🧮 algebra

1. The problem involves simplifying and understanding expressions with variables and division by zero. 2. Division by zero is undefined in mathematics, so any expression like $\fra

1. Problema: Se consideră mulțimea A = \left\{\frac{1}{4}, \frac{4}{6}, \frac{2}{5}, \frac{6}{9}, \frac{8}{12}, \frac{6}{10}, \frac{7}{12}, \frac{10}{15}, \frac{20}{30}\right\}. Tr

1. Stating the problem: We are given a set of fractions and asked to solve the first distinct problem, which is to simplify and compare fractions such as $\frac{12}{5}$ and $\frac{

1. **State the problem:** Simplify the expression $\frac{2^3 \times 2^2}{2^4}$. 2. **Recall the exponent rules:** When multiplying powers with the same base, add the exponents: $a^

1. **State the problem:** Simplify the expression $$\frac{5}{(r+4)(r-7)} \times \frac{r-7}{r+6}$$ as a single fraction in simplest form. 2. **Write the expression:**

1. **Problem statement:** (a) Write $14M$ as a product of its prime factors in index form.

1. Let's clarify the problem: You asked if anything involving negatives will flip the sign. 2. The rule about negatives flipping signs applies specifically when multiplying or divi

1. The problem asks: When does an equality sign flip? 2. Actually, equality signs (=) do not flip in mathematics. They always indicate that two expressions are exactly equal.

1. **Problem statement:** In a school, there are 3 classes of students taking Additional Mathematics. Class A has 42 students and class B has 40 students. Class A students constitu

1. **State the problem:** Solve for $c$ in the equation $$63.47 = \frac{6.25}{c \times 2}$$. 2. **Rewrite the equation:** The denominator is $c \times 2$, so the equation is $$63.4

1. **Problem statement:** We need to find the height of point A above the ground on a roller coaster drop of 65 m horizontal distance and 65 m vertical height, divided into two sec

1. **State the problem:** We need to calculate the value of $-68 \div -4$. 2. **Recall the rule for division of negative numbers:** Dividing two negative numbers results in a posit

1. **State the problem:** We have a function machine where an unknown input $x$ is first multiplied by $-7$, then $3$ is added, resulting in an output of $-11$. 2. **Write the equa

1. **State the problem:** We need to divide $\frac{1}{5}$ by the mixed number $2 \frac{6}{7}$. Lucinda's working shows a mistake in converting and multiplying fractions. 2. **Expla

1. **State the problem:** Simplify the expression $$\frac{7}{3} + \frac{2}{5u}$$ where $u$ is a variable. 2. **Formula and rules:** To add fractions, they must have a common denomi

1. **State the problem:** Simplify the expression $$\frac{7}{c} + \frac{3}{2}$$ into a single fraction. 2. **Formula and rules:** To add fractions, they must have a common denomina

1. **State the problem:** Simplify the expression $$\frac{5w}{3} - \frac{9}{2}$$. 2. **Formula and rules:** To subtract fractions, they must have a common denominator. The common d

1. The problem is to write the expression $\frac{11}{3} + \frac{q}{5}$ as a single fraction in simplest form. 2. To add fractions, they must have a common denominator. The denomina

1. **State the problem:** Simplify the expression $\frac{5u}{6} + \frac{u}{12}$ into a single fraction in simplest form. 2. **Find a common denominator:** The denominators are 6 an

1. **State the problem:** We need to find a number such that when it is doubled and then decreased by 9, the result is 19. 2. **Set up the equation:** Let the number be $x$. Doubli

1. **State the problem:** Simplify the expression $$\frac{3n^2}{30n}$$. 2. **Recall the rules:** When simplifying fractions with variables, divide coefficients and subtract exponen