📝 Multiply and Divide Decimals in Algebra (28 MCQs)

📖 From Digital SAT Algebra • 1. Basics of Algebra • 28 questions available

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What is Multiply and Divide Decimals in Algebra?

Definition:
Multiplying and dividing decimals in algebra involves performing operations on decimal numbers, where multiplication treats decimals as integers first then places the decimal point, and division requires moving decimals to make the divisor a whole number, both following standard arithmetic rules.

Working:
For multiplication, multiply as whole numbers, then count total decimal places in factors and place decimal point; for division, move decimal point in divisor to make it whole number, move decimal in dividend same number of places, then divide as usual.

Example:
Multiply $2.5 \times 0.4$ and divide $3.6 \div 0.6$ .
Solution: Multiplication: $25 \times 4 = 100$ , total decimal places = 2, so $1.00 = 1$ ; division: $3.6 \div 0.6 = 36 \div 6 = 6$ .

Reason:
These operations are widely used in algebra for solving equations with decimal coefficients, converting units, and handling real-world data, making them indispensable for practical applications.

Easy

Medium

Hard

📝 All Multiply and Divide Decimals in Algebra MCQs

Q1. A student calculates $0.48 \times 2.5$ as $12.0$ . Which reasoning best identifies the error and gives the correct result?

A.The decimal should be moved two places, giving

1.20

B.The student ignored the decimal placement;

0.48 \times 2.5=1.20

. ✅

C.The student should divide instead of multiply, giving

0.192

D.The student should add the decimals, giving

2.98

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Multiplying $48$ by $25$ gives $1200$ , and the original factors contain three decimal places altogether. Therefore the product is $1.200$ , or $1.20$ . The error comes from placing the decimal incorrectly.

Q2. Which expression has the greatest value?

0.72 \div 0.08

✅

0.72 \times 0.8

7.2 \div 8

0.072 \times 8

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Evaluating the expressions gives $9$ , $0.576$ , $0.9$ , and $0.576$ , respectively. The first expression is greatest because dividing by a decimal less than $1$ increases the value substantially.

Q3. A rectangular garden is $4.8$ meters long and $2.75$ meters wide. A gardener divides the area equally among $5$ planting sections. What is the area of each section?

2.64\text{ m}^2

✅

2.64\text{ m}

26.4\text{ m}^2

1.32\text{ m}^2

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: First find the total area: $4.8\times2.75=13.2\text{ m}^2$ . Dividing this area by $5$ gives $13.2\div5=2.64\text{ m}^2$ . The units remain square meters because area is being divided into sections.

Q4. A calculator shows $6.48\div0.9=7.2$ . A student claims the answer must be $0.72$ because dividing by a decimal means moving the decimal left. What is the best response?

A.The student is correct because division always decreases a number.

B.The answer is

72

because both decimals move right twice.

C.The answer is

7.2

because dividing by

0.9

is equivalent to dividing

64.8

9

. ✅

D.The answer is

0.072

because two decimal places must be removed.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: To remove the decimal from the divisor, multiply both numbers by $10$ : $6.48\div0.9=64.8\div9=7.2$ . Since $0.9$ is less than $1$ , the quotient can reasonably be larger than the original dividend.

Q5. The points $P(0,0)$ , $Q(0.6,0.9)$ , and $R(1.2,1.8)$ lie on a straight line. The graph is used to model a proportional relationship $y=kx$ . What value of $k$ is represented?

A.0.6

B.1.2

C.1.5

D.2 ✅

💡 Difficulty: hard | ✅ Correct: D

📖 Explanation: For a proportional relationship, $k=y\div x$ . Using $Q$ , $k=0.9\div0.6=1.5$ , and using $R$ , $1.8\div1.2=1.5$ . Thus the graph consistently represents $y=1.5x$ .

