Preparing for the no-calculator part of GED math

What the first part rewards

Without a calculator, speed comes from knowing facts cold, not from long hand computation. If you find yourself doing a page of long division, step back. There is almost always a shorter route, such as simplifying a fraction first, rounding to compare choices, or noticing that one answer is the only one with the right sign.

Plan to finish the first part with a few minutes to spare and use them to recheck your work. Treat the end of the part as final: review every answer before you move on, since you should not count on returning to it once the calculator section begins.

• Multiplication facts through 12 × 12, without hesitation.
• Perfect squares from 1² to 15² and cubes from 1³ to 5³.
• Rules for adding, subtracting, multiplying, and dividing negative numbers.
• Common fraction, decimal, and percent equivalents.
• Divisibility rules for 2, 3, 5, 9, and 10.

Signed numbers and absolute value

Negative numbers cause more lost points on this part than any hard formula. For multiplication and division, two numbers with the same sign give a positive result, and two with different signs give a negative result. For a longer product, count the negative factors: an even number of them gives a positive answer, and an odd number gives a negative one.

Subtracting a negative is the same as adding a positive: 7 − (−4) = 7 + 4 = 11. When adding numbers with different signs, subtract the smaller size from the larger and keep the sign of the larger: −15 + 9 = −6. Absolute value is the distance from zero, so it is never negative. Bars act like parentheses: work out what is inside first, then take the distance from zero.

Exponents, roots, and scientific notation

An exponent tells how many times to use the base as a factor: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Watch the parentheses with negatives. (−3)² = 9 because the negative is squared, but −3² = −9 because only the 3 is squared. Any nonzero number to the zero power is 1, and a negative exponent means a reciprocal: 10⁻² = 1/100.

A square root undoes squaring, so knowing perfect squares lets you find roots instantly: √144 = 12. For a number that is not a perfect square, find the two perfect squares around it. Since 49 < 50 < 64, √50 is between 7 and 8, and very close to 7. That is often enough to pick the right choice or place a point on a number line.

Scientific notation writes a number as a value from 1 up to 10 times a power of ten: 45,000 = 4.5 × 10⁴. To multiply, multiply the front numbers and add the exponents, then adjust if the front number is 10 or more.

Mental math shortcuts

A few shortcuts turn awkward arithmetic into steps you can do in your head or with a line or two of scratch work.

• Round and adjust: 298 + 457 is 300 + 457 − 2 = 755.
• Split a factor: 7 × 48 is 7 × 50 − 7 × 2 = 350 − 14 = 336.
• Regroup to make easy numbers: 25 × 36 is 25 × 4 × 9 = 100 × 9 = 900.
• Halve and double: 16 × 35 is 8 × 70 = 560.
• Cancel before you divide: 84 ÷ 12 is the same as 28 ÷ 4 = 7, after dividing both by 3.

Use the answer choices and practice daily

The answer choices are information. Before computing, estimate. If you need 4.8 × 0.25, notice that 0.25 is 1/4, so the answer is 4.8 ÷ 4 = 1.2, and any choice above 4.8 is impossible. Check the sign: if the expression must be negative, eliminate every positive choice. Check the last digit: 37 × 23 must end in 1, because 7 × 3 = 21. When an equation is involved, plug a choice back in rather than solving from scratch.

Build the skill with short, daily sessions. Spend ten minutes a day on arithmetic with your phone and calculator out of reach. Mix signed numbers, exponents, roots, and quick fraction problems, and time yourself once a week to see your speed improve. Keep your scratch work in neat rows, one step per line, so you can find an error quickly when you recheck.