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Compare NonEquivalent Fractions
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 We'll learn how to compare fractions using benchmarks.
 That we can also compare fractions by finding common denominators.
 And we'll discover that this knowledge can help us share a snack, track the battery life on our electronics, and compete in sports!

Discussion Questions

Before VideoWhat does the denominator tell you in a fraction?ANSWER

How many equalsized pieces the whole is divided into.

How many equalsized pieces we have.

[ggfrac]4/6[/ggfrac], [ggfrac]6/9[/ggfrac], [ggfrac]8/12[/ggfrac]. I can find equivalent fractions by multiplying both the numerator and denominator in [ggfrac]2/3[/ggfrac] by any number, as long as it is the same number.

Since 6 × 4 is 24, I also need to multiply 5 by 4 to get an equivalent fraction. The equivalent fraction is [ggfrac]20/24[/ggfrac].

20 is a multiple of 5, so I can multiply the denominator, 5, by 4 to get 20. [ggfrac]2x4/5x4[/ggfrac] = [ggfrac]8/20[/ggfrac]. The fractions are equivalent.


After VideoWhat benchmark fraction can you use to compare [ggfrac]1/3[/ggfrac] and [ggfrac]3/4[/ggfrac]? Why? ANSWER

I can use [ggfrac]1/2[/ggfrac] as a benchmark fraction. [ggfrac]1/2[/ggfrac] = [ggfrac]2/4[/ggfrac], so [ggfrac]3/4[/ggfrac] is more than [ggfrac]1/2[/ggfrac]. Since [ggfrac]1/3[/ggfrac] is less than [ggfrac]1/2[/ggfrac], we know that [ggfrac]3/4[/ggfrac] is greater than [ggfrac]1/3[/ggfrac].

[ggfrac]1/2[/ggfrac] is not very useful because both [ggfrac]4/5[/ggfrac] and [ggfrac]6/7[/ggfrac] are greater than [ggfrac]1/2[/ggfrac].

Denominators tell the size of the unit, so if I have two different denominators, it is like comparing different numbers of differentsized slices.

I can find equivalent fractions for each fraction until I find two that have the same denominator.

I could cut the slice in the first lasagna into three equalsized pieces, and cut each of the slices in the second lasagna into two equalsized pieces. Now each of the lasagnas can be expressed using 6 as a denominator.



Vocabulary

Fraction
DEFINE
A number that represents a part of a whole.

Numerator
DEFINE
The top number in a fraction, which tells us how many parts have been counted.

Denominator
DEFINE
The bottom number in a fraction, which tells us how many parts are in the whole.

Equivalent fractions
DEFINE
Fractions that represent the same amount.

Nonequivalent fractions
DEFINE
Fractions that represent different amounts.

Benchmark fraction
DEFINE
A familiar fraction that we can compare other fractions to.

Common denominator
DEFINE
Having the same denominator in two fractions.

