The cost formula connects the total cost, the number of units, and the price per unit (the rate): total cost = (number of units) × (price per unit), or c = nr. Here, per again means “for every one,” so “$3 per package” means each package costs $3. Like the distance formula, if you know any two of the three values you can find the third by rewriting: r = c ÷ n (price per unit) and n = c ÷ r (how many units you can buy). The same triangle idea works: cover the quantity you want. For multi-step problems, you may first calculate a total cost, then compare totals, or subtract from the money you have to find the change. Watch the units: a price per pound times pounds gives dollars; dollars divided by price per item gives items. If a problem mentions tax, discounts, or delivery fees, handle each as its own step.
Every digit in a whole number has a place value that depends on where it sits. Moving one place to the left makes a digit worth ten times as much, so in 2,507,364 the first 2 is worth 2,000,000 while the 4 on the far right is worth only 4. The places, from right to left, are ones, tens, hundreds, thousands, ten thousands, hundred thousands, and millions. Commas split a number into groups of three digits to make it readable: each comma marks the end of one group (ones, thousands, millions). To read a number, say the number in each group followed by the group name, skipping any group that is all zeros: 2,507,364 is “two million, five hundred seven thousand, three hundred sixty-four.” A 0 is still important as a placeholder: 2,507,364 and 257,364 are very different numbers. On the GED Mathematical Reasoning Test you will often need to identify the digit in a particular place or the value of a digit, so practice naming places quickly.
Worked Example: In 4,086,517, name the digit in the thousands place, find the value of the 8, and write the number in words.
Place the digits: 4 millions, 0 hundred thousands, 8 ten thousands, 6 thousands, 5 hundreds, 1 ten, 7 ones. So the thousands digit is 6. The 8 is in the ten-thousands place, so its value is 80,000 (not 8).
In words: four million, eighty-six thousand, five hundred seventeen. Notice the 0 in the hundred-thousands place means there is no “hundred thousand” part to read.
1. In 4,615,382, which digit is in the hundred thousands place?
Explanation: Reading from the left: 4 is millions, 6 is hundred thousands, 1 is ten thousands, 5 is thousands. The digit is 6.
2. What is the value of the 5 in 3,052,914?
Explanation: The digits are 3 (millions), 0 (hundred thousands), 5 (ten thousands). A 5 in the ten-thousands place is worth 50,000.
3. Which number is “two million, four hundred six thousand, eighteen”?
Explanation: Two million = 2, four hundred six thousand = 406, then eighteen = 018. Writing the groups together gives 2,406,018, with zeros holding the empty places.
4. What digit is in the tens place of 91,347?
Explanation: From the right: 7 is ones, 4 is tens, 3 is hundreds.
5. In 8,260,719, the digit 2 has a value of
Explanation: The 2 is the second digit from the left, in the hundred-thousands place, so it is worth 200,000.
To compare numbers, line up their place values and compare digit by digit starting at the left, the largest place. The number with more digits is greater (when there are no leading zeros), so 4,309 is greater than 438. If two numbers have the same number of digits, find the first place where the digits differ: the larger digit wins. To put several numbers in order, compare them two at a time, or sort them by the first place where they differ. Least to greatest means smallest first (ascending); greatest to least means largest first. Know the inequality symbols: < means “is less than,” > means “is greater than,” ≤ means “is less than or equal to,” and ≥ means “is greater than or equal to.” The open end of the symbol always faces the larger number. Real-life ordering problems are common: for example, stacking boxes with the heaviest at the bottom means ordering the weights from greatest to least.
Worked Example: Put 6,205; 625; 6,250; and 6,198 in order from least to greatest, then compare 6,205 and 6,198 using a symbol.
625 has only three digits, so it is the smallest. The other three have four digits, so compare the thousands: all are 6. Compare hundreds: 6,205 has 2; 6,250 has 2; 6,198 has 1, so 6,198 comes next. Between 6,205 and 6,250 compare tens: 0 < 5.
