Place >, <, or = between each of the following pairs to make true sentence
(a) 4/5 and 120/150
(b) -6/5 and -7/6
(c) -4/20 and 4/-20
just make the denimantor equal and see which numenator is bigger and fill it in.
Here is a neat way to do these:
write down the two fractions beside each other, leave out the relation sign
on the left, write down the product of top-left by bottom right
on the right, write down the product of top-right by bottom-left
Whatever the correct sign is needed to relate the two numbers, use that same symbol between the two original fractions.
If one fraction is + and the other -, you shouldn't need any calculation, the positive is clearly the larger.
e.g.
4/5 vs 13/21
84 65 , It would be 84 > 65 , so
4/5 > 13/21
Of course you could change both fractions to decimals and then decide.
Many people would find that easiest.
To determine whether a fraction is greater than (>), less than (<), or equal to (=) another fraction, we can compare their values by finding a common denominator for each pair.
Let's solve each pair of fractions step by step:
(a) 4/5 and 120/150:
Step 1: Find a common denominator: The smallest number that both 5 and 150 divide evenly into is 150.
Step 2: Convert both fractions to have a denominator of 150:
- 4/5 * 30/30 = 120/150
- 120/150 = 120/150 (unchanged)
Therefore, the fractions 4/5 and 120/150 are equal (4/5 = 120/150).
(b) -6/5 and -7/6:
Step 1: Find a common denominator: The smallest number that both 5 and 6 divide evenly into is 30.
Step 2: Convert both fractions to have a denominator of 30:
- (-6/5) * 6/6 = (-36/30)
- (-7/6) * 5/5 = (-35/30)
Comparing -36/30 and -35/30, we can see that -36/30 is less than -35/30.
Therefore, the fraction -6/5 is less than -7/6 (-6/5 < -7/6).
(c) -4/20 and 4/-20:
Step 1: Find a common denominator: The smallest number that both 20 and -20 divide evenly into is 20.
Step 2: Convert both fractions to have a denominator of 20:
- (-4/20) * -1/-1 = (4/20)
- (4/-20) * -1/-1 = (4/20)
Since both fractions are now 4/20, they are equal.
Therefore, the fractions -4/20 and 4/-20 are equal (-4/20 = 4/-20).
In summary:
(a) 4/5 = 120/150
(b) -6/5 < -7/6
(c) -4/20 = 4/-20