Mathematics
Grade 7
15 min
Compare fractions: word problems
Compare fractions: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Interpret word problems involving the comparison of fractions.
Convert fractions to decimals to facilitate comparison.
Compare two or more fractions by converting them to decimals.
Use common denominators as an alternative strategy to compare fractions.
Solve real-world problems that require comparing fractional quantities.
Justify their comparisons using mathematical reasoning.
Ever wonder who got the bigger slice of cake or which team completed more of their project? 🍰 Knowing how to compare fractions helps us answer these questions every day!
In this lesson, you'll learn how to tackle word problems that ask you to compare different fractional amounts. We'll focus on using decimals as a powerful tool for comparison, but also touch on other...
2
Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole. It is written as a numerator (top number) over a denominator (bottom number).In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator, representing 3 parts out of 4 equal parts.
DecimalA number that uses a decimal point to represent parts of a whole, based on powers of ten.0.75 is a decimal that represents seventy-five hundredths, which is equivalent to $\frac{3}{4}$.
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $\frac{5}{8}$, the numerator is 5.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts that make up the whole.In $\frac{5}{8}$, the denominator is 8.
Equivalent FractionsFractions that represent the...
3
Core Formulas
Converting a Fraction to a Decimal
$\frac{a}{b} = a \div b$
To convert any fraction to a decimal, divide the numerator by the denominator. This is a powerful method for comparing fractions, especially when denominators are different or when comparing fractions to decimals.
Comparing Decimals
Compare digits from left to right, starting with the largest place value (e.g., ones, then tenths, then hundredths).
When comparing two decimals, align their decimal points. Start comparing the digits in the largest place value. The number with the larger digit in the first differing place value is the greater number. Add trailing zeros if needed to make the numbers have the same number of decimal places.
Comparing Fractions with a Common Denominator
If $\frac{a}{c}$ and $\frac{b}{...
5 more steps in this tutorial
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Challenging
On a construction project, Crew A completed 1/4 of their assigned section on Monday and 1/3 on Tuesday. Crew B completed 3/5 of their section in the same two days. If both sections were the same size, which crew completed a greater portion of their section?
A.Crew A
B.Crew B
C.Both crews completed the same portion.
D.It's impossible to tell without knowing the section size.
Challenging
A tank is being filled from two pipes. Pipe A fills 3/16 of the tank per hour. Pipe B fills 1/5 of the tank per hour. After 30 minutes, which pipe has added more water to the tank?
A.Pipe A
B.Pipe B
C.They have added the same amount of water.
D.The comparison depends on the tank's total volume.
Challenging
At a dog show with 120 dogs, 1/3 are retrievers and 2/5 are terriers. The rest are other breeds. Is the fraction of retrievers greater or smaller than the fraction of terriers?
A.Smaller
B.Greater
C.They are equal.
D.Depends on the number of other breeds.
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