Fraction
DEFINE

Reading Material
Download as PDF Download PDF View as Separate PageWHAT ARE NONEQUIVALENT FRACTIONS?NonEquivalent fractions represent different fractions of a whole. You can use common denominators to compare fractions.
To better understand comparing nonequivalent fractions…
WHAT ARE NONEQUIVALENT FRACTIONS?. NonEquivalent fractions represent different fractions of a whole. You can use common denominators to compare fractions. To better understand comparing nonequivalent fractions…LET’S BREAK IT DOWN!
Balloons
Adesina, April, and Marcos prepare balloons for a party. They have one helium tank that is [ggfrac]3/4[/ggfrac] full, and another that is [ggfrac]2/5[/ggfrac] full. Which tank is more full? The two fractions have different denominators, which makes it harder to directly compare them. One way we can compare fractions is by using a benchmark fraction. Let’s use [ggfrac]1/2[/ggfrac] as a benchmark. Since [ggfrac]1/2[/ggfrac] is equivalent to [ggfrac]2/4[/ggfrac], we can see that [ggfrac]3/4[/ggfrac] is more than [ggfrac]1/2[/ggfrac]. We also know that [ggfrac]2/5[/ggfrac] is less than [ggfrac]1/2[/ggfrac]. Then, since [ggfrac]2/5[/ggfrac] is less than [ggfrac]1/2[/ggfrac], and [ggfrac]3/4[/ggfrac] is more than [ggfrac]1/2[/ggfrac], [ggfrac]3/4[/ggfrac] is greater than [ggfrac]2/5[/ggfrac]! Now you try: Use a benchmark fraction to determine which is greater, [ggfrac]5/8[/ggfrac] or [ggfrac]3/7[/ggfrac].
Balloons Adesina, April, and Marcos prepare balloons for a party. They have one helium tank that is [ggfrac]3/4[/ggfrac] full, and another that is [ggfrac]2/5[/ggfrac] full. Which tank is more full? The two fractions have different denominators, which makes it harder to directly compare them. One way we can compare fractions is by using a benchmark fraction. Let’s use [ggfrac]1/2[/ggfrac] as a benchmark. Since [ggfrac]1/2[/ggfrac] is equivalent to [ggfrac]2/4[/ggfrac], we can see that [ggfrac]3/4[/ggfrac] is more than [ggfrac]1/2[/ggfrac]. We also know that [ggfrac]2/5[/ggfrac] is less than [ggfrac]1/2[/ggfrac]. Then, since [ggfrac]2/5[/ggfrac] is less than [ggfrac]1/2[/ggfrac], and [ggfrac]3/4[/ggfrac] is more than [ggfrac]1/2[/ggfrac], [ggfrac]3/4[/ggfrac] is greater than [ggfrac]2/5[/ggfrac]! Now you try: Use a benchmark fraction to determine which is greater, [ggfrac]5/8[/ggfrac] or [ggfrac]3/7[/ggfrac].Remote Control Cars
April and Marcos drive remote control cars. Both cars have the same size battery. Marcos’s car has [ggfrac]2/3[/ggfrac] of its battery power left, and April's car has [ggfrac]5/6[/ggfrac] left. Whose battery has more power left? Since both [ggfrac]2/3[/ggfrac] and [ggfrac]5/6[/ggfrac] represent more than [ggfrac]1/2[/ggfrac], we can't use the benchmark of [ggfrac]1/2[/ggfrac] to compare them. Instead, we can use common denominators. We can use our knowledge of equivalent fractions to rewrite [ggfrac]2/3[/ggfrac] and [ggfrac]5/6[/ggfrac] so that they have the same denominator. 3 x 2 = 6, so we can multiply the numerator and denominator of [ggfrac]2/3[/ggfrac] by 2 to get an equivalent fraction with a denominator of 6. [ggfrac]2x2/3x2[/ggfrac] = [ggfrac]4/6[/ggfrac]. Now we compare [ggfrac]4/6[/ggfrac] to [ggfrac]5/6[/ggfrac]. Both fractions have the same denominator, so we can compare the fractions using their numerators. 5 > 4, so [ggfrac]5/6[/ggfrac] is greater than [ggfrac]4/6[/ggfrac]. April's battery has more power left. Now you try: Use common denominators to compare [ggfrac]3/5[/ggfrac] and [ggfrac]7/10[/ggfrac].
