📘 arithmetic

1. **State the problem:** We need to calculate $12.75 \div 0.15$. 2. **Rewrite the division to avoid decimals:** Multiply both the dividend and divisor by 100 to eliminate decimals

1. **State the problem:** Calculate the difference between $\frac{9}{1/3}$ minus $4 \frac{5}{6}$. 2. **Rewrite the mixed number:** $4 \frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac

1. **State the problem:** Calculate the sum of 1 plus 1. 2. **Formula used:** Addition of two numbers is given by $a + b$.

1. The problem is to subtract the mixed numbers $4 \frac{1}{3} - 3 \frac{2}{3}$. 2. To subtract mixed numbers, it is often helpful to convert the whole number part to a fraction to

1. **State the problem:** Calculate the sum of 6 and 7. 2. **Formula used:** Addition of two numbers is given by $a + b$.

1. The problem is to compare the mixed number $3 \frac{1}{8}$ and the percentage $75\%$. 2. First, convert the mixed number $3 \frac{1}{8}$ to an improper fraction or decimal for e

1. **Stating the problem:** We are given the ages of three people: you (9 years), your elder sister (14.5 years), and your mother who is 31.5 years older than you. We need to find:

1. **State the problem:** Calculate the value of the fraction $$\frac{898.2 \times 4.314}{1725.4}$$ and round the answer to 3 significant figures. 2. **Write the formula:** The exp

1. **State the problem:** Calculate the product of the numbers 2, 3, 5, 7, and 11. 2. **Formula used:** Multiplication of integers is associative and commutative, so we can multipl

1. The problem asks to find 10% of 1500. 2. The formula to find a percentage of a number is: $$\text{Percentage value} = \frac{\text{Percentage}}{100} \times \text{Total value}$$

1. **State the problem:** Calculate the division $1899 \div 21$ using long division. 2. **Recall the division formula:** For numbers $a$ and $b$, division is $a \div b = q$ where $

1. The problem asks for the quotient of $-24 \div 6$. 2. The quotient is the result of division, so we use the division operation.

1. **State the problem:** Calculate the sum of 5 and 5. 2. **Formula used:** Addition of two numbers is given by $a + b$.

1. **State the problem:** Calculate the sum of 9979 and 94738. 2. **Formula used:** Addition of two numbers is given by $$a + b$$ where $a=9979$ and $b=94738$.

1. **State the problem:** Calculate the sum of 91387 and 2998.74. 2. **Write the addition expression:**

1. State the problem: Compute $91387 + 2998,74$. 2. Formula and rules: Addition is commutative and associative, so $a+b=b+a$ and when adding decimals you must align decimal places

1. The problem is to multiply the numbers 291387 and 299874. 2. The multiplication formula is straightforward: $$a \times b$$ where $a=291387$ and $b=299874$.

1. **State the problem:** Calculate the sum of 4723.30 and 5337. 2. **Formula used:** Addition of two numbers is done by summing their values digit by digit.

1. **State the problem:** Calculate the sum of 4967.83 and 7489. 2. **Formula used:** Addition of decimal numbers is done by aligning the decimal points and adding corresponding di

1. **State the problem:** Calculate the value of $7 \times \left(1 \frac{5}{7}\right) + 2$ and compare it to $9 + 5$. 2. **Convert the mixed number to an improper fraction:**

1. **State the problem:** We need to divide 472 by 11. 2. **Write the division expression:**