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3 years ago

Whats the answer to these? (These are called Proper fractions.)

Mathematics

2 answers:

inna [77]3 years ago

8 0

Answer and Step-by-step explanation:

1. Convert $\frac{2}{5}$ to have a denominator of 10.

$\frac{2}{5}$ × $\frac{2}{2}$ = $\frac{4}{10}$

$\frac{3}{10} + \frac{4}{10} = \frac{7}{10}$

Jeremiah ran $\frac{7}{10}$ of a mile in total.

2. Convert the denominators of all the fractions to have a 10.

$\frac{1}{2}$ × $\frac{5}{5} =\frac{5}{10}$

$\frac{4}{5}$ × $\frac{2}{2} = \frac{8}{10}$

Daniel read $\frac{3}{10}$ more books than Edgar, since 8 books is more than 5 books by 3 books.

3. Convert $\frac{1}{4}$ to have a denominator of 8.

$\frac{1}{4}$ × $\frac{2}{2} = \frac{2}{8}$

$\frac{2}{8} +\frac{2}{8}= \frac{4}{8}, or\frac{1}{2}$

Jared drove $\frac{4}{8}$ , or $\frac{1}{2}$ miles in total.

#teamtrees #PAW (Plant And Water)

Darya [45]3 years ago

5 0

Answer to the first question: 7/10ths of a mile

Explaination: When adding fractions, you need to have a common denominator. Since dividing 3/10 by 2 to get a denominator of 5 makes 3 a decimal, it's easier to multiply 2/5 by 2 to get a denominator of 10. You do the same to the top that you do to the bottom: $\frac{2*2}{5*2} = \frac{4}{10}$ . From there, just add 4/10 and 3/10 to get the answer: 7/10ths of a mile.

Answer to the second question: Daniel read three (3/10) more books

Explaination: Since you can't evenly multiply 5 or 2 to get the opposite number, it's easier to multiply to the lowest common multiple. The easiest way to find that is to multiply both denominators (5*2=10). You'll have to multiply the numerator by the same amount you multipled the denominator by. For Daniel, that would mean: $\frac{4*2}{5*2} = \frac{8}{10}$ . For Edgar, that would mean: $\frac{1*5}{2*5} = \frac{5}{10}$ . So, Daniel read 3 more books than Edgar.

Answer to the third question: 2/4 mile (or 1/2 a mile)

Explaination: 2/8 can be simplified, by dividing the top and bottom by 2, resulting in 1/4. Since both fractions have the same denominator (/4), you can add them to get 2/4ths. This can be simplified further to half (1/2) a mile.

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What are the two ratios that are equivalent to 2:9

weeeeeb [17]

Answer:

Step-by-step explanation:

2:9 is equivalent to

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3 years ago

Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.

Mice21 [21]

Answer:

LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

Step-by-step explanation:

Making factors of $8y^{6}+ 144y^{5}+ 640y^{4}$

Taking $8y^{4}$ common:

$\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)$

Using factorization method:

$\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times 4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)$

Now, Making factors of $2y^{4} + 40y^{3} + 200y^{2}$

Taking $2y^{2}$ common:

$\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)$

Using factorization method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. HCF is $2y^{2} (y+ 10)$ .

We know the relation between LCM, HCF of the two numbers 'p' , 'q' and the numbers themselves as:

$HCF \times LCM = p \times q$

Using equations (1) and (2): $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$