Mathematics
Grade 7
15 min
Multiply a decimal by a multi-digit whole number
Multiply a decimal by a multi-digit whole number
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1
Introduction & Learning Objectives
Learning Objectives
Accurately multiply a decimal by a multi-digit whole number.
Correctly determine the placement of the decimal point in the product.
Use estimation to check the reasonableness of their answers.
Apply the standard multiplication algorithm to problems involving decimals.
Solve real-world problems requiring the multiplication of decimals by multi-digit whole numbers.
Identify and correct common errors in decimal multiplication.
Ever wondered how stores calculate the total cost when you buy multiple items priced at, say, $3.75 each? 🛍️ It's all about multiplying decimals by whole numbers!
In this lesson, you'll learn the step-by-step process for multiplying a decimal by a multi-digit whole number. Understanding this skill is crucial for everyday fin...
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Key Concepts & Vocabulary
TermDefinitionExample
DecimalA number that contains a decimal point, separating the whole number part from the fractional part (e.g., 3.14, 0.5, 12.00).In the number 5.75, '5' is the whole number part and '.75' is the decimal part.
Whole NumberA number without fractions or decimals; it can be positive, negative, or zero (e.g., 1, 5, 100, 0).Numbers like 12, 250, and 7 are whole numbers.
Multi-Digit Whole NumberA whole number composed of two or more digits (e.g., 10, 56, 345, 1,200).15, 203, and 1,000 are examples of multi-digit whole numbers.
ProductThe result obtained when two or more numbers are multiplied together.In the equation 3 x 4 = 12, the number 12 is the product.
FactorsThe numbers that are multiplied together to get a product.In the equation 3 x 4 = 12, the...
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Core Formulas
The Decimal Multiplication Algorithm
1. Multiply the numbers as if they were whole numbers, ignoring the decimal point initially.
2. Count the total number of decimal places in the decimal factor.
3. Place the decimal point in the product by counting from the right the same number of places as found in step 2.
This rule outlines the standard procedure for multiplying a decimal by a whole number. It simplifies the multiplication process by temporarily treating decimals as whole numbers, then reintroducing the decimal point at the end.
Estimating the Product
Round the decimal factor to the nearest whole number before multiplying by the multi-digit whole number. This provides a quick check for the reasonableness of your final answer.
Use this rule to quickly verify if your calc...
5 more steps in this tutorial
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Challenging
A contractor is buying floor tiles for three rooms. Room A needs 120 tiles, Room B needs 85 tiles, and Room C needs 150 tiles. Each tile costs $3.45. The contractor gets a bulk discount of $100 off the total cost if the order is over $1,000. What is the final price the contractor pays?
A.$1,224.75
B.$1,124.75
C.$1,324.75
D.$1,224.25
Challenging
If 0.XYZ represents a decimal number where X, Y, and Z are non-zero digits, and it is multiplied by a two-digit whole number 'AB', the product is calculated as 43210. Where should the decimal point be placed in 43210 to get the correct product?
A.Between 4 and 3 (4.3210)
B.Between 3 and 2 (43.210)
C.Between 2 and 1 (432.10)
D.Between 1 and 0 (4321.0)
Challenging
A student multiplied 3.08 by 45. They correctly calculated that 308 x 45 = 13860, but they wrote the final answer as 13.860. Another student correctly calculated the same problem. What is the difference between the correct answer and the incorrect answer?
A.124.74
B.138.60
C.1247.4
D.1.386
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