2.1 Whole-Number Addition, Subtraction, Multiplication & Long Division

Elsevier's description of the HESI A2 Math subtest begins with basic addition, subtraction and multiplication, and division sits underneath every fraction, decimal and dosage problem in this guide. An on-screen calculator is provided, but whole-number fluency still matters: it lets you estimate before you key, catch a mistyped digit, and finish simple items in seconds. This section reviews the four whole-number operations, the regrouping steps that cause most errors, and how to interpret remainders in word problems.

1. Place Value and Column Addition

Whole numbers are written in base 10: each place is worth ten times the place to its right (ones, tens, hundreds, thousands). To add, line the numbers up by place value and start with the ones column on the right.

When a column adds to 10 or more, write the ones digit and carry the tens digit to the next column.

Worked Example: $1{,}486 + 397 + 2{,}058$

The total is $\mathbf{3{,}941}$.

Clinical use: A patient drinks $1{,}250\text{ mL}$, receives $480\text{ mL}$ of IV fluid, and takes $360\text{ mL}$ and $240\text{ mL}$ with meals. Total intake is $1{,}250 + 480 + 360 + 240 = 2{,}330\text{ mL}$.

2. Subtraction with Borrowing (Regrouping)

Subtract column by column from the right. When the top digit is smaller than the bottom digit, borrow 1 from the next column to the left, which adds 10 to the current column.

Borrowing across zeros is the classic trap. A zero cannot lend, so you borrow from the first non-zero digit to the left and turn each zero you pass into a 9.

Worked Example: $2{,}005 - 1{,}368$

1. Ones: $5 - 8$ is not possible. The tens and hundreds digits are 0, so borrow from the thousands: the 2 becomes 1, the hundreds 0 becomes 9, the tens 0 becomes 9, and the ones 5 becomes 15.
2. Ones: $15 - 8 = 7$.
3. Tens: $9 - 6 = 3$.
4. Hundreds: $9 - 3 = 6$.
5. Thousands: $1 - 1 = 0$.

The difference is $\mathbf{637}$. Check by adding: $637 + 1{,}368 = 2{,}005$.

Clinical use: A $1{,}000\text{ mL}$ IV bag has infused $365\text{ mL}$. The volume left is $1{,}000 - 365 = 635\text{ mL}$.

3. Multi-Digit Multiplication

Multiplication facts through $12 \times 12$ should be automatic, because they are the building blocks of every longer product, fraction reduction and dosage setup.

To multiply multi-digit numbers, multiply the top number by each digit of the bottom number, shift each partial product to match the digit's place value, and add the partial products.

Worked Example: $347 \times 26$

1. $347 \times 6 = 2{,}082$
2. $347 \times 20 = 6{,}940$ (the 2 is in the tens place, so this partial product ends in 0)
3. Add: $2{,}082 + 6{,}940 = \mathbf{9{,}022}$

Estimation check: $350 \times 25 = 8{,}750$, so an answer near 9,000 is reasonable. An answer of $902$ or $90{,}220$ would signal a place-value slip.

Mental Shortcuts

Clinical use: An IV pump set at $125\text{ mL/hr}$ for 24 hours delivers $125 \times 24 = 3{,}000\text{ mL}$.

4. Long Division and Remainders

In $a \div b$, $a$ is the dividend, $b$ is the divisor, the answer is the quotient, and anything left over is the remainder. Long division repeats four steps: Divide, Multiply, Subtract, Bring down.

Worked Example: $1{,}575 \div 7$

1. $7$ does not go into $1$, so start with $15$: $15 \div 7 = 2$; $2 \times 7 = 14$; $15 - 14 = 1$.
2. Bring down the $7$ to make $17$: $17 \div 7 = 2$; $2 \times 7 = 14$; $17 - 14 = 3$.
3. Bring down the $5$ to make $35$: $35 \div 7 = 5$; $5 \times 7 = 35$; the remainder is $0$.

The quotient is $\mathbf{225}$. Check: $225 \times 7 = 1{,}575$.

Worked Example with a Remainder: $1{,}000 \div 24$

Because $24 \times 41 = 984$ and $1{,}000 - 984 = 16$, the result is $41$ remainder $16$. The remainder can also be written as a fraction or a decimal:

$$41\frac{16}{24} = 41\frac{2}{3} \approx 41.67$$

Clinical use: $1{,}000\text{ mL}$ infused evenly over 24 hours runs at about $41.7\text{ mL/hr}$.

Interpreting Remainders in Word Problems

The question decides what you do with a remainder:

5. Divisibility Shortcuts

Divisibility rules speed up long division and help you reduce fractions in Chapter 3.

6. Checking with Inverse Operations

Every operation has an inverse that checks it in a few seconds:

• Subtraction is checked by addition: the difference plus the number subtracted equals the starting number.
• Division is checked by multiplication: quotient $\times$ divisor $+$ remainder $=$ dividend. For $1{,}000 \div 24$: $41 \times 24 + 16 = 984 + 16 = 1{,}000$.

If a check fails, look first for a borrowing slip, a misaligned partial product, or a remainder larger than the divisor, which means a quotient digit was too small.