Remote Control Cars April and Marcos drive remote control cars. Both cars have the same size battery. Marcos’s car has [ggfrac]2/3[/ggfrac] of its battery power left, and April's car has [ggfrac]5/6[/ggfrac] left. Whose battery has more power left? Since both [ggfrac]2/3[/ggfrac] and [ggfrac]5/6[/ggfrac] represent more than [ggfrac]1/2[/ggfrac], we can't use the benchmark of [ggfrac]1/2[/ggfrac] to compare them. Instead, we can use common denominators. We can use our knowledge of equivalent fractions to rewrite [ggfrac]2/3[/ggfrac] and [ggfrac]5/6[/ggfrac] so that they have the same denominator. 3 x 2 = 6, so we can multiply the numerator and denominator of [ggfrac]2/3[/ggfrac] by 2 to get an equivalent fraction with a denominator of 6. [ggfrac]2x2/3x2[/ggfrac] = [ggfrac]4/6[/ggfrac]. Now we compare [ggfrac]4/6[/ggfrac] to [ggfrac]5/6[/ggfrac]. Both fractions have the same denominator, so we can compare the fractions using their numerators. 5 > 4, so [ggfrac]5/6[/ggfrac] is greater than [ggfrac]4/6[/ggfrac]. April's battery has more power left. Now you try: Use common denominators to compare [ggfrac]3/5[/ggfrac] and [ggfrac]7/10[/ggfrac].Carnival
April and Marcos are at a carnival strength challenge. They swing a mallet and a machine records the strength of the blow, up to a marker. Marcos strikes with his mallet and he scores [ggfrac]3/4[/ggfrac] of the way to the marker. April strikes with her mallet and she scores [ggfrac]4/5[/ggfrac] of the way to the marker. Who got the greater score? We can use equivalent fractions to compare. 5 is not a multiple of 4, so we need to rewrite both fractions to make the fractions have a common denominator. Some equivalent fractions of [ggfrac]3/4[/ggfrac] are [ggfrac]6/8[/ggfrac], [ggfrac]9/12[/ggfrac], [ggfrac]12/16[/ggfrac], [ggfrac]15/20[/ggfrac], and [ggfrac]18/24[/ggfrac]. Some equivalent fractions of [ggfrac]4/5[/ggfrac] are [ggfrac]8/10[/ggfrac], [ggfrac]12/15[/ggfrac], and [ggfrac]16/20[/ggfrac]. Both fractions have an equivalent fraction with a denominator of 20: [ggfrac]3/4[/ggfrac] = [ggfrac]15/20[/ggfrac] and [ggfrac]4/5[/ggfrac] = [ggfrac]16/20[/ggfrac]. Now that the fractions have the same denominator, we can compare the numerators. 16 > 15, so [ggfrac]16/20[/ggfrac] > [ggfrac]15/20[/ggfrac]. Since [ggfrac]16/20[/ggfrac] = [ggfrac]4/5[/ggfrac], and [ggfrac]15/20[/ggfrac] = [ggfrac]3/4[/ggfrac], we know that [ggfrac]4/5[/ggfrac] > [ggfrac]3/4[/ggfrac]. There is a faster way to find the common denominators than listing equivalent fractions. For each fraction, multiply the numerator and the denominator by the denominator of the other fraction. For example, to compare [ggfrac]3/4[/ggfrac] and [ggfrac]4/5[/ggfrac], multiply [ggfrac]4/5[/ggfrac] by [ggfrac]4/4[/ggfrac] to get [ggfrac]16/20[/ggfrac], and multiply [ggfrac]3/4[/ggfrac] by [ggfrac]5/5[/ggfrac] to get [ggfrac]15/20[/ggfrac]. That was faster! Now you try: Use common denominators to decide which is greater, [ggfrac]6/7[/ggfrac] or [ggfrac]4/5[/ggfrac].
