6th Grade Math Quiz: Perform Operations With Multi Digit Decimals

20 questions · exam conditions

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Perform Operations With Multi Digit DecimalsQuestion 1 of 20

A water bottle has $45.60$ ounces of water. After a workout, $12.75$ ounces are left. How many ounces were used? Compute $45.60 - 12.75$ by aligning decimal points.

32.85

32.95

33.15

3.285

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6th Grade Math Quiz

6th Grade Math Quiz: Perform Operations With Multi Digit Decimals

Practice Perform Operations With Multi Digit Decimals in 6th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Perform Operations With Multi Digit Decimals, giving you a quick way to practice the rules, question types, and explanations that matter most for 6th Grade Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A water bottle has $45.60$ ounces of water. After a workout, $12.75$ ounces are left. How many ounces were used? Compute $45.60 - 12.75$ by aligning decimal points.

$32.85$ (correct answer)
$32.95$
$33.15$
$3.285$

Explanation: This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For subtraction, align decimal points vertically, such as 45.60 over 12.75, and subtract columns from right to left, borrowing as needed; addition follows similar alignment; multiplication ignores decimals first, then counts places; division shifts decimals to whole numbers. For example, subtracting 45.60 - 12.75: align as 45.60 and 12.75, hundredths 0-5 requires borrowing (10-5=5, tenths become 5), tenths 5-7 requires borrowing (15-7=8, units become 4), units 4-2=2, tens 4-1=3, resulting in 32.85. The correct amount used is 45.60 - 12.75 = 32.85 ounces, which is choice A. A common error is improper borrowing, such as not adjusting for decimals leading to 33.15 or 32.95, or misalignment causing 3.285. Standard algorithms ensure precision: align decimals, subtract with borrowing, and keep the decimal in place. Verification via addition, like 32.85 + 12.75 = 45.60, confirms the result; this applies to measurements like tracking fluid ounces.

Question 2

A water bottle holds $45.60$ ounces when full. After practice, $12.75$ ounces are left. Using the standard subtraction algorithm (align decimal points), how many ounces were drunk?

$33.15$
$32.85$ (correct answer)
$32.95$
$33.85$

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (45.60 over 12.75, decimals line up), add/subtract columns right to left (0-5 can't borrow to 10-5=5, 5-7 can't borrow to 15-7=8 with carryover effects, resulting in 32.85), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this subtraction, align 45.60 and 12.75, subtract with borrowing to get 32.85 ounces drunk. A common error is misalignment or improper borrowing, like subtracting without borrow leading to 32.95 or arithmetic mistakes. Standard algorithms: subtract with alignment and regrouping; verification by adding back (32.85 + 12.75 = 45.60 checks out). In measurement contexts like ounces, this ensures precise calculations.

Question 3

A runner jogged $18.45$ km on Saturday and $7.80$ km on Sunday. How many kilometers did the runner jog in total? (Align decimals to add.)

$26.25$ (correct answer)
$25.35$
$26.35$
$25.25$

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this question, add 18.45 + 7.80 by aligning decimals: 18.45 + 7.80 = 26.25. A common error is misalignment, such as adding without carrying over, resulting in 25.25. Standard algorithms: add/subtract (align decimals, operate, decimal below), multiply (ignore decimals, multiply, count places, insert decimal), divide (move decimals right, divide, quotient has decimal); verification and contexts like tracking distances help avoid mistakes like forgetting to carry.

Question 4

Calculate: $15.6 \div 1.2$ . (Make the divisor a whole number by moving the decimal, and move the decimal in the dividend the same number of places.)

$0.13$
$130$
$13$ (correct answer)
$1.3$

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this question, divide 15.6 ÷ 1.2 by moving decimals one place to get 156 ÷ 12 = 13. A common error is not moving the decimal in both numbers, leading to incorrect quotients like 1.3 or 130. Standard algorithms promote accuracy, verifiable by multiplication (13 × 1.2 = 15.6), useful in contexts like speed calculations with decimal times.

Question 5

A science beaker has $90.25$ mL of solution. A student pours out $38.70$ mL. Using the standard subtraction algorithm (align decimals and regroup if needed), how much solution remains?

$61.55$
$52.45$
$51.45$
$51.55$ (correct answer)

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (90.25 over 38.70, decimals line up), add/subtract columns right to left (5-0=5, 2-7 can't borrow leading to 51.55 after regrouping), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this subtraction, align 90.25 and 38.70, subtract with borrowing to get 51.55 mL remaining. A common error is improper regrouping, like 52.45 without full borrowing or arithmetic like 61.55. Standard algorithms: align and subtract with regrouping; verification by addition (51.55 + 38.70 = 90.25 checks out). In volume contexts like mL, this prevents errors.

