Mathematics
Grade 7
15 min
Division with decimal quotients and rounding
Division with decimal quotients and rounding
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1
Introduction & Learning Objectives
Learning Objectives
Divide whole numbers by whole numbers to produce decimal quotients.
Divide decimals by whole numbers to produce decimal quotients.
Divide decimals by decimals to produce decimal quotients.
Identify the correct place value for rounding a decimal quotient.
Round decimal quotients to a specified place value (e.g., nearest tenth, hundredth).
Apply division with decimal quotients and rounding to solve real-world problems.
Ever wondered how to split a bill evenly among friends when the total isn't a perfect whole number? 💰 Or how to calculate your average speed if you travel a certain distance in a specific time? ⏱️
In this lesson, you'll learn the essential skills of dividing numbers to get decimal answers and how to round those answers accurately....
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Key Concepts & Vocabulary
TermDefinitionExample
DividendThe number that is being divided in a division problem.In 15 ÷ 4, 15 is the dividend.
DivisorThe number by which another number (the dividend) is divided.In 15 ÷ 4, 4 is the divisor.
QuotientThe result obtained from dividing one number by another.In 15 ÷ 4 = 3.75, 3.75 is the quotient.
Decimal QuotientA quotient that contains a decimal point, indicating that the division resulted in a non-whole number.When 10 is divided by 3, the decimal quotient is 3.333...
RoundingThe process of approximating a number to a specified place value, making it simpler while keeping its value close to the original.Rounding 3.78 to the nearest tenth gives 3.8.
Place ValueThe value of a digit based on its position in a number (e.g., ones, tens, hundreds, tenths, hundredths).In 5.67...
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Core Formulas
Long Division with Decimals
To divide a number (dividend) by a whole number (divisor), perform standard long division. If there's a remainder, add a decimal point and zeros to the dividend and continue dividing. Place the decimal point in the quotient directly above the decimal point in the dividend.
This rule extends basic long division to handle cases where the quotient is not a whole number, allowing for precise decimal answers.
Transforming Decimal Divisors
To divide by a decimal, first move the decimal point in the divisor to the right until it becomes a whole number. Then, move the decimal point in the dividend the *same number of places* to the right. Add zeros to the dividend if necessary. Finally, perform long division using the new whole number divisor and adjus...
5 more steps in this tutorial
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Challenging
A family drove 320.5 miles on Monday using 12.8 gallons of gas. On Tuesday, they drove 285.2 miles using 11.1 gallons. What was their average gas mileage (miles per gallon) for the entire two-day trip, rounded to the nearest tenth?
A.25.3
B.25.1
C.25.7
D.25.4
Challenging
A student was asked to divide 6.3 by 0.09. Their work is shown:
Step 1: 6.3 ÷ 0.09 becomes 63 ÷ 9.
Step 2: 63 ÷ 9 = 7.
Step 3: The answer is 7.0.
What was the student's critical mistake?
A.They rounded incorrectly in the final step.
B.They placed the decimal incorrectly in the final quotient.
C.They moved the decimal in the divisor (0.09) two places but only moved it one place in the dividend (6.3).
D.They should not have added a zero after the 7 in the final answer.
Challenging
The result of dividing a number by 0.7, when rounded to the nearest tenth, is 5.4. Which of the following could have been the original number (the dividend)?
A.3.80
B.3.70
C.3.90
D.3.74
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