EIAT math section: decimals, fractions and algebra by hand

Mathematics is 30 of the EIAT's 100 questions, according to NEIEP's study guide. The topics are school arithmetic and basic algebra. What makes the section hard for many applicants is doing that arithmetic by hand, on paper, at pace.

What comes up

NEIEP's study guide names two areas: arithmetic — addition, subtraction, multiplication, division, fractions, decimals and percentages — and algebra, meaning solving equations and manipulating formulas.

Its three example questions show the level more precisely: a decimal long division, a mixed number multiplied by a fraction, and a multi-step expression that has to be worked in the right order. Not hard, but fiddly by hand. Our EIAT study guide works through methods for all three.

Calculators

NEIEP's public study guide and FAQ do not say whether a calculator is allowed. The examples are clearly designed to be done by hand, so prepare without one and follow the instructions for your own test session.

The fifth option

Each of NEIEP's example math questions offers five answers, and the fifth is "No answer". Treat it as a real option: if your result matches none of the four figures, it is the logical choice, so do not just pick the closest number.

One caution from the official examples: in the decimal division example, the keyed answer is the result rounded to one decimal place. So compare your working with the precision the options are written in before you decide nothing matches. On our math section, "No answer" is correct on around one question in nine, so checking becomes a habit.

What to actually practice

Long division with decimals

Move the decimal point in the divisor until it is a whole number, move it the same number of places in the number being divided, then divide normally. Practice until you do not have to think about which way the point moves.

Fractions and mixed numbers

Turn mixed numbers into improper fractions before doing anything else. To multiply, multiply across the top and the bottom. To divide, turn the second fraction upside down and multiply. Cancel before you multiply and the numbers stay small enough to handle.

Order of operations

Parentheses first, then multiply and divide, then add and subtract. A nested expression is safest worked one line at a time, writing the intermediate result down. Trying to hold three steps in your head is where the marks go.

Percentages

Ten percent is a decimal point moved one place. Everything else builds from that: five percent is half of it, twenty percent is double, so fifteen percent is ten plus five. Far faster than multiplying by 0.15.

Simple algebra

Get the term with the letter on its own, then divide. Whatever you do to one side of the equation you do to the other.

How to practice it

On paper, with a clock, and no calculator. That is not a detail. Doing these on a phone with a calculator open is practicing a different skill entirely. Work the way you will work on the day: pencil, scrap paper, and an eye on the time.

Our EIAT math practice keeps the five-option format with "No answer" in its proper place at the bottom, and shows the full working for every question.