Question 6

A student buys a notebook for $12.50 and a pack of pens for $15.75. What is the total cost? (Use the standard addition algorithm by aligning decimal points.)

$282.5
$18.25
$27.35
$28.25 (correct answer)

Explanation: This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For addition, align the decimal points vertically, such as 12.50 over 15.75, and add columns from right to left, carrying over as needed; for subtraction, align similarly and borrow when necessary; multiplication involves ignoring decimals initially, multiplying whole numbers, then placing the decimal based on total decimal places; division requires shifting decimals in both divisor and dividend to make the divisor whole, then dividing as usual. For example, adding 12.50 + 15.75: align as 12.50 and 15.75, add hundredths 0+5=5, tenths 5+7=12 (write 2, carry 1), units 2+5+1=8, tens 1+1=2, resulting in 28.25. The correct total cost is $12.50 + $15.75 = $28.25, which is choice B. A common error is misalignment, such as adding without aligning decimals leading to $282.5, or arithmetic mistakes like forgetting to carry over resulting in $27.35. Standard algorithms ensure accuracy: align decimals for addition and subtraction, operate column by column, and place the decimal directly below. Verification can be done by subtracting one addend from the sum, like $28.25 - $15.75 = $12.50, confirming the addition; this skill applies to contexts like calculating total costs in money.

Question 7

Verify this calculation using an inverse operation: A student says $34.70 - 18.55 = 16.15$ . Which check correctly verifies the subtraction?

Check by multiplying: $18.55 \times 16.15 = 34.70$
Check by adding: $34.70 + 18.55 = 16.15$
Check by adding: $18.55 + 16.15 = 34.70$ (correct answer)
Check by subtracting: $18.55 - 16.15 = 34.70$

Explanation: This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division, with verification using inverse operations. To verify subtraction like 34.70 - 18.55 = 16.15, use inverse addition: add the result to the subtracted number (16.15 + 18.55 = 34.70); multiplication and division have their inverses too. For example, checking 34.70 - 18.55: adding 18.55 + 16.15 gives 34.70, confirming accuracy. The correct verification is checking by adding 18.55 + 16.15 = 34.70, which is choice B. A common error is using the wrong inverse, like subtracting instead or adding incorrectly, leading to invalid checks. Standard verification: for subtraction, add back to original; this ensures reliability in calculations. Contexts include financial transactions, and mistakes often involve confusing operations or arithmetic errors.

Question 8

A rectangular sticker is $14.2$ cm long and $3.6$ cm wide. Using the standard multiplication algorithm (multiply as whole numbers, then place the decimal), what is the area $14.2\times 3.6$ in square centimeters?

$511.2$
$50.12$
$5.112$
$51.12$ (correct answer)

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (14.2×3.6→142×36=5112), count total decimal places in factors (14.2 has 1, 3.6 has 1, total 2), place decimal in product from right (5112 with 2 places: 51.12). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this multiplication, ignore decimals to multiply 142×36=5112, then place decimal two places from right to get 51.12 square cm. A common error is incorrect decimal placement, like 5.112 or 511.2, or multiplication mistake like 50.12. Standard algorithms: multiply then count places; verification by division (51.12 ÷ 3.6 = 14.2 checks out). In area contexts, this ensures correct calculations.

Question 9

Calculate: $12.6 \times 4.5$ . (Multiply as whole numbers, then place the decimal using the total number of decimal places.)

$56.7$ (correct answer)
$0.567$
$5.67$
$567$

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this question, multiply 12.6 × 4.5 as 126 × 45 = 5670, with 2 decimal places total, so 56.70 or 56.7. A common error is wrong decimal count, like placing it to get 5.67 or 567. Standard algorithms and verification by division support accurate computations in real-world scaling problems.

Question 10

A class is making bracelets. Each bracelet uses $12.5$ cm of string, and they make $3.2$ bracelets' worth of string into one long piece for a project. What is the total length of string needed? Compute $12.5 \times 3.2$ using the standard algorithm.

$4.0$
$40.0$ (correct answer)
$400$
$0.40$

Question 11

A ribbon is $12.5$ cm long and another ribbon is $3.75$ cm long. What is the total length? Compute $12.5 + 3.75$ using the standard algorithm (write $12.50 + 3.75$ ).