Order: 625, 6,198, 6,205, 6,250. For the symbol, the hundreds digits 2 and 1 decide it: 6,205 > 6,198.
1. Which list shows 4,309; 438; 4,290; 4,311 from least to greatest?
Explanation: 438 has three digits, so it is least. Among the four-digit numbers, compare hundreds then tens: 4,290 < 4,309 < 4,311.
2. Which symbol makes this true? 12,450 ___ 12,540
Explanation: The first difference is in the hundreds place: 4 < 5, so 12,450 < 12,540.
3. Which is the greatest: 56,780; 56,708; 57,068; 56,870?
Explanation: All have five digits and start with 5. In the thousands place 57,068 has a 7 while the others have 6, so it is greatest.
4. Four boxes weigh 62, 58, 65, and 60 pounds. Starting at the bottom, in what order should they be stacked, heaviest at the bottom?
Explanation: The heaviest goes on the bottom, so list the weights from greatest to least: 65, 62, 60, 58.
5. Which statement is true?
Explanation: 100,000 has six digits and 99,999 has five, so 100,000 is greater. In the others, 2,305 < 2,350, 8,090 > 8,009, and 1,000 > 999.
Rounding replaces a number with a nearby, simpler number so that it is easier to work with. To round to a place: (1) find the digit in the place you are rounding to; (2) look at the digit immediately to its right; (3) if that digit is 5 or more, round up (add 1 to your digit); if it is 4 or less, keep your digit; (4) change every digit to the right of your place to 0. A number line shows why: 3,672 is closer to 3,700 than to 3,600. Rounding can carry: 995 rounded to the nearest ten is 1,000, because 99 tens plus 1 more ten makes 100 tens. Estimating means rounding the numbers in a problem first and then calculating. This is a fast way to check that your exact answer is reasonable, and on multiple-choice questions it can eliminate answer choices that are far too large or small. Round only the digit to the right of your target place; do not round in several steps (rounding 2,449 to the hundreds is 2,400, not 2,500).
Worked Example: Round 3,672 to the nearest hundred, and estimate 6,142 + 2,879 by rounding to the nearest thousand.
The hundreds digit is 6, and the digit to its right is 7, which is 5 or more, so round up: 3,672 → 3,700.
For the estimate: 6,142 → 6,000 (next digit 1) and 2,879 → 3,000 (next digit 8). So 6,142 + 2,879 ≈ 6,000 + 3,000 = 9,000. (The exact sum is 9,021, which is close.)
1. Round 3,672 to the nearest hundred.
Explanation: The digit to the right of the hundreds place is 7 (5 or more), so the hundreds digit 6 goes up to 7 and the rest become zeros.
2. Round 48,951 to the nearest thousand.
Explanation: The thousands digit is 8 and the next digit is 9, so round up to 9 thousand: 49,000.
3. Round 1,525 to the nearest thousand.
Explanation: The thousands digit is 1 and the next digit is 5, which rounds up. So 1,525 rounds to 2,000.
4. Round 995 to the nearest ten.
Explanation: The tens digit is 9 and the next digit is 5, so round up: 99 tens + 1 ten = 100 tens = 1,000.
5. Estimate 6,142 + 2,879 by rounding each number to the nearest thousand.
Explanation: 6,142 rounds to 6,000 and 2,879 rounds to 3,000, and 6,000 + 3,000 = 9,000.
You add to combine amounts. The answer is the sum or total. Words that signal addition include total, altogether, combined, in all, sum, and increase. To add by hand, write the numbers in a column so that the place values line up (ones under ones, tens under tens), then add the columns from right to left starting with the ones. If a column adds to 10 or more, write the ones digit in the answer and regroup (carry) the tens digit to the next column on the left. Adding more than two numbers works the same way: just stack them all. Addition can be done in any order (3 + 5 = 5 + 3), but alignment matters, since adding 56 to 218 in the wrong columns changes every place. Estimating first gives a quick check: if your exact sum is not close to the rounded sum, look for a misplaced digit or a missed carry.
