x + 3.4 = 5$
• 22. on one roll of a 1–6 number cube, what is the probability that the upturned face will show an even number of dots?
23. arrange these measurements in order from shortest to longest:
1 in., 3 cm, 20 mm
24. larry correctly answered 45% of the questions.
    a. explain did larry correctly answer more than or less than half the questions? how do you know?
    b. write 45% as a reduced fraction.
25. justify describe how to mentally calculate $\frac{1}{10}$ of $12.50.
26. reduce: $\frac{2 \cdot 5 \cdot 2 \cdot 3 \cdot 3 \cdot 7}{2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 7}$
• 27. analyze what is the sum of the decimal numbers represented by points x and y on this number line?
    (number line with 1, 2, 3 marked, x between 1 and 2, y between 2 and 3)
28. model draw a rectangle that is $1\frac{1}{2}$ inches long and $\frac{3}{4}$ inch wide. then draw a segment that divides the rectangle into two triangles.
29. what is the perimeter of the rectangle drawn in problem 28?
• 30. if $a = lw$, and if $l = 1.5$ and $w = 0.75$

Accepted Answer

### Problem 21: Solve $ x + 3.4 = 5 $
# Explanation:
## Step 1: Isolate $ x $
To solve for $ x $, we subtract $ 3.4 $ from both sides of the equation. This is based on the subtraction property of equality, which states that if $ a = b $, then $ a - c = b - c $.
$$
x + 3.4 - 3.4 = 5 - 3.4
$$
## Step 2: Calculate the result
Simplify both sides of the equation.
$$
x = 1.6
$$
# Answer:
$ x = 1.6 $

### Problem 22: Solve $ 0.32w = 32 $
# Explanation:
## Step 1: Isolate $ w $
To solve for $ w $, we divide both sides of the equation by $ 0.32 $. This is based on the division property of equality, which states that if $ a = b $ and $ c
eq 0 $, then $ \frac{a}{c} = \frac{b}{c} $.
$$
w=\frac{32}{0.32}
$$
## Step 2: Calculate the result
Simplify the right - hand side. $ \frac{32}{0.32}=\frac{32\times100}{0.32\times100}=\frac{3200}{32} = 100 $
# Answer:
$ w = 100 $

### Problem 23: Probability of even number on a 1 - 6 number cube
# Explanation:
## Step 1: Identify total and favorable outcomes
A standard 1 - 6 number cube has 6 possible outcomes (the numbers 1, 2, 3, 4, 5, 6). The even numbers on a number cube are 2, 4, 6. So there are 3 favorable outcomes.
## Step 2: Calculate probability
The formula for probability $ P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} $. Substituting the values, we get $ P = \frac{3}{6} $
## Step 3: Simplify the fraction
Simplify $ \frac{3}{6}=\frac{1}{2} $
# Answer:
The probability is $ \frac{1}{2} $

### Problem 24a: Larry's correct answers
# Brief Explanations:
Half of the questions is 50%. Larry answered 45% of the questions. Since $ 45\%<50\% $, Larry answered less than half the questions.
# Answer:
Larry answered less than half the questions because 45% is less than 50% (half).

### Problem 24b: Write 45% as a reduced fraction
# Explanation:
## Step 1: Convert percentage to fraction
To convert a percentage to a fraction, we write it over 100. So $ 45\%=\frac{45}{100} $
## Step 2: Simplify the fraction
We find the greatest common divisor (GCD) of 45 and 100. The GCD of 45 and 100 is 5. Divide both the numerator and the denominator by 5: $ \frac{45\div5}{100\div5}=\frac{9}{20} $
# Answer:
$ \frac{9}{20} $

### Problem 25: Mentally calculate $ \frac{1}{10} $ of $12.50$
# Brief Explanations:
To find $ \frac{1}{10} $ of a number, we can use the rule that dividing a number by 10 is the same as moving the decimal point one place to the left. For $12.50$, moving the decimal point one place to the left gives $1.25$. So $ \frac{1}{10} $ of $12.50$ is $1.25$.
# Answer:
$ \frac{1}{10} $ of $12.50$ is $1.25$ (by moving the decimal point of $12.50$ one place to the left).

### Problem 26: Reduce $ \frac{2\cdot5\cdot2\cdot3\cdot3\cdot7}{2\cdot2\cdot2\cdot5\cdot5\cdot7} $
# Explanation:
## Step 1: Cancel out common factors
We can cancel out the common factors in the numerator and the denominator.
- For the factor 2: There are two 2s in the numerator and three 2s in the denominator. We can cancel two 2s from numerator and denominator.
- For the factor 5: There is one 5 in the numerator and two 5s in the denominator. We can cancel one 5.
- For the factor 7: There is one 7 in the numerator and one 7 in the denominator. We can cancel one 7.

After canceling, the numerator becomes $ 3\times3=9 $ and the denominator becomes $ 2\times5 = 10 $
## Step 2: Write the simplified fraction
The simplified fraction is $ \frac{9}{10} $
# Answer:
$ \frac{9}{10} $

### Problem 27: Sum of $ x $ and $ y $ on the number line
# Explanation:
## Step 1: Determine the value of $ x $
The number line has marks between 1 and 2. The distance between 1 and 2 is 1, and it is divided into 8 equal parts. So each part represents $ \frac{1}{8}=0.125 $. The point $ x $ is 5 parts away from 1. So $ x=1 + 5\times0.125=1 + 0.625 = 1.625 $
## Step 2: Determine the value of $ y $
The distance between 2 and 3 is 1, and it is divided into 8 equal parts. Each part is 0.125. The point $ y $ is 3 parts away from 2. So $ y = 2+3\times0.125=2 + 0.375=2.375 $
## Step 3: Calculate the sum of $ x $ and $ y $
$ x + y=1.625+2.375 = 4 $
# Answer:
The sum of $ x $ and $ y $ is 4.

### Problem 29: Perimeter of the rectangle (from problem 28)
# Explanation:
## Step 1: Recall the formula for the perimeter of a rectangle
The formula for the perimeter $ P $ of a rectangle is $ P = 2(l + w) $, where $ l $ is the length and $ w $ is the width.
## Step 2: Substitute the values of $ l $ and $ w $
Given $ l = 1\frac{1}{2}=\frac{3}{2}=1.5 $ inches and $ w=\frac{3}{4} = 0.75 $ inches. Substitute into the formula: $ P=2(1.5 + 0.75) $
## Step 3: Simplify the expression
First, calculate the sum inside the parentheses: $ 1.5+0.75 = 2.25 $. Then multiply by 2: $ P = 2\times2.25=4.5 $ inches.
# Answer:
The perimeter of the rectangle is 4.5 inches (or $ 4\frac{1}{2} $ inches)

### Problem 30: Find $ A $ when $ A=lw $, $ l = 1.5 $ and $ w = 0.75 $
# Explanation:
## Step 1: Substitute the values into the formula
Given $ A=lw $, $ l = 1.5 $ and $ w = 0.75 $. Substitute these values into the formula: $ A=1.5\times0.75 $
## Step 2: Calculate the product
$ 1.5\times0.75 = 1.125 $
# Answer:
$ A = 1.125 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 21: Solve \( x + 3.4 = 5 \)

Step 1: Isolate \( x \)

Step 2: Calculate the result

Step 1: Isolate \( w \)

Step 2: Calculate the result

Step 1: Identify total and favorable outcomes

Step 2: Calculate probability

Step 3: Simplify the fraction

Answer:

Problem 22: Solve \( 0.32w = 32 \)