Divide by Two-Digit Divisors Practice Test

A library has $1{,}176$ books to place equally on $28$ shelves. A student says, “I can check my division by multiplying the quotient by $28$ to get $1{,}176$.” Use place value reasoning (like $28 \times 40 = 1{,}120$ and then adjust) to find the quotient.

What is the quotient of $1{,}176 \div 28$?

A library is putting $1{,}152$ books on shelves. Each shelf holds $32$ books. A student estimates $1{,}152\div 32$ by noting $32\times 30=960$ and $32\times 6=192$, and $960+192=1{,}152$. What is the quotient, and how does multiplication show the result makes sense?