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krok68 [10]
2 years ago
9

Which expression is equivalent? Please see pictures attached!

Mathematics
1 answer:
VMariaS [17]2 years ago
5 0

hey, u didn’t rlly attach anything :/

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When would the product of the denominators and the least common denominator of the denominators be the same?
Bas_tet [7]

Answer:

Example 1:

Find the common denominator of the fractions.

16 and 38

We need to find the least common multiple of 6 and 8 . One way to do this is to list the multiples:

6,12,18,24−−,30,36,42,48,...8,16,24−−,32,40,48,...

The first number that occurs in both lists is 24 , so 24 is the LCM. So we use this as our common denominator.

Listing multiples is impractical for large numbers. Another way to find the LCM of two numbers is to divide their product by their greatest common factor ( GCF ).

Example 2:

Find the common denominator of the fractions.

512 and 215

The greatest common factor of 12 and 15 is 3 .

So, to find the least common multiple, divide the product by 3 .

12⋅153=3 ⋅ 4 ⋅ 153=60

If you can find a least common denominator, then you can rewrite the problem using equivalent fractions that have like denominators, so they are easy to add or subtract.

Example 3:

Add.

512+215

In the previous example, we found that the least common denominator was 60 .

Write each fraction as an equivalent fraction with the denominator 60 . To do this, we multiply both the numerator and denominator of the first fraction by 5 , and the numerator and denominator of the second fraction by 4 . (This is the same as multiplying by 1=55=44 , so it doesn't change the value.)

512=512⋅55=2560215=215⋅44=860

512+215=2560+860                 =3360

Note that this method may not always give the result in lowest terms. In this case, we have to simplify.

=1130

The same idea can be used when there are variables in the fractions—that is, to add or subtract rational expressions .

Example 4:

Subtract.

12a−13b

The two expressions 2a and 3b have no common factors, so their least common multiple is simply their product: 2a⋅3b=6ab .

Rewrite the two fractions with 6ab in the denominator.

12a⋅3b3b=3b6ab13b⋅2a2a=2a6ab

Subtract.

12a−13b=3b6ab−2a6ab                   =3b − 2a6ab

Example 5:

Subtract.

x16−38x

16 and 8x have a common factor of 8 . So, to find the least common multiple, divide the product by 8 .

16⋅8x8=16x

The LCM is 16x . So, multiply the first expression by 1 in the form xx , and multiply the second expression by 1 in the form 22 .

x16⋅xx=x216x38x⋅22=616x

Subtract.

x16−38x=x216x−616x                  =x2 − 616x\

4 0
2 years ago
15 less than twice a number g is 19. Find g.
Helga [31]

Answer:

<h2>g = 17</h2>

Step-by-step explanation:

15 less than twice a number g is 19

2g - 15 = 19      <em>add 15 to both sides</em>

2g - 15 + 15 = 19 + 15

2g = 34       <em>divdie both sides by 2</em>

2g : 2 = 34 : 2

g = 17

4 0
3 years ago
Mr.O'Brien is paid $10 per hour for the first 40 hours he works in a week. He is paid 1.5 times that rate for each hour after th
erma4kov [3.2K]


In first 40 hours he earns = 7.30 x 40 = $292
Each hour after his rate = 7.20 x 1.5 = $10.80 per hour
In extra four hours he earns = 10.80 x 4 =  $43.20 

Total earnings = $292 + $43.20 = $335.20 
Therefore you don't agree
Hoped this helped you

8 0
3 years ago
Round to the place value of the underlined digit 862,840 underlined 6
omeli [17]

Answer:

900,000

Step-by-step explanation:

there you go bud

4 0
3 years ago
Bruce drew a rectangle with a length of 8 3/4 inches and width of 6 inches. Brandon drew a rectangle with dimensions that were 1
AysviL [449]
The correct answer is D.
5 0
3 years ago
Read 2 more answers
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