Mathematics
Grade 4
15 min
Benchmark fractions
Benchmark fractions
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the benchmark fractions 0, 1/2, and 1.
Locate benchmark fractions and other simple fractions on a number line.
Determine if a given fraction is greater than, less than, or equal to 1/2.
Determine if a given fraction is less than, equal to, or greater than 1.
Use benchmark fractions to compare two fractions with unlike numerators and denominators.
Explain their reasoning when comparing fractions using benchmark numbers.
If you ate 3/8 of a pizza and your friend ate 5/6 of a pizza, who ate more? 🍕 Let's find an easy way to figure it out!
In this lesson, we will learn about 'benchmark fractions' like 0, 1/2, and 1. These are simple, friendly fractions that help us quickly estimate and compare other, more complicated fractions withou...
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Key Concepts & Vocabulary
TermDefinitionExample
Benchmark FractionA common, easy-to-picture fraction that you can use to measure, compare, or order other fractions. The most common benchmarks are 0, 1/2, and 1.To compare 4/10, we can think about the benchmark 1/2. Since 5/10 is exactly 1/2, we know 4/10 is a little less than 1/2.
FractionA number that represents a part of a whole or a part of a group.3/4 means we have 3 parts out of a whole that is divided into 4 equal parts.
NumeratorThe top number in a fraction. It tells you how many equal parts you have.In the fraction 5/8, the numerator is 5.
DenominatorThe bottom number in a fraction. It tells you how many equal parts the whole is divided into.In the fraction 5/8, the denominator is 8.
Number LineA line with numbers placed in their correct position. It helps...
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Core Formulas
The 'Compare to 1/2' Rule
For a fraction a/b: If 2 * a < b, then a/b < 1/2. If 2 * a = b, then a/b = 1/2. If 2 * a > b, then a/b > 1/2.
Use this rule to quickly check if a fraction is bigger or smaller than one-half. Double the numerator and compare it to the denominator.
The 'Compare to 1' Rule
For a fraction a/b: If a < b, then a/b < 1. If a = b, then a/b = 1.
Use this rule to see if a fraction is a whole number. If the numerator is smaller than the denominator, the fraction is less than one whole.
The 'Compare to 0' Rule
For a fraction a/b: If a = 0, then a/b = 0.
Any fraction with a numerator of 0 is equal to 0.
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Challenging
Both 5/8 and 6/10 are greater than 1/2. Which statement gives the correct comparison and reasoning?
A.5/8 is greater because it is 1/8 more than 1/2, while 6/10 is only 1/10 more than 1/2, and 1/8 is a bigger piece than 1/10.
B.6/10 is greater because 6 and 10 are larger numbers than 5 and 8.
C.They are equal because both are just a little more than 1/2.
D.5/8 is greater because its denominator is smaller.
Challenging
Order these three fractions from LEAST to GREATEST: 9/8, 4/9, 6/12.
A.9/8, 6/12, 4/9
B.4/9, 6/12, 9/8
C.6/12, 4/9, 9/8
D.4/9, 9/8, 6/12
Challenging
Four students have cards with fractions: Amy has 5/10, Ben has 3/4, Chloe has 2/6, and David has 8/7. Which student has a fraction that is NOT less than 1?
A.Amy
B.Ben
C.Chloe
D.David
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