Carnival April and Marcos are at a carnival strength challenge. They swing a mallet and a machine records the strength of the blow, up to a marker. Marcos strikes with his mallet and he scores [ggfrac]3/4[/ggfrac] of the way to the marker. April strikes with her mallet and she scores [ggfrac]4/5[/ggfrac] of the way to the marker. Who got the greater score? We can use equivalent fractions to compare. 5 is not a multiple of 4, so we need to rewrite both fractions to make the fractions have a common denominator. Some equivalent fractions of [ggfrac]3/4[/ggfrac] are [ggfrac]6/8[/ggfrac], [ggfrac]9/12[/ggfrac], [ggfrac]12/16[/ggfrac], [ggfrac]15/20[/ggfrac], and [ggfrac]18/24[/ggfrac]. Some equivalent fractions of [ggfrac]4/5[/ggfrac] are [ggfrac]8/10[/ggfrac], [ggfrac]12/15[/ggfrac], and [ggfrac]16/20[/ggfrac]. Both fractions have an equivalent fraction with a denominator of 20: [ggfrac]3/4[/ggfrac] = [ggfrac]15/20[/ggfrac] and [ggfrac]4/5[/ggfrac] = [ggfrac]16/20[/ggfrac]. Now that the fractions have the same denominator, we can compare the numerators. 16 > 15, so [ggfrac]16/20[/ggfrac] > [ggfrac]15/20[/ggfrac]. Since [ggfrac]16/20[/ggfrac] = [ggfrac]4/5[/ggfrac], and [ggfrac]15/20[/ggfrac] = [ggfrac]3/4[/ggfrac], we know that [ggfrac]4/5[/ggfrac] > [ggfrac]3/4[/ggfrac]. There is a faster way to find the common denominators than listing equivalent fractions. For each fraction, multiply the numerator and the denominator by the denominator of the other fraction. For example, to compare [ggfrac]3/4[/ggfrac] and [ggfrac]4/5[/ggfrac], multiply [ggfrac]4/5[/ggfrac] by [ggfrac]4/4[/ggfrac] to get [ggfrac]16/20[/ggfrac], and multiply [ggfrac]3/4[/ggfrac] by [ggfrac]5/5[/ggfrac] to get [ggfrac]15/20[/ggfrac]. That was faster! Now you try: Use common denominators to decide which is greater, [ggfrac]6/7[/ggfrac] or [ggfrac]4/5[/ggfrac].Marathon
April and Marcos are training for a race. April ran [ggfrac]3/5[/ggfrac] of a mile and Marcos ran [ggfrac]5/6[/ggfrac] of a mile. Who ran farther? We need to find a common denominator to compare fractions that have different denominators. Multiply the numerator and denominator of [ggfrac]3/5[/ggfrac] by 6: [ggfrac]3x6/5x6[/ggfrac] = [ggfrac]25/30[/ggfrac]. Multiply the numerator and denominator of [ggfrac]5/6[/ggfrac] by 5: [ggfrac]5x5/6x5[/ggfrac] = [ggfrac]25/30[/ggfrac]. Now that the denominators are the same, compare the numerators. Since 25 > 18, [ggfrac]25/30[/ggfrac] > [ggfrac]18/30[/ggfrac]. So[ggfrac]5/6[/ggfrac] > [ggfrac]3/5[/ggfrac]. Now you try: Which is greater, [ggfrac]2/3[/ggfrac] or [ggfrac]3/4[/ggfrac]?
Marathon April and Marcos are training for a race. April ran [ggfrac]3/5[/ggfrac] of a mile and Marcos ran [ggfrac]5/6[/ggfrac] of a mile. Who ran farther? We need to find a common denominator to compare fractions that have different denominators. Multiply the numerator and denominator of [ggfrac]3/5[/ggfrac] by 6: [ggfrac]3x6/5x6[/ggfrac] = [ggfrac]25/30[/ggfrac]. Multiply the numerator and denominator of [ggfrac]5/6[/ggfrac] by 5: [ggfrac]5x5/6x5[/ggfrac] = [ggfrac]25/30[/ggfrac]. Now that the denominators are the same, compare the numerators. Since 25 > 18, [ggfrac]25/30[/ggfrac] > [ggfrac]18/30[/ggfrac]. So[ggfrac]5/6[/ggfrac] > [ggfrac]3/5[/ggfrac]. Now you try: Which is greater, [ggfrac]2/3[/ggfrac] or [ggfrac]3/4[/ggfrac]? 
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Use a benchmark fraction to show which is greater, [ggfrac]4/6[/ggfrac] or [ggfrac]3/8[/ggfrac].
Use common denominators to determine which is greater, [ggfrac]2/5[/ggfrac] or [ggfrac]3/10[/ggfrac].
Use common denominators to determine which is greater, [ggfrac]3/5[/ggfrac] or [ggfrac]2/3[/ggfrac].
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