Worked Example: Add 56 + 218 + 37.
Stack the numbers by place value and start with the ones: 6 + 8 + 7 = 21. Write 1 in the ones place and regroup 2 tens. Tens column: 5 + 1 + 3 + 2 (carried) = 11. Write 1 and regroup 1 hundred. Hundreds column: 2 + 1 (carried) = 3.
12 56 218 + 37 ----- 311
The sum is 311. Check by estimating: 60 + 220 + 40 = 320, which is close.
1. Find 2,386 + 1,692.
Explanation: Ones: 6 + 2 = 8. Tens: 8 + 9 = 17, write 7 carry 1. Hundreds: 3 + 6 + 1 = 10, write 0 carry 1. Thousands: 2 + 1 + 1 = 4. The sum is 4,078.
2. Find 108,755 + 22,442.
Explanation: Align the digits: 108,755 + 022,442. Ones 5 + 2 = 7; tens 5 + 4 = 9; hundreds 7 + 4 = 11 (write 1, carry 1); thousands 8 + 2 + 1 = 11 (write 1, carry 1); ten thousands 0 + 2 + 1 = 3; hundred thousands 1. The sum is 131,197.
3. Three boxes weigh 24 pounds, 8 pounds, and 56 pounds. What is the total weight?
Explanation: 24 + 8 + 56 = 88 pounds. Be careful to add 24 + 8 = 32 before adding 56.
4. A delivery driver makes three stops with 245, 318, and 407 packages. How many packages in all?
Explanation: 245 + 318 = 563 and 563 + 407 = 970. A quick estimate, 250 + 300 + 400 = 950, confirms the answer is close.
5. A student adds 4,872 + 3,129. Which is the best estimate to check the answer?
Explanation: Rounding to thousands gives 5,000 + 3,000 = 8,000. The exact sum 8,001 is very close, so it passes the check.
You subtract to find the difference between two amounts, to take away, or to find how much is left or how much more. Signal words include difference, left, remain, fewer, more than, how many more, and change. Write the greater number on top and line up the place values, then subtract from right to left. When the top digit in a column is smaller than the bottom digit, regroup (borrow) 1 from the next place to the left: reduce that place by 1 and add 10 to the column you are working in. If the next place is a 0, keep going left to the first nonzero digit, borrow from it, and pass 10s back down the line (for example, a 0 in the tens place becomes 9 after borrowing and passing along). Subtraction is not commutative, so order matters. You can always check by adding: the difference plus the number subtracted must equal the starting number.
Worked Example: Find 82 − 47, and then 304 − 78.
For 82 − 47: 2 is less than 7, so borrow 1 ten. The 8 tens becomes 7 tens and the 2 becomes 12. Then 12 − 7 = 5 and 7 − 4 = 3, so the answer is 35. Check: 35 + 47 = 82.
For 304 − 78: 4 < 8, but the tens digit is 0, so borrow from the hundreds. The 3 hundreds becomes 2, the tens becomes 10 and then lends 1 to the ones, leaving 9 tens, and the ones become 14. Now 14 − 8 = 6, 9 − 7 = 2, 2 − 0 = 2. The answer is 226. Check: 226 + 78 = 304.
2 9 14 3 0 4 − 7 8 ---------- 2 2 6
1. Find 1,250 − 350.
Explanation: Subtract hundreds and tens: 1,250 − 350 = 900. Check: 900 + 350 = 1,250.
2. Find 2,500 − 383.
Explanation: Borrowing across the zeros: 2,500 − 383 = 2,117. Check by adding: 2,117 + 383 = 2,500.
3. Find 44,789 − 13,890.
Explanation: Ones: 9 − 0 = 9. Tens: 8 < 9, borrow: 18 − 9 = 9. Hundreds: 6 − 8 needs a borrow: 16 − 8 = 8. Thousands: 3 − 3 = 0. Ten thousands: 4 − 1 = 3. The result is 30,899.
