Answer:
3/5 < 3/4 (The symbol you need is <.)
Step-by-step explanation:
The problem is asking you to compare the fractions 3/5 and 3/4. You need to supply a comparison symbol, one of {<, =, >}.
Comparing values
In general, when you are asked to compare two values, you are being asked which one is greater (or smaller). Sometimes, you are being asked for the amount by which one is greater than the other (their difference), and sometimes you are being asked for the factor by which one is greater than the other (their ratio).
You can do the arithmetic to find the appropriate difference or ratio, or you can use your number sense to identify the larger (or smaller) number.
Fractions
As you know, the denominator of a fraction tells you how many pieces the pie has been divided into.
In the fraction 3/5, the 5 tells you each piece is 1/5 of the whole, that there are 5 equal pieces.
In the fraction 3/4, the 4 tells you each piece is 1/4 of the whole, that there are 4 equal pieces.
A pie divided into 5 pieces instead of 4 has smaller pieces. That is ...
1/5 < 1/4
When there are 3 pieces of each, this relation still holds:
3×(1/5) < 3×(1/4) ⇒ 3/5 < 3/4
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Additional comment
Here, the numerators are the same, so we only need to compare the denominators to find the relationship. If the denominators are the same, we can compare the numerators.
If neither is the same, it is often useful to multiply one or the other or both of the fractions by some value so they will have a common numerator or denominator. The usual recommendation is to give the fractions a common denominator.
Here, the denominators can be made to be 20 in each case.
[tex]\dfrac{3}{5}=\dfrac{3}{5}\cdot\dfrac{4}{4}=\dfrac{12}{20}\\\\\dfrac{3}{4}=\dfrac{3}{4}\cdot\dfrac{5}{5}=\dfrac{15}{20}[/tex]
The denominators are now the same, so we can compare values by comparing the numerators. 12 < 15, so 12/20 < 15/20 and 3/5 < 3/4.