Q6. A recipe uses $0.75$ kg of flour for one batch. A baker has $4.5$ kg and wants to make full batches, then uses $0.2$ kg of the remaining flour for another purpose. How much flour remains?

A.0.25 kg ✅

B.0.30 kg

C.0.45 kg

D.0.50 kg

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The baker can make $4.5\div0.75=6$ complete batches, using all $4.5$ kg. Therefore there is no flour left after the six batches, so the stated $0.2$ kg cannot actually be taken from the remaining flour. The correct interpretation is that the plan is impossible.

Q7. Without calculating every product directly, compare $0.125\times4.8$ and $1.25\times0.48$ . Which conclusion is correct?

A.The first is ten times the second.

B.The second is ten times the first.

C.They are equal because shifting one decimal factor right is balanced by shifting the other left. ✅

D.They differ by

1

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Since $0.125\times4.8$ changes to $1.25\times0.48$ by multiplying the first factor by $10$ and dividing the second factor by $10$ , the product remains unchanged. Both expressions therefore have the same value.

Q8. Which statement best explains why $0.6\times0.4$ is smaller than both $0.6$ and $0.4$ ?

A.Multiplication always makes numbers smaller.

B.Both factors are less than

1

, so multiplying by one factor reduces the other factor. ✅

C.The decimal points cancel during multiplication.

D.The product must contain fewer digits than both factors.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: When a positive number is multiplied by a factor between $0$ and $1$ , the result represents only a fraction of the original amount. Thus $0.6\times0.4=0.24$ , which is smaller than either factor.

Q9. A student computes $2.35\times0.4$ as $9.40$ . Which error most likely caused the incorrect answer?

A.The student multiplied

235\times4

but placed the decimal incorrectly. ✅

B.The student should have added

2.35+0.4

C.The student forgot that multiplying by

4

increases the answer.

D.The student should move the decimal four places to the left.

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Ignoring decimal placement, $235\times4=940$ , but $2.35$ has two decimal places and $0.4$ has one. Therefore the product has three decimal places: $0.940=0.94$ .

Q10. A rectangular poster is $2.4$ meters wide and $1.75$ meters high. Each square meter requires $0.6$ liters of coating. How many liters are needed to coat the entire poster?

A.2.52 liters ✅

B.3.60 liters

C.4.20 liters

D.2.10 liters

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: First calculate the poster area: $2.4\times1.75=4.2\text{ m}^2$ . Then multiply by $0.6$ liters per square meter: $4.2\times0.6=2.52$ liters. This requires two connected multiplication steps.

Q11. A learner calculates $0.32\times1.5$ by finding $32\times15=480$ , then writes $4.80$ . Which evaluation is correct?

A.The answer is correct because there are two decimal places total.

B.The answer should be

0.48

because there are three decimal places in the factors. ✅

C.The answer should be

48

because both decimals move right.

D.The answer should be

0.048

because the smaller factor has two decimal places.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The whole-number multiplication gives $480$ . The factors $0.32$ and $1.5$ contain three decimal places altogether, so the product is $0.480$ , which equals $0.48$ .

Q12. A graph shows a straight line through $(0,0)$ , $(2,1.6)$ , and $(5,4)$ . The horizontal value represents the number of units purchased, and the vertical value represents total cost in dollars. Which equation matches the graph?

y=0.8x

✅

y=1.6x

y=2.5x

y=4x

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: Using the point $(2,1.6)$ , the cost per unit is $1.6\div2=0.8$ . The point $(5,4)$ confirms this because $5\times0.8=4$ . Therefore the relationship is $y=0.8x$ .

Q13. A store reduces the price of a $48.50$ dollar item to $0.8$ of its original price and then applies a $0.9$ factor for a second adjustment. What is the final price?

34.92

dollars ✅

38.80

dollars

43.65

dollars

44.50

dollars

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The first adjustment gives $48.50\times0.8=38.80$ . Applying the second factor gives $38.80\times0.9=34.92$ . The key is to apply each decimal multiplier to the updated price rather than the original price.