4. Celia’s share of lunch is $7. If she pays with a $20 bill, how much change should she get?
Explanation: Change is the difference: $20 − $7 = $13. Check: $13 + $7 = $20.
5. 205 − 67 = 138. Which addition checks this answer?
Explanation: To check subtraction, add the difference to the number subtracted: 138 + 67 should equal 205.
You multiply to combine the same amount several times: 24 + 24 + 24 is 3 × 24. The answer is the product, and the numbers multiplied are factors. Signal words include product, each, per, times, of, and twice. Knowing the multiplication tables up to 12 × 12 saves valuable time on the test. To multiply by a multi-digit number, use partial products: multiply the top number by each digit of the bottom number, starting from the ones. When you multiply by the tens digit, write a placeholder zero in the ones place first, because you are really multiplying by a multiple of 10 (for example by 50, not 5). Regroup (carry) whenever a digit product is 10 or more, adding the carried amount after you multiply the next digit. Finally, add the partial products to get the total. Multiplying by 10, 100, or 1,000 is quick: just attach that many zeros. If you are multiplying more than two numbers, multiply two of them first, then multiply the result by the next.
Worked Example: Find the product of 37 and 52.
First multiply by the ones digit 2: 2 × 7 = 14 (write 4, carry 1), 2 × 3 = 6, plus 1 is 7, so the first partial product is 74. Then multiply by the tens digit 5. Write a placeholder 0 in the ones place, and compute 5 × 7 = 35 (write 5, carry 3), 5 × 3 = 15, plus 3 is 18, giving 1,850.
37 × 52 ----- 74 1850 ----- 1924
The product is 1,924. Estimate: 40 × 50 = 2,000, which is close.
1. Find 342 × 8.
Explanation: 8 × 2 = 16 (write 6, carry 1); 8 × 4 = 32, plus 1 is 33 (write 3, carry 3); 8 × 3 = 24, plus 3 is 27. The product is 2,736.
2. Find 45 × 30.
Explanation: 45 × 3 = 135, and multiplying by 30 attaches one zero: 1,350.
3. Find 211 × 16.
Explanation: 211 × 6 = 1,266 and 211 × 10 = 2,110. Add the partial products: 1,266 + 2,110 = 3,376.
4. A gardener plants 8 seedlings in each row. How many seedlings are in 9 rows?
Explanation: “Each” signals multiplication: 8 × 9 = 72.
5. Which expression is the same as 24 + 24 + 24 + 24 + 24?
Explanation: Adding the same number 5 times is 5 × 24 = 120.
To divide means to split an amount into equal parts or to find how many groups fit. The amount being divided is the dividend, the number you divide by is the divisor, and the answer is the quotient. Signal words include each, per, shared equally, split, average, and how many groups. Use long division, working left to right through the dividend with four repeating steps: divide (how many times does the divisor fit into the current number?), multiply (quotient digit times divisor), subtract, and bring down the next digit. If the divisor does not fit into the first digit, use the first two digits instead. When you run out of digits and something is left that is smaller than the divisor, it is the remainder, written as r. For example, 2,053 ÷ 5 = 410 r 3. In a word problem, think about what the remainder means: if you are filling boxes, the remainder is the leftover items, not an extra box. You can check division with multiplication: quotient × divisor + remainder = dividend. Never divide the smaller number by the larger by mistake; the dividend is the amount being split.
Worked Example: Divide 2,053 ÷ 5. Then, if $84 is shared equally by 4 people, how much does each person get?
5 does not go into 2, so use 20: 5 goes into 20 four times (write 4 over the 0). 4 × 5 = 20, and 20 − 20 = 0. Bring down 5: 5 goes into 5 once. 1 × 5 = 5, so the remainder is 0. Bring down 3: 5 goes into 3 zero times (write 0), remainder 3. The quotient is 410 r 3. Check: 410 × 5 + 3 = 2,053.
