📘 arithmetic

1. **State the problem:** A carpenter has a piece of wood 8.1 metres long and saws off 6.2 metres from it. 2. **What is asked:** Find the length of the remaining piece of wood.

1. **State the problem:** Tessa first added 0.6 grams of salt to the soup, then added 0.9 grams more. We need to find the total amount of salt added. 2. **Formula used:** To find t

1. **State the problem:** Simplify the expression $2 - \frac{1}{3}$. 2. **Recall the rule:** To subtract a fraction from a whole number, convert the whole number to a fraction with

1. The problem is to subtract the mixed number $-5 \frac{7}{15}$ from the decimal $-5.52$. 2. First, convert the mixed number $-5 \frac{7}{15}$ to an improper fraction or decimal f

1. The problem is to explain what an area model is in mathematics. 2. An area model is a visual representation used to multiply numbers, especially useful for understanding multipl

1. The problem asks to make three numbers each having five digits from the number 47102. 2. A five-digit number must have digits from 0 to 9 and cannot start with 0.

1. **State the problem:** Multiply the numbers 5.732 and 222. 2. **Recall the multiplication rule:** To multiply decimals, multiply as if they were whole numbers, then place the de

1. The problem states that 24 is 6 times as many as 4, which means 24 equals 6 multiplied by 4. 2. The formula for multiplication is:

1. The problem is to multiply 13.6 by 2.1. 2. The multiplication formula is straightforward: $a \times b = c$ where $a=13.6$ and $b=2.1$.

1. **State the problem:** We need to estimate and then find the exact difference of the mixed numbers $2 \frac{1}{4}$ and $1 \frac{3}{5}$. 2. **Convert mixed numbers to improper fr

1. The problem is to subtract two decimal numbers: $3.428 - 5.42$. 2. To subtract, align the decimal points:

1. **State the problem:** We need to divide 2,515 by 5. 2. **Recall the division formula:** Division is the process of finding how many times the divisor fits into the dividend. He

1. a) (-8) + (+16) = 8 1. b) (-9) + (-6) = -15

1. The problem is to perform addition or subtraction of numbers. 2. The general rule is: when adding numbers, combine their values; when subtracting, take away the second number fr

1. Problem statement: Compute $5!$. 2. Formula and rule: For integer $n\ge 0$ the factorial is defined by $$n! = n \times (n-1) \times \dots \times 2 \times 1$$.

1. The problem is to calculate the sum of 3528 and 4. 2. The formula for addition is $a + b = c$, where $a$ and $b$ are numbers to add, and $c$ is the result.

1. **State the problem:** We need to divide 945 by 35 using the partial quotients method. 2. **Explain the method:** Partial quotients division involves subtracting multiples of th

1. Stating the problem: Find one third of eleven sixteenths, which means calculate $\frac{1}{3} \times \frac{11}{16}$. 2. Formula used: To multiply fractions, multiply the numerato

1. **State the problem:** A recipe calls for 8 cups of flour and 5 cups of cocoa powder for one batch of brownies. The baker wants to make 3 batches. We need to find how many cups

1. **State the problem:** We need to divide 68964325 by 7439. 2. **Write the division expression:**

1. The problem is to evaluate the expression 7.1. 2. Since 7.1 is already a decimal number, there is no further simplification or calculation needed.