Mathematics
Grade 7
15 min
Divide decimals by whole numbers
Divide decimals by whole numbers
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Introduction & Learning Objectives
Learning Objectives
Identify the dividend, divisor, and quotient in a decimal division problem.
Accurately place the decimal point in the quotient when dividing a decimal by a whole number.
Perform long division to divide decimals by single-digit whole numbers.
Perform long division to divide decimals by multi-digit whole numbers, including adding zeros to the dividend.
Estimate quotients of decimals divided by whole numbers to check for reasonableness.
Solve real-world problems involving the division of decimals by whole numbers.
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Key Concepts & Vocabulary
TermDefinitionExample
DividendThe number that is being divided in a division problem.In 12.5 ÷ 5, 12.5 is the dividend.
DivisorThe number by which another number (the dividend) is divided.In 12.5 ÷ 5, 5 is the divisor.
QuotientThe result obtained from dividing one number by another.In 12.5 ÷ 5 = 2.5, 2.5 is the quotient.
Decimal PointA symbol used to separate the whole number part from the fractional part of a number.In 7.85, the dot between 7 and 8 is the decimal point.
Place ValueThe value of a digit based on its position in a number (e.g., ones, tenths, hundredths).In 3.45, the '4' is in the tenths place, and the '5' is in the hundredths place.
Terminating DecimalA decimal that has a finite number of digits after the decimal point (the division ends with a zero rema...
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Core Formulas
Decimal Point Placement Rule
When dividing a decimal by a whole number using long division, place the decimal point in the quotient directly above the decimal point in the dividend.
This rule is critical for maintaining the correct place value of each digit in your answer. It ensures that your quotient accurately reflects the magnitude of the dividend.
Adding Zeros to the Dividend
If the division does not terminate and you need a more precise answer or a zero remainder, you can add zeros to the right of the last digit in the decimal dividend and continue the long division process.
This allows you to extend the division into smaller place values (tenths, hundredths, thousandths, etc.) until the division is complete or you reach a desired level of precision.
Standard Long...
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Challenging
A team of 5 runners ran a total of 41.5 kilometers in a relay race. What was the average distance run per person? If their goal was to average 8.5 km per person, how many more kilometers would each person have needed to run on average?
A.8.3 km; they were 0.2 km short on average.
B.8.3 km; they needed to run 0.2 km more on average.
C.8.5 km; they met their goal exactly.
D.8.2 km; they needed to run 0.3 km more on average.
Challenging
A student solved 1.89 ÷ 9 and wrote the answer 2.1. Their reasoning was: 'I ignored the decimal, 189 divided by 9 is 21. Then I put the decimal in the middle.' What was their critical mistake?
A.They should have gotten 0.21, because the answer must be smaller than the dividend.
B.They misplaced the decimal point; it should have been placed directly above the dividend's decimal point *before* dividing, resulting in 0.21.
C.They forgot to add a zero to the dividend before starting.
D.Their basic division of 189 ÷ 9 was incorrect.
Challenging
When a certain decimal number is divided by 8, the quotient is 4.5. The division results in a zero remainder. What is the original decimal number?
A.3.6
B.0.5625
C.32.5
D.36.0
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