For the sharing problem, 84 ÷ 4: 4 into 8 is 2, and 4 into 4 is 1, so each person gets $21.
1. Find 735 ÷ 7.
Explanation: 7 into 7 is 1; bring down 3: 7 into 3 is 0; bring down 5: 7 into 35 is 5. So the quotient is 105. Check: 105 × 7 = 735.
2. Find 189 ÷ 9.
Explanation: 9 × 21 = 189, so the quotient is 21.
3. Find 225 ÷ 15.
Explanation: 15 × 15 = 225, so 225 ÷ 15 = 15.
4. A baker packs 100 cupcakes into boxes of 12. How many full boxes can she fill, and how many cupcakes are left over?
Explanation: 100 ÷ 12 = 8 remainder 4 (since 12 × 8 = 96). The remainder is leftover cupcakes, not another box.
5. Find 114 ÷ 19.
Explanation: 19 × 6 = 114, so the quotient is 6.
Word problems turn up all over the GED Mathematical Reasoning Test, and a steady five-step process keeps you from guessing. Step 1: What is the question asking me to find? State the question in your own words. Step 2: What information do I need? Underline only the numbers that matter. Many problems include extra information, and wrong answer choices are often built from it. Step 3: Which operation do I need? Add to combine amounts of different sizes; subtract to find the difference between amounts; multiply to combine the same amount several times; divide to separate one amount into equal-size groups. Step 4: What is my solution? Carry out the operation. Step 5: Does my answer make sense? Reread the question, check units and size, and estimate. Wrong choices usually come from the wrong operation (like dividing when you should multiply) or from using unneeded numbers. A good habit is to write the units next to your numbers (yards, dollars, miles) so that your answer ends in the right unit.
Worked Example: Marcus needs 9 yards of ribbon for each banner. Ribbon costs $6 per yard. How many yards of ribbon does he need for 4 banners?
Step 1: find the total yards for 4 banners. Step 2: 9 yards per banner and 4 banners; the price of $6 per yard is not needed. Step 3: the same amount repeated, so multiply. Step 4: 9 × 4 = 36. Step 5: 36 yards is a sensible length for 4 banners at 9 yards each.
Common wrong answers: dividing 9 ÷ 4 (the wrong operation), or 36 × 6 = 216 (using the price when the question asks for yards).
1. Priya wants to paint walls with a total area of 2,400 square feet. One gallon covers 300 square feet. How many gallons does she need?
Explanation: Divide the total area into equal parts, one per gallon: 2,400 ÷ 300 = 8 gallons.
2. 14 children are coming to a party and each child gets 3 favors. The favors cost $2 each. How many favors are needed?
Explanation: The question asks for the number of favors, not the cost: 14 × 3 = 42. The price of $2 is extra information; using it gives the wrong answers 84 or 28.
3. Sarah lives 25 miles from the office and Kate lives 30 miles from the office. How many miles farther from the office does Kate live?
Explanation: “How many farther” asks for the difference: 30 − 25 = 5 miles. Adding gives 55, which does not answer the question.
4. A salon service takes 30 minutes for a haircut, 90 minutes for a color, and 20 minutes for a style. How many minutes will 3 haircuts take?
Explanation: Only the haircut time is needed: 3 × 30 = 90 minutes. The other times are extra information.
5. Sumayyah received $189 from selling her hats and gloves and spent $27 on yarn. How much did she earn from her knitting?
Explanation: Earnings are what is left after the cost, so subtract: $189 − $27 = $162.
Many GED problems need more than one operation. The most common mistake is to stop too early and give a partial answer that is one of the multiple-choice options. The five-step process helps: after your first calculation, go back to Step 1 and ask, “Did I answer the question?” Before you start, plan the sequence: what do I need to find first, and what will I do with it? Write each result with a label so you do not confuse it with the final answer. Questions often use a table: read the row and column headings carefully, find only the cells you need, and build the answer step by step (for example, price × quantity for each item, then add the items). Tricky wording like “for the first 4 cases… for each additional case” means splitting the quantity into two parts, pricing each, and adding. Always check that your final answer is in the unit the question asks for (dollars, cases, minutes).