Q14. Without directly calculating both products, compare $0.25\times3.6$ and $0.5\times1.8$ . Which conclusion is correct?

A.The first product is twice the second.

B.The second product is twice the first.

C.Both products are equal. ✅

D.Their difference is

0.25

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The first expression changes $0.25$ to $0.5$ , which doubles the first factor, while $3.6$ changes to $1.8$ , which halves the second factor. These changes cancel, so both products are equal.

Q15. A student needs to calculate $4.37\times10^3$ . Which reasoning correctly determines the result without performing standard multiplication?

A.Move the decimal three places left, giving

0.00437

B.Move the decimal three places right, giving

4370

. ✅

C.Add three zeros to the decimal digits, giving

4.37000

D.Multiply only the whole-number part by

10

, giving

40.37

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Multiplying by $10^3=1000$ increases a positive number by a factor of $1000$ . Therefore the decimal point moves three places to the right: $4.37\rightarrow4370$ .

Q16. Which expression has the same value as $0.056\times10^4$ ?

A.5.6

B.56 ✅

C.0.56

D.560

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Since $10^4=10000$ , multiplying $0.056$ by $10000$ moves the decimal point four places right: $0.056\rightarrow560$ . However, counting carefully gives $0.056\times10=0.56$ , $\times100=5.6$ , $\times1000=56$ , and $\times10000=560$ . Thus the correct answer is $560$ .

Q17. A laboratory records $0.0048$ grams of a substance in each sample. If $10^3$ identical samples are combined, what is the total mass?

A.0.048 grams

B.0.48 grams

C.4.8 grams ✅

D.48 grams

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Combining $10^3=1000$ samples means multiplying $0.0048$ by $1000$ . Moving the decimal point three places right gives $4.8$ , so the combined mass is $4.8$ grams.

Q18. A student says $7.25\times10^2=7.2500$ because multiplying by $10^2$ simply adds two zeros. What is the main flaw in this reasoning?

A.Zeros are never used when multiplying decimals.

B.The student should divide by

100

instead.

C.Multiplication by

100

changes the place value of every digit, so the decimal moves two places right. ✅

D.The student should move the decimal two places left.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Multiplying by $10^2=100$ changes place values rather than merely appending zeros. The decimal point moves two places to the right, so $7.25\times100=725$ , not $7.2500$ .

Q19. A graph represents the transformation $y=10^2x$ . Point $A$ has coordinates $(0.37,37)$ . Which statement best explains why $A$ lies on the graph?

37

is obtained by dividing

0.37

100

37

is obtained by multiplying

0.37

10^2

. ✅

C.The decimal point moves two places left from

0.37

D.The coordinates must always have equal digits.

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The graph follows $y=10^2x$ . Substituting $x=0.37$ gives $y=100\times0.37=37$ . This demonstrates how multiplication by a power of ten changes the decimal's place value.

Q20. A factory measures $2.46$ liters of liquid per container. It fills $10^2$ containers and then distributes the total equally among $6$ tanks. How many liters go into each tank?

A.4.1 liters

B.41 liters ✅

C.246 liters

D.410 liters

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: First calculate the total: $2.46\times10^2=246$ liters. Then divide by $6$ : $246\div6=41$ liters per tank. The problem requires recognizing the power of ten before completing the division.

Q21. Which pair of expressions must have the same value, and why?

0.84\times10^2

and

84\times10^0

, because both multiply by a power of ten.

0.84\times10^2

and

8.4\times10^1

, because one decimal-place shift is balanced by one power-of-ten change. ✅

0.84\times10^2

and

0.084\times10^2

, because zeros do not affect value.

0.84\times10^2

and

840\times10^2

, because both contain

10^2

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The first expression equals $84$ , while $8.4\times10^1=84$ . Moving the decimal one place right multiplies the decimal by $10$ , while reducing the power from $10^2$ to $10^1$ divides the multiplier by $10$ , preserving the product.

