Is 1/6 Less Than 1/2

Making Equivalent Fractions with One

We'll be making a lot of "like fractions" in this department (fractions with common denominators). Remember that 1 can exist represented by a fraction when the numerator and denominator are the same value. two/two is the same as one. 9/ix is the same as one. 52/52 is the same as one. If that is disruptive, think of it as a division problem. 2÷ii=ane. 9÷9=1. 52÷52=1. Also, remember that in multiplication anything multiplied by i is the same value. two*ane=2. ix*ane=9. 52*one=52. That math fact is chosen the identity property of multiplication. We're going to use this play tricks to make like fractions.

We know that 1/three * 1 = 1/iii. Allow'south say our fraction problem needed the solution to have the denominator 18 (bottom number). Use the concept that i is equivalent to 6/6. That means...

• Starting time: 1/3 * 1 = 1/3
• Swap: ane/three * 6/6 = 1/iii
• Multiply the Fractions: (i*half dozen)/(3*6) = 6/18
• Simplify to Check Answer: half dozen/18 = 1/3

We used the identity property to create equivalent fractions. We created the same denominator for all of our terms.

Comparing Fractions

You volition get a lot of problems where you lot are asked to compare fractions. Is 1/2 bigger or smaller than i/3? You should already know about "greater than" and "less than" symbols.

It'south easier with whole numbers...
• Compare 2 and one. You know that two is greater than one.
• Compare 13 and 27. You know that thirteen is less than xx-seven.
• Compare -forty and -2. We have worked with negative integers before. -xl is less than -2.

So what most fractions? Ane some levels it's just as easy. Fractions with larger denominators (bottom number) have more pieces that are possible. When you accept more pieces that are possible in the aforementioned space, the pieces take to be smaller. If the number of pieces (numerator) in each fraction is the same, the 1 with the larger denominator will always be less than the other. This only works when y'all can compare the same number of pieces.

Examples:
Compare 1/2 and ane/5.
Think most a pie. Ane pie is cut into two pieces and one is cut into 5 pieces. Which piece is bigger? One-half of a pie is bigger than one 5th of a pie. So 1/2 is greater than 1/5.

Compare 5/viii and 5/10.
First by noticing that you have v pieces of each. Since they are the same number, nosotros can ignore them. Then await at the denominators and think virtually pieces of a pie. An 8th of a pie is bigger than a tenth of a pie. Basically, you lot have five bigger pieces compared to five smaller pieces. So five/eight is greater than 5/10.

When the numerators are the aforementioned, nosotros don't have to worry about converting any numbers. Allow's look at like fractions (same denominators). They are easy. You lot only need to focus on the values of the numerators without converting annihilation.

Examples:
Compare 2/9 and half-dozen/ix.
You have the same denominators, so the size of the pieces is the same. Now wait up to the numerators. Two pieces compared to six pieces. You lot accept this i. If 2 < 6 and then...
2/9 < 6/9

Compare 8/17 to 3/17
Over again, you have the same denominators. The pieces are the same size. Compare eight to iii. Since eight is greater than three...
8/17 > 3/17

The like shooting fish in a barrel ones are out of the way at present. Just what happens when you have different fractions (unlike denominators) with dissimilar numerators? You are going to need to make them "like fractions" to really compare them. That means you will need the same lesser numbers (common denominators) for each fraction. You're going to demand a little multiplication to practice this ane.

Examples:
Compare 5/6 and 17/xviii
We have sixths and eighteenths for denominators. We need to brand them like fractions. They have the common factor of 6 (6x3=xviii). That'due south skilful, we only accept to deal with the 5/6 term. The 17/18 tin stay the mode it is. Since we know that 6x3=xviii, let's multiply the numerator and the denominator by 3. Use the offset-swap-multiply process from higher up.
5/6 = five/6 * one = five/6 * 3/3 = (five*3)/(6*3) = fifteen/18
Now you lot can compare 15/eighteen and 17/18. No problem.
15/18 < 17/18

Compare 6/9 and 3/4.
Notice that nosotros take ninths and fourths for denominators. At that place are no common factors on this problem. The fast way is to create equivalent fractions for each term and compare them. How? Multiply the first term past 4/4 and the second by 9/9. In other words, nosotros volition be multiplying both the top and bottom numbers of one term by the denominator of the other. Use the start-bandy-multiply process from above for both terms.

6/9 = 6/nine * 1 = six/9 * 4/4 = (6*four)/(ix*four) = 24/36
3/iv = 3/4 * 1 = 3/4 * 9/ix = (iii*9)/(4*9) = 27/36

Did you see that? When y'all multiply by the denominator of the other term, you wind upwardly with similar fractions. Now we can compare 24/36 and 27/36. Easy as pie.
24/36 < 27/36

Fractions and Decimals

Overview
Number Types
Factors
Fractions

Structure
Reducing
More or Less
Mixed Numbers
Mixed Numbers ii
Addition
Subtraction one
Subtraction 2
Multiplication
Sectionalization
Give-and-take Problems
Existent Earth

Decimals
Percentages
Interpretation
Ratios
Money
Activities
More than Maths Topics

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Useful Reference Materials

Wikipedia:
https://en.wikipedia.org/wiki/Fraction_%28mathematics%29
Encyclopædia Britannica:
http://world wide web.britannica.com/topic/fraction
Academy of Delaware:
https://sites.google.com/a/udel.edu/fractions/