Worked Example 1: A school club must sell 90 tickets in 3 days. It sells 28 on day 1 and 35 on day 2. How many must it sell on day 3?
First find the tickets sold so far: 28 + 35 = 63. That is only a partial answer. Then subtract from the goal: 90 − 63 = 27 tickets. (If you stopped at 63 you would have chosen the partial-solution trap.)
Worked Example 2 (table): Coffee costs $18 per case, tea $12 per case, and cocoa $9 per case. How much did Cafe B spend on coffee and tea?
| Cafe | Coffee (cases) | Tea (cases) | Cocoa (cases) |
|---|---|---|---|
| Cafe A | 4 | 2 | 5 |
| Cafe B | 3 | 6 | 0 |
| Cafe C | 5 | 0 | 4 |
Cafe B ordered 3 cases of coffee and 6 cases of tea. Coffee: 3 × $18 = $54. Tea: 6 × $12 = $72. Add: $54 + $72 = $126. The cocoa column is not needed (and B ordered 0 anyway).
1. Using the table above (coffee $18, tea $12, cocoa $9 per case), which cafe spent the most on coffee and tea combined?
Explanation: Cafe A: 4 × 18 + 2 × 12 = 72 + 24 = $96. Cafe B: 3 × 18 + 6 × 12 = 54 + 72 = $126. Cafe C: 5 × 18 + 0 = $90. Cafe B spent the most.
2. Delivery costs $3 per case for the first 4 cases and $2 per case for each additional case. Cafe C ordered 5 coffee and 4 cocoa cases. What was its delivery charge?
Explanation: Cafe C ordered 5 + 0 + 4 = 9 cases. First 4: 4 × $3 = $12. Additional 5: 5 × $2 = $10. Total: $12 + $10 = $22.
3. Paper comes in packages of 500 sheets. A student needs 4 binders with 120 sheets each. If she buys one package, how many sheets are left?
Explanation: First find the sheets needed: 4 × 120 = 480. Then subtract from the package: 500 − 480 = 20 sheets. The partial answer 480 is a wrong choice.
4. Each batch of muffins needs 3 cups of flour. A bag holds 20 cups. How many whole batches can be made?
Explanation: 20 ÷ 3 = 6 remainder 2. Only whole batches count, so 6 batches (the 2 left-over cups are not enough for a seventh).
5. A family pays $3,000 per year for health insurance. They have $750 in medical expenses, and the plan pays 100 percent of them. What is the total they pay for the year?
Explanation: The plan pays the medical expenses, so the family’s cost is just the premium of $3,000. The $750 is extra information.
When something moves at a constant rate, use the distance formula: distance = rate × time, or d = rt. Rate is a speed, such as 55 miles per hour, where the word per means “for every one.” Time must be in the same unit as the rate (hours with miles per hour). If you know two of the three variables you can solve for the third by rewriting the formula: r = d ÷ t (find the rate) and t = d ÷ r (find the time). The triangle below is a memory aid: cover the variable you want and read what is left. Multiplication can be written in several ways, such as n × r, nr, n(r), and n·r, and division can be written as c ÷ n or as a fraction c/n, so recognize all of them. A good habit is to substitute your answer back into the formula to check it: if 3 hours at 90 mph gives 270 miles, your numbers fit. Always write the unit in your answer: miles, miles per hour, or hours.
Worked Example: (a) How far does a bus travel at an average speed of 62 miles per hour for 4 hours? (b) A train goes 270 miles in 6 hours. What is its average speed?
(a) You know r = 62 and t = 4, and you want d. Use d = rt = 62 × 4 = 248 miles.
(b) You know d = 270 and t = 6, and you want r. Rewrite as r = d ÷ t = 270 ÷ 6 = 45 miles per hour. Check: 45 × 6 = 270.