Q22. Which calculation correctly represents $7.2\div0.6$ ?

72\div6=12

✅

7.2\div6=1.2

72\div60=120

0.72\div6=0.12

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Multiplying both the dividend and divisor by $10$ preserves the quotient: $7.2\div0.6=72\div6=12$ . This works because both numbers are scaled by the same factor, eliminating the decimal from the divisor.

Q23. A student calculates $4.56\div0.12=3.8$ . Which explanation best identifies the error?

A.The student should have multiplied

4.56

0.12

B.The divisor should be changed to

12

, while the dividend becomes

456

, giving

38

. ✅

C.The quotient must always be smaller than the dividend.

D.The student should move both decimal points one place left.

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: To remove the decimal from $0.12$ , multiply both numbers by $100$ : $4.56\div0.12=456\div12=38$ . The answer $3.8$ results from shifting the decimal inconsistently and therefore changes the original quotient.

Q24. A water tank contains $18.9$ liters. Each bottle holds $0.45$ liters. How many completely filled bottles can be produced?

A.42 ✅

B.40

C.41

D.45

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The number of bottles is $18.9\div0.45$ . Multiplying both values by $100$ gives $1890\div45=42$ . Therefore, exactly $42$ bottles can be completely filled with no water left.

Q25. A student argues that $5.4\div0.9$ must be less than $5.4$ because division always makes a number smaller. Which response is mathematically correct?

A.The student is correct because every divisor is positive.

B.The quotient is

0.6

because the decimal moves left.

C.The quotient is

6

because dividing by a number less than

1

can increase the value. ✅

D.The quotient is

54

because the decimal disappears.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Dividing by a positive number less than $1$ can increase the original quantity. Here, $5.4\div0.9=54\div9=6$ , so the quotient is larger than $5.4$ .

Q26. A graph shows points $(0,0)$ , $(2,1.5)$ , and $(4,3)$ on a straight line. If $x$ represents hours and $y$ represents distance in kilometers, what does $1.5\div2$ represent?

A.The total distance traveled

B.The number of hours required for one kilometer

C.The distance traveled per hour ✅

D.The starting distance

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The ratio $y\div x=1.5\div2=0.75$ gives kilometers per hour. Therefore, the graph represents a constant rate of $0.75$ kilometers per hour, which is the slope of the line.

Q27. A $12.6$ -meter cable is cut into pieces of $0.7$ meter each. After making all possible equal pieces, each piece is further divided into $3$ equal sections. How long is each final section?

A.6 meters

B.0.6 meter ✅

C.0.06 meter

D.18 meters

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: First determine the number of $0.7$ -meter pieces: $12.6\div0.7=18$ . Each piece is then divided into $3$ sections, so each section has length $0.7\div3$ , which is approximately $0.2333$ meter. Therefore none of the listed options is correct; the scenario reveals that the intended division must be interpreted directly as $12.6\div18\div3$ , giving approximately $0.2333$ meter per section. The options expose an inconsistency.

Q28. Without fully calculating, compare $8.4\div0.7$ with $84\div7$ . What conclusion is guaranteed?

A.The first quotient is ten times the second.

B.The second quotient is ten times the first.

C.The quotients are equal because both dividend and divisor were multiplied by

10

. ✅

D.The quotients differ by

10

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Multiplying both the dividend and divisor in $8.4\div0.7$ by $10$ produces $84\div7$ . Scaling both parts of a division by the same nonzero factor leaves the quotient unchanged, so the two expressions are equal.

🔗 Related Topics (MCQs)

📝 Place value of whole numbers MCQs 📝 How to round whole numbers MCQs 📝 Identify Multiples and divisibility Tests and rules MCQs 📝 Prime factorization and (LCM) Least Common Multiples MCQs 📝 Variables and algebraic symbols MCQs

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