🧮 algebra

1. **Problem a:** Simplify and solve \(\left(2 \frac{1}{3} + \frac{1}{2} - \frac{1}{12}\right) - 2 \left(\frac{1}{3} + \frac{1}{4}\right) - \sqrt{\frac{1}{9}}\). 2. Convert mixed n

1. **Problem 9a:** Predict the next three numbers in the pattern: $-1, \frac{1}{2}, -\frac{7}{8}, -\frac{1}{4}, \frac{3}{8}, ...$ - Observe the pattern: signs alternate and fractio

1. **Problem:** Lori owes her mother 39. She pays back 1/3 of this debt, then 1/4 of the remaining debt. How much does she still owe? 2. **Formula and rules:** To find the remainin

1. Calculate the following sums and differences of rational numbers. 1.a) $\frac{3}{10} + \frac{1}{5}$

1. Calculate $\frac{3}{10} + \frac{1}{5}$. Step 1: State the problem.

1. **State the problem:** Solve the equation $y = 2x + \frac{14}{15}$ for $y$ in terms of $x$. 2. **Understand the equation:** This is a linear equation where $y$ depends on $x$.

1. **State the problem:** If 1.5 chickens lay 1.5 eggs in 1.5 days, how many eggs does 1 chicken lay in 3 days? 2. **Understand the problem:** We want to find the egg-laying rate p

1. Calculate the sum or difference of the given rational numbers. **a)** $\frac{3}{10} + \frac{1}{5}$

1. The problem is to find the next number in the sequence: 5, 11, 23, 47, ? 2. Let's analyze the pattern by looking at the differences between consecutive terms:

1. The problem is to find the next number in the sequence: 5, 11, 23, 47, ? 2. Observe the pattern in the differences between consecutive terms:

1. **Problem Statement:** Understand and apply the basic exponent rules with examples. 2. **Exponent Rules:**

1. **Problem statement:** Two arithmetic progressions (APs) have the same common difference. The difference between their 100th terms is 100. We need to find the difference between

1. **State the problem:** We have two sequences \(\{a_n\}\) and \(\{c_n\}\). We need to find the sum of the first 4 terms of \(\{a_n\}\), denoted \(S_4\), and then find the product

1. The problem is to analyze the sequence defined by $a_n = n^2 - 3$ and determine its properties. 2. The formula for the sequence is $a_n = n^2 - 3$, where $n$ is a positive integ

1. **Problem Statement:** Find the domain and range of the line segment starting at the open circle (-4, 2) and ending at the closed dot (1, 5). 2. **Domain:** The domain is the se

1. The problem is to find the value of $y$ when $x=0$ in the equation $15x + 5 = y$. 2. The formula given is $y = 15x + 5$.

1. **State the problem:** Solve the equation $$2000(0.8)^{\frac{x}{2}} = 1000(1.15)^x$$ for $x$. 2. **Rewrite the equation:** Divide both sides by 1000 to simplify:

1. **State the problem:** Simplify the expression $2x + 32x$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same.

1. **Stating the problem:** We have a square ABCD with side length $n$ cm, where $n$ is a natural number. The area of quadrilateral AECF is given as 66 cm². We want to find the per

1. The problem is to simplify the expression $3x + 2x$ using algebra tiles. 2. Algebra tiles represent variables and constants visually: a long rectangle for $x$ and small squares

1. The problem is to represent an algebraic equation using algebra tiles. 2. Algebra tiles are visual tools that represent variables and constants: typically, a large square for $x