1. A car travels at an average of 60 miles per hour for 3 hours. How far does it travel?
Explanation: d = rt = 60 × 3 = 180 miles.
2. How long does it take to drive 90 miles at an average rate of 30 miles per hour?
Explanation: t = d ÷ r = 90 ÷ 30 = 3 hours.
3. A train travels 270 miles in 3 hours. What is its average speed?
Explanation: r = d ÷ t = 270 ÷ 3 = 90 miles per hour. Check: 90 × 3 = 270.
4. A truck driver traveled 275 miles in 5 hours. What was his average speed in miles per hour?
Explanation: r = d ÷ t = 275 ÷ 5 = 55 miles per hour. Multiplying (1,375) would be the wrong operation.
5. Which formula can be used to find the time t when you know distance d and rate r?
Explanation: Starting with d = rt, divide both sides by r to get t = d ÷ r.
The cost formula connects the total cost, the number of units, and the price per unit (the rate): total cost = (number of units) × (price per unit), or c = nr. Here, per again means “for every one,” so “$3 per package” means each package costs $3. Like the distance formula, if you know any two of the three values you can find the third by rewriting: r = c ÷ n (price per unit) and n = c ÷ r (how many units you can buy). The same triangle idea works: cover the quantity you want. For multi-step problems, you may first calculate a total cost, then compare totals, or subtract from the money you have to find the change. Watch the units: a price per pound times pounds gives dollars; dollars divided by price per item gives items. If a problem mentions tax, discounts, or delivery fees, handle each as its own step.
Worked Example: (a) A teacher buys 6 packs of markers at $4 per pack. What is the total cost before tax? (b) Max pays $48 for a set of 8 floor mats. How much is one mat?
(a) c = nr = 6 × $4 = $24.
(b) You know c = $48 and n = 8 and need r, so r = c ÷ n = $48 ÷ 8 = $6 per mat. Check: 8 × $6 = $48.
1. Find the total cost of 12 boxes of cookies if each box costs $3.
Explanation: c = nr = 12 × $3 = $36.
2. If 4 tires cost $320, how much does a single tire cost?
Explanation: r = c ÷ n = $320 ÷ 4 = $80 per tire.
3. How many raffle tickets can you buy for $25 if each ticket costs $5?
Explanation: n = c ÷ r = $25 ÷ $5 = 5 tickets.
4. A company sold $640 worth of gift boxes. If each gift box costs $20, how many gift boxes did it sell?
Explanation: n = c ÷ r = $640 ÷ $20 = 32 gift boxes. Check: 32 × $20 = $640.
5. Which formula finds the number of units n when you know total cost c and price per unit r?
Explanation: Start with c = nr and divide both sides by r to get n = c ÷ r.
Place value is the value of a digit based on its position in a number. The digit 5 means 5 in the ones place, 50 in the tens place, and 500 in the hundreds place. It matters for reading numbers, comparing them, rounding, and lining up columns for operations.
Add to combine amounts of different sizes, subtract to find a difference or what is left, multiply to combine the same amount several times, and divide to split an amount into equal groups. Signal words like total, difference, each, and shared equally help.
Look at the digit in the tens place. If it is 5 or more, round the hundreds digit up; if it is 4 or less, leave it. Then change the tens and ones digits to zeros. For example, 3,672 rounds to 3,700 and 3,641 rounds to 3,600.
It depends on the question. Sometimes the remainder is the answer (leftover items), sometimes it means you need one more group (buses needed for 100 people with 40 per bus is 3 buses), and sometimes you ignore it (whole batches only).
Estimate with rounded numbers, reread the question to be sure you answered it, check that units match, and substitute your answer back into the formula or into the original situation.
The test covers number sense and operations, algebra, geometry, and data and statistics, using multiple-choice and other question types. This lesson covers the number sense and problem-solving skills that the rest of the test builds on.
The GED Math practice in the GED Math QBank gives you more practice on this topic, and you can browse every other topic in the full GED Math QBank.