$500$
$16.25$ (correct answer)
$15.25$
$16.05$

Explanation: This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For addition, align decimal points vertically, writing 12.50 + 3.75, and add from right to left with carrying; subtraction aligns similarly with borrowing; multiplication counts total decimal places after whole-number multiplication; division moves decimals equally. For example, adding 12.50 + 3.75: align as 12.50 and 3.75, hundredths 0+5=5, tenths 5+7=12 (write 2, carry 1), units 2+3+1=6, tens 1+0=1, resulting in 16.25. The correct total length is 12.5 + 3.75 = 16.25 cm, which is choice B. A common error is not aligning decimals, such as treating them as whole numbers to get 500, or carry-over mistakes leading to 16.05 or 15.25. Standard algorithms promote accuracy: align decimals, add column by column, and place the decimal below. Contexts include measurements like lengths in cm, and verification by subtraction, such as 16.25 - 3.75 = 12.5, ensures correctness.

Question 12

A recipe uses $48.75$ ounces of smoothie mix to make $2.5$ equal servings. Using the standard division algorithm (move the decimal to make the divisor a whole number), how many ounces are in each serving: $48.75\div 2.5$ ?

$19.5$ (correct answer)
$195$
$1.95$
$0.195$

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (2.5→25 move 1 place), move dividend same amount (48.75→487.5), divide as whole numbers (487.5÷25=19.5). For this division, move decimals one place to get 487.5÷25=19.5 ounces per serving. A common error is moving decimals incorrectly, like 48.75÷2.5 as 1.95 or 195 without adjustment. Standard algorithms: equal decimal moves then divide; verification by multiplication (19.5 × 2.5 = 48.75 checks out). In recipe contexts, this avoids portion errors.

Question 13

A rectangular sticker is $3.5$ inches wide and $2.4$ inches tall. What is its area? Compute $3.5 \times 2.4$ using the standard multiplication algorithm (multiply as whole numbers, then place the decimal).

$0.84$
$8.4$ (correct answer)
$8.04$
$84.0$

Explanation: This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For multiplication, ignore decimals and multiply as whole numbers (3.5 as 35, 2.4 as 24, 35×24=840), then count total decimal places (1+1=2) and place the decimal accordingly (8.40 or 8.4); addition and subtraction align decimals; division shifts to whole numbers. For example, 3.5×2.4: 35×24=840, with 2 decimal places, becomes 8.40=8.4. The correct area is 3.5 × 2.4 = 8.4 square inches, which is choice C. A common error is incorrect decimal placement, such as using 1 place to get 84.0 or 3 places for 0.84, or arithmetic errors like 35×24=800 leading to 8.00. Standard algorithms for multiplication: ignore decimals, multiply, count places, insert decimal from the right. Verification by division, like 8.4 ÷ 2.4 = 3.5, confirms; this applies to areas and measurements.

Question 14

At a bakery, cupcakes are sold in boxes. Small boxes hold 8.25 dozen cupcakes and cost $24.75. Large boxes hold 12.5 dozen cupcakes and cost $35.50. What is the difference in price per dozen cupcakes between small and large boxes?

$0.26 per dozen difference in pricing
$0.16 per dozen difference in pricing (correct answer)
$0.84 per dozen difference in pricing
$0.58 per dozen difference in pricing

Explanation: When you encounter unit rate problems like this, you need to find the cost per unit for each option, then compare them. This question asks for the difference in price per dozen cupcakes between box sizes. First, calculate the price per dozen for small boxes:

\frac{\$24.75}{8.25 \text{ dozen}} = \$3.00

per dozen. Next, find the price per dozen for large boxes:

\frac{\$35.50}{12.5 \text{ dozen}} = \$2.84

per dozen. The difference is

\$3.00 - \$2.84 = \$0.16

per dozen, making choice B correct. Let's examine why the other answers are wrong. Choice A (

0.26) might result from calculation errors when dividing the costs by the quantities. Choice C (

0.84) could come from mistakenly subtracting $2.84 from

3.68 (if you incorrectly calculated one of the unit rates) or from other computational mistakes. Choice D (

0.58) might arise from errors in the division process or mixing up which values to subtract. The key insight here is that large boxes offer a better deal per dozen cupcakes, which makes economic sense since bulk purchases typically cost less per unit. Study tip: For unit rate comparison problems, always set up your fractions as

\frac{\text{total cost}}{\text{total quantity}}

for each option, calculate carefully, then find the difference. Double-check your division by ensuring your unit rates make sense - larger quantities usually mean lower per-unit costs.

Question 15

A rectangular garden measures 12.8 meters by 9.45 meters. If fencing costs $7.50 per meter, what is the total cost to fence the entire perimeter of the garden?

