Mathematics
Grade 10
15 min
Divide larger numbers by 2-digit numbers: word problems
Divide larger numbers by 2-digit numbers: word problems
What you'll learn
- Solve word problems involving division of up to 4-digit numbers by 2-digit numbers with at least 80% accuracy.
- Explain the steps used to solve a division word problem with a 2-digit divisor, including interpreting remainders in the context of the problem, in their own words.
- Identify the key information needed to solve a division word problem with a 2-digit divisor from a given text.
- Apply the standard algorithm for division to accurately divide up to 4-digit numbers by 2-digit numbers in the context of a word problem.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Analyze word problems to identify similar figures and their corresponding parts.
Set up correct proportions to represent the relationships between similar figures.
Calculate the scale factor of similar figures by accurately dividing larger numbers by 2-digit numbers.
Determine unknown side lengths or perimeters of similar figures using a calculated scale factor.
Solve multi-step word problems involving geometric similarity that require precise long division.
Interpret the quotient from a division calculation as a scale factor in a real-world context.
How do city planners use a small map to manage a huge city, or how does an artist scale a sketch to a giant mural? 🗺️ It's all about similarity, and the key is precise division!
This tutorial connects a...
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Key Concepts & Vocabulary
TermDefinitionExample
Similar PolygonsPolygons that have the same shape but may have different sizes. For two polygons to be similar, their corresponding angles must be congruent, and the ratio of their corresponding side lengths must be constant.A rectangle with sides 10 cm and 20 cm is similar to a larger rectangle with sides 50 cm and 100 cm. The ratio of corresponding sides is 50/10 = 5 and 100/20 = 5.
Scale Factor (k)The constant ratio between the corresponding side lengths of two similar figures. It is calculated by dividing the length of a side on the new figure (the image) by the length of the corresponding side on the original figure (the pre-image).A model car has a length of 18 cm. The actual car is 450 cm long. The scale factor from the model to the actual car is 450 ÷ 18 = 25...
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Core Formulas
Scale Factor Formula
k = \frac{\text{length of image side}}{\text{length of corresponding pre-image side}}
Use this formula to find the scale factor (k). In our word problems, this will typically involve dividing a larger number (the dividend) by a 2-digit number (the divisor).
Proportionality of Sides
\text{If Polygon } ABCDE \sim \text{Polygon } VWXYZ, \text{ then } \frac{AB}{VW} = \frac{BC}{WX} = \frac{CD}{XY} = k
This rule establishes that the ratios of all pairs of corresponding sides in similar polygons are equal. You can set up a proportion using the calculated scale factor to find any unknown side length.
Proportionality of Perimeters
\frac{\text{Perimeter of Image}}{\text{Perimeter of Pre-image}} = k
The ratio of the perimeters of two similar figures is equa...
4 more steps in this tutorial
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Challenging
A rectangular field (pre-image) measures 45 meters by 60 meters. A larger, similar field (image) has its shorter side measuring 2610 meters. Fencing for the larger field costs $28 per meter. What is the total cost to fence the perimeter of the larger field?
A.$170,520
B.$97,440
C.$12,180
D.$341,040
Challenging
Two similar regular polygons, Polygon A (pre-image) and Polygon B (image), are being studied. Polygon B has a side length of 882 units. Polygon A has a perimeter of 216 units and the same number of sides as Polygon B. If the scale factor of enlargement is 49, how many sides does each polygon have?
A.49
B.18
C.12
D.Cannot be determined
Challenging
A student is solving this problem: 'Two similar triangles, ΔTUV and ΔXYZ, are given. TU = 36 cm and its corresponding side XY = 2232 cm. The perimeter of ΔTUV is 94 cm. Find the perimeter of ΔXYZ.' The student's work is shown:
Step 1: k = 36 ÷ 2232 ≈ 0.016
Step 2: P_XYZ = 94 * 0.016 ≈ 1.504 cm
What is the primary conceptual error in the student's work?
A.The student mismatched the corresponding sides for the calculation.
B.The student confused the area ratio (k²) with the perimeter ratio (k).
C.The student inverted the scale factor ratio by dividing the pre-image by the image.
D.The student made a long division error in Step 1.
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Divide larger numbers by 2-digit numbers: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Divide larger numbers by 2-digit numbers: word problems?
You'll be able to: Solve word problems involving division of up to 4-digit numbers by 2-digit numbers with at least 80% accuracy; Explain the steps used to solve a division word problem with a 2-digit divisor, including interpreting remainders in….
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How many practice questions are included with Divide larger numbers by 2-digit numbers: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.