Number Sense: Fractions, Decimals, GCF/LCM & Absolute Value Distance
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Lesson overview
Ordering fractions and decimals on a number line, finding greatest common factor (GCF) and least common multiple (LCM), and using absolute value to represent distance on the GED Math test.
Go to lesson quiz →Exam guidance · GED Reasoning & Formula-Sheet Lens
Pacing
~2–2.5 minutes per item with an on-screen calculator and official formula sheet.
How GED marks this
Translating word scenarios, charts, and tables into equations rather than rote formula memorisation.
Watch out for
Answering the wrong target quantity (e.g., solving for x when the prompt asks for 2x + 5 or percentage change).
Lesson content
Why Indicator Q.1 Opens the Non-Calculator Section of GED Math
The first five questions of the GED Mathematical Reasoning exam are completed WITHOUT the TI-30XS MultiView calculator. Indicator Q.1—ordering fractions and decimals (both positive and negative) on a number line, finding greatest common factors (GCF) and least common multiples (LCM), and evaluating absolute value expressions for distance—sits right at the center of those non-calculator items. When ordering numbers on a number line, values always increase from left to right. While positive numbers get larger as their digits grow (0.4 < 0.75), negative numbers behave like temperatures below zero: −0.4 is to the RIGHT of −0.75, so −0.4 > −0.75. Equally important is recognizing that the distance between any two points A and B on a number line is ALWAYS given by the absolute value of their difference: Distance = |A − B| = |B − A|, which is never negative.
Ordering Rationals, GCF vs LCM & Number-Line Distance
1. Ordering Fractions and Decimals (Without a Calculator): • Convert every fraction to a two- or three-place decimal (memorize 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875; 1/3 ≈ 0.333, 2/3 ≈ 0.667; 1/5 = 0.2, 1/4 = 0.25), OR convert to a common denominator. • Separate negative numbers from positive numbers first. Among negative numbers, the number with the LARGER absolute value lies FURTHER to the left (is smaller): since |−5/4| = 1.25 > |−7/8| = 0.875, we have −5/4 < −7/8. 2. Factors & Multiples — GCF vs LCM: • Greatest Common Factor (GCF): The largest whole number that divides evenly into two or more numbers. In word problems, use GCF when splitting items into the 'largest possible equal-sized groups/kits/rows with nothing left over'. • Least Common Multiple (LCM): The smallest positive whole number that is a multiple of two or more numbers. In word problems, use LCM when two repeating cycles (bus schedules, blinking lights, gear teeth, or packaging counts of hot dogs and buns) align again at the same time. 3. Absolute Value and Distance on a Number Line: • |x| is the distance of x from 0 on the number line, so |−9| = 9 and |9| = 9. • The distance between two numbers a and b on a number line is ALWAYS |a − b| = |b − a|. When an operation is inside absolute value bars, treat the bars like parentheses first: evaluate the expression inside, then make the result non-negative.
Worked Example 1: Ordering Positive and Negative Fractions & Decimals
Place the following five numbers in order from least to greatest (without a calculator): −3/4, 0.6, −0.85, 5/8, −2/5
Active Worked Example · Predict Step 1
4 stepsWrite down the formula, rule, or first move you would make before revealing Step 1.
Worked Example 2: GCF Kit-Making & Absolute Value Elevation Change
Part A: A community volunteer has 48 notebooks and 72 pencils. She wants to assemble the greatest possible number of identical school-supply kits using all the notebooks and pencils with none left over. How many kits can she make, and how many pencils will be in each kit? Part B: A desert research station is at an elevation of −42.5 meters (below sea level), and a nearby weather tower is at an elevation of +118.3 meters. Write two equivalent absolute-value expressions for the vertical distance between them and find the distance.
Active Worked Example · Predict Step 1
4 stepsWrite down the formula, rule, or first move you would make before revealing Step 1.
Non-Calculator GED Traps to Avoid
• Negative sign outside vs inside absolute value bars: |−12| = 12, but −|−12| = −12 because the minus sign outside the bars is applied AFTER taking the absolute value! • Subtracting a negative inside |A − B|: The distance between 8 and −5 is |8 − (−5)| = |8 + 5| = 13, NOT |8 − 5| = 3.
Key Takeaways
• On a number line, values increase from left to right; for negative numbers, larger digit magnitudes lie further left (−0.85 < −0.40). • Use GCF when dividing two quantities into the greatest number of equal groups; use LCM when finding when two repeating cycles coincide. • The distance between points A and B on a number line is always |A − B| = |B − A| ≥ 0.
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