Mathematics
Grade 8
15 min
Divide whole numbers by unit fractions using models
Divide whole numbers by unit fractions using models
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1
Introduction & Learning Objectives
Learning Objectives
Represent whole numbers and unit fractions using various visual models.
Interpret the division of a whole number by a unit fraction as 'how many groups of the unit fraction are in the whole number'.
Apply area models to solve division problems involving whole numbers and unit fractions.
Apply number line models to solve division problems involving whole numbers and unit fractions.
Connect the visual representation of dividing by a unit fraction to the inverse operation of multiplication.
Solve real-world problems involving dividing whole numbers by unit fractions using models.
Ever wondered how many small pieces you can get from a whole cake if each piece is a tiny fraction? 🎂 Let's explore how to find out!
In this lesson, we'll lear...
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Key Concepts & Vocabulary
TermDefinitionExample
Whole NumberA number without fractions or decimals (e.g., 0, 1, 2, 3...).In the problem $3 \div \frac{1}{4}$, '3' is the whole number.
Unit FractionA fraction where the numerator is 1 and the denominator is a positive integer (e.g., $\frac{1}{2}, \frac{1}{3}, \frac{1}{5}$).In the problem $3 \div \frac{1}{4}$, '$\frac{1}{4}$' is the unit fraction.
DivisionThe process of splitting a number into equal parts or determining how many times one number is contained within another.$6 \div 2 = 3$ means 6 is split into 2 equal parts of 3, or there are 3 groups of 2 in 6.
Visual ModelA diagram or physical representation used to illustrate mathematical concepts.Drawing rectangles or number lines to represent quantities and operations.
Area ModelA rectangular d...
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Core Formulas
Interpreting Division as 'How Many Groups Of'
$a \div \frac{1}{b}$ asks 'How many groups of size $\frac{1}{b}$ are there in $a$?'
This rule helps to conceptualize division visually. When you divide a whole number by a unit fraction, you are essentially finding out how many times that small fractional piece fits into the whole number.
Visualizing Division with Area Models
To model $a \div \frac{1}{b}$:
1. Draw $a$ whole units (e.g., rectangles).
2. Divide each whole unit into $b$ equal parts.
3. Count the total number of parts.
This rule provides a systematic way to use area models. Each whole is broken down into the fractional parts, and then all parts are counted to find the quotient.
Visualizing Division with Number Line Models
To model $a \div \f...
5 more steps in this tutorial
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Challenging
A number line model was used to solve a problem of the form W ÷ 1/8, where W is a whole number. The model shows a total of 32 jumps of size 1/8. What was the whole number W?
A.256
B.4
C.32
D.8
Challenging
If W is a positive whole number and U is a unit fraction 1/n (where n is an integer > 1), which statement ALWAYS describes the visual model for W ÷ U?
A.The model would involve drawing W wholes and dividing each one into n parts.
B.The model would show that the result is less than W.
C.The model would show a result that is sometimes a fraction.
D.The model would involve drawing n wholes and dividing each one into W parts.
Challenging
A factory produces 5 tons of granola, which is packaged into large 1-ton containers for shipping. For retail, the granola is sold in small bags, each containing 1/16 of a ton. The factory has 20 employees working on the packaging line. How many retail bags can be produced from the 5 tons of granola?
A.4
B.80
C.1/80
D.100
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