Mathematics
Grade 7
15 min
Compare percents and fractions: word problems
Compare percents and fractions: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Convert percents to fractions and decimals, and vice versa.
Identify the most efficient common form (fraction, decimal, or percent) for comparison in a given word problem.
Compare quantities expressed as percents and fractions to determine which is greater, smaller, or if they are equal.
Solve real-world word problems involving the comparison of percents and fractions.
Justify comparisons by showing equivalent forms of numbers.
Interpret and apply comparison results to answer specific questions in word problems.
Ever wonder if 3/4 of a pizza is more or less than 70% of a different pizza? 🍕 Let's find out how to compare these different ways of describing parts of a whole!
In this lesson, you'll learn how to compare quantities given as percents...
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Key Concepts & Vocabulary
TermDefinitionExample
PercentA way to express a number as a fraction of 100. 'Per cent' means 'per hundred'.25% means 25 out of 100, which can be written as 25/100 or 0.25.
FractionA number that represents a part of a whole. It is written as a numerator over a denominator.3/4 means 3 parts out of 4 equal parts. It can also be written as 0.75 or 75%.
DecimalA number that uses a decimal point to represent parts of a whole, based on powers of ten.0.75 is equivalent to 75/100 or 3/4. It can also be written as 75%.
Equivalent FormsDifferent ways to write the same value (e.g., 1/2, 0.5, and 50% all represent the same amount).To compare 1/2 and 40%, it's helpful to know that 1/2 is equivalent to 0.5 or 50%.
ComparisonThe act of determining whether one quantity is greater...
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Core Formulas
Percent to Fraction Conversion
$P\% = \frac{P}{100}$
To convert a percent to a fraction, write the percent as a number over 100 and simplify. This is useful when comparing a percent with a fraction, especially if the fraction has a denominator that is a factor of 100.
Fraction to Percent Conversion
$\frac{a}{b} = (a \div b) \times 100\%$
To convert a fraction to a percent, first convert it to a decimal by dividing the numerator by the denominator, then multiply by 100 and add the percent symbol. This is useful when you want to compare a fraction to a percent.
Percent to Decimal Conversion
$P\% = P \div 100$
To convert a percent to a decimal, divide the percent by 100 (or move the decimal point two places to the left). This is often the easiest way to compare differen...
5 more steps in this tutorial
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Challenging
In Mr. Smith's class, 18 out of 24 students passed the final exam. In Ms. Jones' class, 70% of the students passed. Which class had a higher passing rate?
A.Mr. Smith's class
B.Ms. Jones' class
C.The passing rates were equal
D.It's impossible to tell without the number of students in Ms. Jones' class
Challenging
A smoothie recipe requires at least 40% of its volume to be fruit. You are making a 500 mL smoothie and have added 3/8 of the total volume as strawberries and 1/10 of the total volume as bananas. Have you met the fruit requirement?
A.No, the total fruit is less than 40%.
B.Yes, the total fruit is greater than 40%.
C.Yes, the total fruit is exactly 40%.
D.It cannot be determined with the given information.
Challenging
A stock's price increased by 50% on Monday. On Tuesday, its new price decreased by 1/3. How does the final price on Tuesday compare to the original price before Monday's increase?
A.The final price is greater than the original price.
B.The final price is less than the original price.
C.The final price is equal to the original price.
D.The comparison depends on the original price.
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