Mathematics Order of Operations and Ratios

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Questions and Answers

How many problems did the student answer correctly if they earned a grade of 90% on a test with 30 problems?

24 (correct)

What percent of 30 is 15?

40%

52%

50% (correct)

47%

What is the total number of problems on a test if a student answered 40 problems correctly and received a grade of 40%?

100

150

50 (correct)

What number is 30 if 30 is 10% of that number?

300 Signup and view all the answers

What percent attendance was recorded if 8 out of 40 carpenters showed up for work?

20% Signup and view all the answers

What is the correct result of the expression $3 + (5 \times 2) \div 2 + 10$?

18 Signup and view all the answers

Which of the following represents a prime number?

2 Signup and view all the answers

What are the prime factors of 40?

2 x 2 x 5 Signup and view all the answers

What is the result of the operation $82 - 32 \times (15 - 12)^{2}$?

1 Signup and view all the answers

Which of these choices is a correct example of prime factorization for the number 90?

3 x 3 x 5 x 2 Signup and view all the answers

In the order of operations, which operation should be performed last?

Addition Signup and view all the answers

Which of the following is NOT a prime factor of 225?

9 Signup and view all the answers

What is the result of $5 + 3 \times 49 - 7 \times 258 \times 0$?

152 Signup and view all the answers

What are the three sides of a triangle if the ratio of the sides is 1:2:3 and the total length is 120 cm?

20, 40, 60 Signup and view all the answers

How do you convert a percentage of 55% to a decimal?

0.55 Signup and view all the answers

What is the base if 20% of it equals 140?

700 Signup and view all the answers

Which formula correctly defines the relationship between percentage, base, and rate?

R = P ÷ B Signup and view all the answers

What percentage does the decimal 0.345 represent?

34.5% Signup and view all the answers

What does the term 'base' refer to in percentage calculations?

The whole amount or total Signup and view all the answers

What is 20% of 700?

140 Signup and view all the answers

How do you convert the decimal 25.5 to a percentage?

2550% Signup and view all the answers

What is the simplified form of the ratio of the belt to the handkerchief?

4:1 Signup and view all the answers

What is the ratio of the number of girls to boys in the class?

11:5 Signup and view all the answers

How many cups of sugar are needed for 6 cups of boiling water?

4 cups Signup and view all the answers

If 4 pipes can fill a tank in 20 minutes, how long will it take 8 pipes to fill the tank?

10 minutes Signup and view all the answers

In a direct proportion situation with the formula $\frac{x_1}{y_1} = \frac{x_2}{y_2}$, if $x_1 = 2$, $y_1 = 3$, and $x_2 = 6$, what is $y_2$?

4 Signup and view all the answers

What type of proportion describes a situation where one quantity increases and another decreases?

Inverse Proportion Signup and view all the answers

If a triangle has sides in the ratio 1:2:3 and a perimeter of 120 cm, what is the length of the largest side?

60 cm Signup and view all the answers

Which of the following equations represents a proportion?

$\frac{6}{9} = \frac{8}{12}$ Signup and view all the answers

What is the numerical expression for 'a number increased by 5'?

x + 5 Signup and view all the answers

Which of the following is the correct verbal expression for the numerical expression '8x - 2'?

Eight times a number decreased by 2 Signup and view all the answers

What does the equation '5x + 3x + 2 = 42' simplify to when isolating for x?

8x = 40 Signup and view all the answers

What is the first step in solving the equation '5x - 3 - x + 2x = 45'?

Transpose -3 Signup and view all the answers

What is the final solution for x in the equation '3x + 2x = 30'?

x = 6 Signup and view all the answers

What does 'x ÷ 7' represent in verbal terms?

A number divided by 7 Signup and view all the answers

Which of the following is a step in solving an algebraic equation?

Subtract the constant from both sides Signup and view all the answers

Which expression translates to 'a number multiplied by 5'?

5x Signup and view all the answers

Study Notes

Order of Operations

PEMDAS is the order of operations: Parenthesis, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right).

Prime Factorization

Prime factorization breaks down a number into its prime factors.
A prime number is greater than 1 and its only factors are 1 and itself.
Example:
- Prime factors of 40 are 2, 2, 2, and 5.
- Prime factors of 24 are 2, 2, 2, and 3.

Ratio

Ratio compares two quantities.
The ratio is expressed in its simplest form.
Example:
- The ratio of girls to boys in a class with 15 boys and 33 girls is 11:5.

Proportion

Proportion is an equality of two ratios.
Direct proportion means that as one quantity increases, the other increases, or as one decreases, the other decreases.
- Formula: x1/y1 = x2/y2
Inverse proportion means that as one quantity increases, the other decreases, and vice versa.
- Formula: (x1)(y1) = (x2)(y2)
Partitive proportion divides a quantity into unequal parts.

Percent

Percent means "per hundred".
Converting percent to decimal: remove the percent symbol and move the decimal point two places to the left.
Converting decimal to percent: move the decimal point two places to the right and add the percent symbol.

Percentage, Rate, and Base

Percentage (P): part of the whole.
Base (B): the whole.
Rate (R): the number in percent.
Formulas:
- P = B × R
- B = P/R
- R = P/B

Algebraic Expressions and Equations

Algebraic expression: a combination of numbers, variables, and operations.
Translating verbal expressions into algebraic expressions:
- Example: "Eight times a number decreased by 2" is translated as 8x - 2.
Algebraic equation: an equation with two algebraic expressions set equal.
Solving algebraic equations:
- Steps: transpose, combine like terms, divide both sides.

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Description

This quiz covers essential mathematical concepts including PEMDAS, prime factorization, ratios, and proportions. Test your knowledge of how to apply these foundational principles in problem-solving. Perfect for students looking to strengthen their understanding of basic math operations.