Whole-number arithmetic

Use the distributive law to work out $8 \times 99$ in your head. (Hint: $99 = 100 - 1$.)

Amina works out $4 \times 17 \times 25$ like this: $4 \times 17 \times 25 = 17 \times (4 \times 25) = 17 \times 100 = 1700$. Which laws make her method correct?

Use the area model to work out $36 \times 24$. Split $36 = 30 + 6$ and $24 = 20 + 4$, and add all four pieces.

Divide $100$ by $7$. What is the remainder?

Kofi says $47 \div 8 = 4$ remainder $15$. He checks: $4 \times 8 + 15 = 32 + 15 = 47$. Is his answer right?

A farm has $1000$ eggs, and each tray holds $30$ eggs. How many trays are needed to hold all the eggs?

What is $6 \div 0$?

Which of these products are not bigger than the first number? (Choose all that apply.)

In Lean, a / b is the quotient and a % b is the remainder when a is divided by b. Gideon wants to state precisely that the remainder is smaller than the number we divide by (for b > 0). Which statement says exactly that?

Write a function divide(a, b) that finds the quotient and remainder by repeated subtraction: keep taking b away from a while at least b is left, counting how many times. Return the pair (q, r). You may assume a >= 0 and b > 0.