6.1 Integers, Fractions, Decimals, and Percent

Why Number Form Matters on GED Math

GED Mathematical Reasoning rarely asks for arithmetic in isolation. It asks whether you can use rational numbers to solve a realistic problem, compare quantities, or judge whether an answer is reasonable. Integers, fractions, decimals, and percents are therefore not separate topics. They are four ways to write the same amount, and roughly a quarter of the 46-item test touches this fluency directly.

The winning strategy is to convert each number into the form that makes the relationship easiest to see. Fractions show exact parts of a whole. Decimals are convenient for money and for the on-screen calculator. Percents express a part of 100 and dominate the tax, discount, tip, commission, interest, and percent-change questions that the GED loves.

Equivalent Forms You Should Know

Memorizing these benchmarks lets you estimate during the 5-question no-calculator section, where the embedded TI-30XS Multiview is locked. A negative integer such as -6 still belongs in this system; it just sits left of zero (think temperature, debt, elevation below sea level, or a yardage loss).

Ordering Rational Numbers

To order mixed forms, pick one format. Decimals are usually fastest.

Worked example: Order -3/4, -0.62, 2/5, and 0.08 from least to greatest.

Convert the fractions: -3/4 = -0.75 and 2/5 = 0.40. Now compare -0.75, -0.62, 0.08, 0.40. The least value sits farthest left, so the order is -3/4, -0.62, 0.08, 2/5.

Notice the negative-number trap: -0.75 is farther from zero than -0.62, which makes it the smaller number, not the larger one. The GED writes at least one ordering item per form specifically to catch students who rank negatives by size of digits.

Operating With Signs

For addition and subtraction, picture movement on the number line. For multiplication and division, track signs separately: like signs give a positive product, unlike signs give a negative product.

Worked example: A freezer reads -8 degrees. It warms 13 degrees, then cools 5 degrees. Final temperature?

Start at -8. Warming adds: -8 + 13 = 5. Cooling subtracts: 5 - 5 = 0 degrees.

When several signed changes stack up, write each change in order before computing. A payment lowers a debt, a fee raises a balance owed, a rise adds, a drop subtracts. Sequencing the changes is far more reliable than guessing the final sign at the end.

Percent Problems

Use one of two setups.

• Percent of a number: part = percent x whole.
• Percent change: percent change = change / original.

Worked example: A $60 tool is marked down 15%, then 8% sales tax is added to the sale price. Final cost?

Discount = 0.15 x 60 = 9, so the sale price is 60 - 9 = 51. Tax = 0.08 x 51 = 4.08. Final cost = 51 + 4.08 = $55.08. The order is fixed: discount the original, then tax the reduced price.

Percent change always uses the original amount as the base. If a value rises from 40 to 50, the change is 10 and the base is 40, so the increase is 10/40 = 25%. Dividing by 50 instead answers a different question and is the single most common percent-change error on the test.

A fast check: a 15% discount drops $60 to a little above $50, and 8% tax adds about $4, so a final answer near $55 is sensible. If your figure lands near $70 or $40, you reversed a step.

Converting Between Forms Reliably

Three conversions appear again and again, so practice them until they are automatic. To turn a fraction into a decimal, divide the numerator by the denominator: 5/8 = 5 / 8 = 0.625. To turn a decimal into a percent, multiply by 100 and add the percent sign: 0.625 becomes 62.5%. To turn a percent into a decimal, divide by 100: 7% becomes 0.07, and 145% becomes 1.45. Notice that percents above 100 are legal; a value can grow to more than its original whole, as when a population rises 145% of its prior size.

A repeating decimal warns that a fraction should be left exact: 1/3 = 0.333... and 2/3 = 0.666..., so keep the fraction and round only if the question asks for it.

Fraction Arithmetic Refresher

GED items still test direct fraction operations, especially in recipe, measurement, and budgeting contexts. To add or subtract, find a common denominator first: 2/3 + 1/4 needs twelfths, giving 8/12 + 3/12 = 11/12. To multiply, multiply across and simplify: 3/4 x 2/9 = 6/36 = 1/6. To divide, multiply by the reciprocal: 3/4 / 2/9 = 3/4 x 9/2 = 27/8 = 3 3/8.

Worked example: A board is 7/8 foot long. A carpenter cuts off 1/3 foot. How much remains?

Use a common denominator of 24: 7/8 = 21/24 and 1/3 = 8/24, so 21/24 - 8/24 = 13/24 foot. A reasonableness check confirms it, since 7/8 is close to 1 and removing about a third should leave a little over half a foot.

A recurring trap is adding numerators and denominators straight across (the false 7/8 + 1/3 = 8/11). That is never how fractions add; only a shared denominator gives equal-size parts that can be combined.