Mathematics
Grade 4
15 min
Scaling whole numbers by fractions (Complete chapter above)
Scaling whole numbers by fractions (Complete chapter above)
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1
Introduction & Learning Objectives
Learning Objectives
Interpret a fraction as a multiplication operation on a whole number.
Use visual models, like area models or number lines, to represent the multiplication of a whole number by a fraction.
Solve problems involving multiplying a whole number by a fraction using the standard algorithm.
Convert an improper fraction that results from multiplication into a whole or mixed number.
Solve one-step word problems that require scaling a whole number by a fraction.
Predict whether the product will be greater than or less than the original whole number based on the fraction.
Understand that finding a 'fraction of' a number means to multiply.
If you have a pizza with 8 slices and you eat 1/4 of it, how many slices did you eat? 🍕
In this lesson, we will lear...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole. It has a top number (numerator) and a bottom number (denominator).The fraction 1/2 means one part out of two equal parts.
NumeratorThe top number in a fraction. It tells you how many parts you have.In the fraction 3/4, the numerator is 3.
DenominatorThe bottom number in a fraction. It tells you how many equal parts the whole is divided into.In the fraction 3/4, the denominator is 4.
Whole NumberA number without any fractions or decimals, like 0, 1, 2, 3, and so on.The number 12 is a whole number.
ScalingTo change the size of a number. When we multiply a whole number by a fraction less than one, we are scaling it down.Finding 1/2 of 10 is scaling 10 down to 5.
ProductThe answer you get when you multiply numbers toget...
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Core Formulas
The 'Of' Means Multiply Rule
\frac{a}{b} \text{ of } c = \frac{a}{b} \times c
In math word problems, the word 'of' is a clue that you need to multiply. For example, 'one-half of ten' is the same as 1/2 times 10.
The Multiplication Rule
c \times \frac{a}{b} = \frac{c \times a}{b}
To multiply a whole number by a fraction, multiply the whole number by the numerator. The denominator stays the same.
The Whole Number as a Fraction Rule
c = \frac{c}{1}
Any whole number can be written as a fraction by putting it over 1. This is helpful because it reminds you to multiply the whole number with the numerator.
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Challenging
A book has 40 pages. On Monday, you read 1/5 of the book. On Tuesday, you read another 2/5 of the book. How many pages are left to read?
A.8
B.16
C.16
D.24
Challenging
If 'a/b' is a fraction where the numerator 'a' is smaller than the denominator 'b', what must be true about the product of 20 x a/b?
A.The product will be less than 20.
B.The product will be greater than 20.
C.The product will be exactly 20.
D.The product will be a whole number.
Challenging
Which of the following word problems can be solved using the expression 5 x 3/4?
A.There are 5 apples and you eat 3/4 of one apple. How much is left?
B.pizza is cut into 5 slices. You eat 3/4 of the whole pizza. How many slices did you eat?
C.You have a rope that is 3/4 of a foot long and another that is 5 feet long. What is the total length?
D.recipe calls for 3/4 of a cup of flour. If you make 5 batches of the recipe, how much flour do you need in total?
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