Solve the following problems: 1. Calculate 0.018 of 200,000 frs. 2. Which is smaller, 1/4 or 7/8? Find their…

Question

Solve the following problems: 1. Calculate 0.018 of 200,000 frs. 2. Which is smaller, 1/4 or 7/8? Find their difference. 3. If X=5 and Y=3 1/2, calculate X-Y. 4. [Incomplete problem description]

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Here are the solutions to the problems:

1.

Set up a proportion based on the given information.
$0.05 \text{ of } 200 = 10$
This means $0.05 \times 200 = 10$ .
Find the value of 0.018 of 200,000.
$0.018 \times 200,000$ $= 18 \times 200$ $= 3,600$
The value of 0.018 of 200,000 frs is $\boxed{\text{3,600 frs}}$ .

2.
Identify the fractions.
The fractions are $\frac{1}{4}$ and $\frac{7}{8}$ .
Determine which fraction is smaller.
To compare, find a common denominator, which is 8.
$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$
Since $\frac{2}{8} < \frac{7}{8}$ , $\frac{1}{4}$ is the smaller fraction.
Subtract the smaller fraction from the bigger one.
$\frac{7}{8} - \frac{1}{4}$ $= \frac{7}{8} - \frac{2}{8}$ $= \frac{7 - 2}{8}$ $= \frac{5}{8}$
The result is $\boxed{\frac{5}{8}}$ .

3.
Write down the given values for X and Y.
$X = 5$ $Y = 3\frac{1}{2}$
Convert Y to an improper fraction.
$Y = 3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$
Simplify $X - Y$ .
$X - Y = 5 - \frac{7}{2}$
Find a common denominator to subtract.
$5 = \frac{5 \times 2}{2} = \frac{10}{2}$ $X - Y = \frac{10}{2} - \frac{7}{2}$ $= \frac{10 - 7}{2}$ $= \frac{3}{2}$
The simplified value of $X - Y$ is $\boxed{\frac{3}{2}}$ .

4.
List the given decimal fractions.
$0.045, 0.371, 0.375$
Arrange them in ascending order of magnitude.
Compare the numbers digit by digit from left to right.
0.045 is the smallest because it has a 0 in the tenths place.
Between 0.371 and 0.375, compare the thousandths place. $1 < 5$ .
So, 0.371 is smaller than 0.375.
The ascending order is $\boxed{0.045, 0.371, 0.375}$ .

5.
Identify the average weight and the number of pigs.
Average weight of 7 pigs = $35 \text{ kg}$ .
Number of pigs = 7.
Calculate the total weight.
Total weight = Average weight $\times$ Number of pigs
$= 35 \text{ kg} \times 7$ $= 245 \text{ kg}$
The total weight is $\boxed{245 \text{ kg}}$ .

6.
Determine the rate of time loss.
A wall clock loses 2 minutes every three hours.
Calculate how many 3-hour intervals are in 15 hours.
Number of intervals = $\frac{15 \text{ hours}}{3 \text{ hours/interval}} = 5 \text{ intervals}$
Calculate the total time lost.
Total time lost = Loss per interval $\times$ Number of intervals
$= 2 \text{ minutes/interval} \times 5 \text{ intervals}$ $= 10 \text{ minutes}$
The clock loses $\boxed{10 \text{ minutes}}$ in 15 hours.

7.
Identify the decimals.
The decimals are 0.124 and 2.5.
Determine which decimal is smaller.
0.124 is smaller than 2.5.
Subtract the smaller decimal from the bigger one.
$2.5 - 0.124$
To subtract, align the decimal points and add trailing zeros to 2.5:
$2.500$ $-0.124$
$-----$
$2.376$
The result is $\boxed{2.376}$ .

8.
Identify the cost of seven books.
Seven books cost $2100 \text{ frs}$ .
Calculate the cost of one book.
Cost per book = $\frac{2100 \text{ frs}}{7 \text{ books}} = 300 \text{ frs/book}$
Calculate the number of books that can be bought with $900 \text{ frs}$ .
Number of books = $\frac{\text{Total money}}{\text{Cost per book}}$
$= \frac{900 \text{ frs}}{300 \text{ frs/book}}$ $= 3 \text{ books}$
The number of books that can be bought is $\boxed{3}$ .

9.
Recall the conversion factor between grams and kilograms.
$1 \text{ kg} = 1000 \text{ g}$
Convert $5400 \text{ g}$ to kilograms.
$5400 \text{ g} = \frac{5400}{1000} \text{ kg}$ $= 5.4 \text{ kg}$
$5400 \text{ g}$ is equal to $\boxed{5.4 \text{ kg}}$ .