$333.75 for complete perimeter fencing (correct answer)
$167.38 for complete perimeter fencing
$668.50 for complete perimeter fencing
$301.13 for complete perimeter fencing

Explanation: Perimeter = 2(length + width) = 2(12.8 + 9.45) = 2(22.25) = 44.5 meters. Cost = 44.5 × $7.50 = $333.75. Choice B is half the correct answer (forgetting to double for both lengths and widths). Choice C is double the correct answer. Choice D results from calculating area instead of perimeter.

Question 16

Emma's car travels 28.4 miles per gallon. On a recent trip, she used 15.75 gallons of gas. If gas costs $3.89 per gallon, what was the total distance traveled and the total cost of gas for this trip?

462.8 miles traveled and $58.94 spent on gas
437.1 miles traveled and $61.27 spent on gas
447.3 miles traveled and $67.52 spent on gas
447.3 miles traveled and $61.27 spent on gas (correct answer)

Explanation: When you encounter a multi-step word problem like this, break it down into separate calculations based on what information you're given and what you need to find. You have three key pieces of information: Emma's car gets 28.4 miles per gallon, she used 15.75 gallons, and gas costs $3.89 per gallon. You need to find both the total distance and total cost. For distance traveled, multiply miles per gallon by gallons used: $

28.4 \times 15.75 = 447.3

miles. For the cost of gas, multiply gallons used by price per gallon:

15.75 \times 3.89 = 61.27

$ dollars. Looking at the wrong answers: Choice A uses an incorrect distance calculation of 462.8 miles, which suggests an error in multiplication, and also has the wrong gas cost. Choice B has the wrong distance (437.1 miles) but happens to get the correct gas cost—this shows someone made an arithmetic error on the first part but calculated the second part correctly. Choice C gets the distance right (447.3 miles) but calculates the gas cost incorrectly as $67.52, possibly by making an error in decimal multiplication. Choice D correctly shows 447.3 miles traveled and $61.27 spent on gas. Study tip: In multi-step problems, solve each part independently and double-check your decimal multiplication. Many mistakes happen when rushing through the arithmetic, so take time to line up decimal places correctly when multiplying.

Question 17

A recipe uses $15.6$ cups of juice to make $1.2$ equal batches. How many cups of juice are in each batch? Compute $15.6 \div 1.2$ by moving the decimal to make the divisor a whole number.

$13$ (correct answer)
$0.13$
$1.3$
$130$

Question 18

A recipe uses $2.75$ cups of flour per batch. You want to make $3$ batches. How many cups of flour do you need? (Compute $2.75 \times 3$ using the standard multiplication algorithm.)

$8.05$
$0.825$
$82.5$
$8.25$ (correct answer)

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this question, multiply 2.75 × 3 as 275 × 3 = 825, with 2 decimal places, so 8.25. A common error is forgetting decimal places, resulting in 825 or 0.825. Standard algorithms facilitate scaling in recipes, verifiable by division, preventing placement errors.

Question 19

A runner jogs $26.45$ miles in one week and $18.9$ miles the next week. What is the total distance jogged? Compute $26.45 + 18.90$ by aligning decimal points.

$453.5$
$45.35$ (correct answer)
$44.45$
$35.35$

Explanation: This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For addition, align decimals vertically, writing 26.45 + 18.90, and add from right to left with carrying; subtraction uses borrowing; multiplication ignores decimals then places them; division shifts decimals. For example, 26.45 + 18.90: align as 26.45 and 18.90, hundredths 5+0=5, tenths 4+9=13 (write 3, carry 1), units 6+8+1=15 (write 5, carry 1), tens 2+1+1=4, resulting in 45.35. The correct total distance is 26.45 + 18.9 = 45.35 miles, which is choice A. A common error is misalignment or not adding zeros, leading to 44.45 or 35.35, or carry-over mistakes like 453.5. Standard algorithms ensure reliability: align decimals, add with carrying, decimal below. Verification by subtraction, such as 45.35 - 18.9 = 26.45, works; applies to tracking distances in sports.

Question 20

A student buys a notebook for $12.50 and a pack of pens for $15.75. Using the standard addition algorithm (align decimal points), what is the total cost?

$29.15
$28.25 (correct answer)
$282.5
$27.35

Explanation: This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 15.75, decimals line up), add/subtract columns right to left (0+5=5, 5+7=12 write 2 carry 1, 2+5+1=8, 1+1+0=2, 0+0=0: sum 28.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this addition, align 12.50 and 15.75, add to get 28.25, which is the total cost. A common error is not aligning decimals, like adding 1250 + 1575 as 2825 without decimal, resulting in $2825 or $28.25 misplaced. Standard algorithms ensure accuracy: for addition, align and add with carry; verification by subtracting one addend from sum (28.25 - 15.75 = 12.50 checks out). In money contexts, this prevents mistakes in totals.