10.
List the elements of sets A and B.
$A = \{3, 6, 9, 12\}$ $B = \{6, 8, 10, 12\}$
Find the intersection of A and B, denoted as $A \cap B$ .
The intersection consists of elements that are common to both sets.
Common elements are 6 and 12.
$A \cap B = \{6, 12\}$
The intersection is $\boxed{\{6, 12\}}$ .

11.
Identify the numbers to be added in base 7.
$344_7 + 235_7$
Add the numbers column by column from right to left, remembering that in base 7, digits range from 0 to 6.
If a sum is 7 or more, divide by 7 to get the carry and the digit.

Units column: $4 + 5 = 9$ .
$9 \div 7 = 1$ remainder 2. Write down 2, carry over 1.

Sevens column: $4 + 3 + 1 \text{ (carry)} = 8$ .
$8 \div 7 = 1$ remainder 1. Write down 1, carry over 1.

Forty-nines column: $3 + 2 + 1 \text{ (carry)} = 6$ .
$6 \div 7 = 0$ remainder 6. Write down 6.

The sum is $\boxed{612_7}$ .

12.
Identify the initial amount and the ratio.
Initial amount = $600 \text{ frs}$ .
Ratio for increase = $5:4$ . This means the new amount is $\frac{5}{4}$ of the original amount.
Calculate the increased amount.
Increased amount = Original amount $\times \frac{5}{4}$
$= 600 \text{ frs} \times \frac{5}{4}$ $= \frac{600 \times 5}{4}$ $= 150 \times 5$ $= 750 \text{ frs}$
The increased amount is $\boxed{750 \text{ frs}}$ .

13.
Write the given equation.
$\frac{2}{3} = \frac{n}{18}$
Solve for $n$ by cross-multiplication.
$2 \times 18 = 3 \times n$ $36 = 3n$
Divide by 3 to find $n$ .
$n = \frac{36}{3}$ $n = 12$
The value of $n$ is $\boxed{12}$ .

14.
Identify the given series.
$2, 5, 8, \dots$
Determine the pattern.
Find the difference between consecutive terms:
$5 - 2 = 3$
$8 - 5 = 3$
The pattern is an arithmetic progression with a common difference of 3.
Find the next number in the series.
Add 3 to the last given term:
$8 + 3 = 11$
The next number in the series is $\boxed{11}$ .

15.
List the numbers.
$3, 8, 24, 1$
Calculate the sum of these numbers.
Sum = $3 + 8 + 24 + 1 = 36$ .
The question states "The sum of 3, 8, 24 and 1 is 36." This confirms our sum.
Count the number of values.
There are 4 numbers.
Calculate the average.
Average = $\frac{\text{Sum of numbers}}{\text{Number of values}}$
$= \frac{36}{4}$ $= 9$
The average of these numbers is $\boxed{9}$ .

Solve the following problems: 1. Calculate 0.018 of 200,000 frs. 2. Which is smaller, 1/4 or 7/8? Find their difference. 3. If X=5 and Y=3 1/2, calculate X-Y. 4. [Incomplete problem description]

Step-by-step solution

Set up a proportion based on the given information.

Find the value of 0.018 of 200,000.

Identify the fractions.

Determine which fraction is smaller.

Subtract the smaller fraction from the bigger one.

Write down the given values for X and Y.

Convert Y to an improper fraction.

Simplify X−YX - YX−Y.

Find a common denominator to subtract.

List the given decimal fractions.

Arrange them in ascending order of magnitude.

Identify the average weight and the number of pigs.

Calculate the total weight.

Determine the rate of time loss.

Calculate how many 3-hour intervals are in 15 hours.

Calculate the total time lost.

Identify the decimals.

Determine which decimal is smaller.

Subtract the smaller decimal from the bigger one.

Identify the cost of seven books.

Calculate the cost of one book.

Calculate the number of books that can be bought with 900 frs900 \text{ frs}900 frs.

Recall the conversion factor between grams and kilograms.

Convert 5400 g5400 \text{ g}5400 g to kilograms.

List the elements of sets A and B.

Find the intersection of A and B, denoted as A∩BA \cap BA∩B.

Identify the numbers to be added in base 7.

Add the numbers column by column from right to left, remembering that in base 7, digits range from 0 to 6.

Identify the initial amount and the ratio.

Calculate the increased amount.

Write the given equation.

Solve for nnn by cross-multiplication.

Divide by 3 to find nnn.

Identify the given series.

Determine the pattern.

Find the next number in the series.

List the numbers.

Calculate the sum of these numbers.

Count the number of values.

Calculate the average.

Still stuck on this one?

More Mathematics Questions

Simplify $X - Y$ .

Calculate the number of books that can be bought with $900 \text{ frs}$ .

Convert $5400 \text{ g}$ to kilograms.

Find the intersection of A and B, denoted as $A \cap B$ .

Solve for $n$ by cross-multiplication.

Divide by 3 to find $n$ .