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ad-work [718]
3 years ago
8

Estimate the sum or difference.

Mathematics
1 answer:
dangina [55]3 years ago
8 0

1) \frac{4}{6}+\frac{1}{8}=\frac{19}{24}

2) \frac{2}{6}+\frac{7}{8}=\frac{29}{24}

3) \frac{5}{6}-\frac{3}{8}=\frac{11}{24}

4) \frac{4}{6}+\frac{3}{8}=\frac{25}{24}

5) \frac{7}{8}-\frac{5}{6}=\frac{1}{24}

6) \frac{1}{6}+\frac{7}{8}=\frac{25}{24}

Step-by-step explanation:

In order to calculate the sum of two fractions, we first have to find the lowest common denominator of the two fractions, then multiply the numerator of each fraction by the ratio between the lowest common denominator and the original denominator, and then add/subtract the two new numerators.

1)

\frac{4}{6}+\frac{1}{8}=

Here the lowest common denominator between 6 and 8 is 24,

So we have to rewrite each fraction as having denominator 24: this means that we have to multiply both numerator and denominator of the 1st fraction by 4 (because 24/6=4), and both numerator and denominator of the 2nd fraction by 3 (because 24/8=3).

So the new numerators of the two fractions are:

4\cdot 4 = 16\\1\cdot 3 = 3

The expression then becomes:

\frac{4}{6}+\frac{1}{8}=\frac{16}{24}+\frac{3}{24}=\frac{16+3}{24}=\frac{19}{24}

2)

\frac{2}{6}+\frac{7}{8}=

Here the lowest common denominator between 6 and 8 is again 24,

so we have again to multiply both numerator and denominator of the 1st fraction by 4, and both numerator and denominator of the 2nd fraction by 3.  

So the new numerators of the two fractions are:

2\cdot 4 = 8\\7\cdot 3 = 21

And we get:

\frac{2}{6}+\frac{7}{8}=\frac{8}{24}+\frac{21}{24}=\frac{8+21}{24}=\frac{29}{24}

3)

\frac{5}{6}-\frac{3}{8}

The denominators are the same, so the lowest common denominator is always 24. So we can adopt the same procedure, and new numerators are:

5\cdot 4 = 20\\3\cdot 3 = 9

And so:

\frac{5}{6}-\frac{3}{8}=\frac{20}{24}-\frac{9}{24}=\frac{20-9}{24}=\frac{11}{24}

4)

\frac{4}{6}+\frac{3}{8}=

Using the same lowest common denominator, 24, the new numerators are:

4\cdot 4 = 16\\3\cdot 3 = 9

And so we can rewrite the expression as

\frac{4}{6}+\frac{3}{8}=\frac{16}{24}+\frac{9}{24}=\frac{16+9}{24}=\frac{25}{24}

5)

\frac{7}{8}-\frac{5}{6}=

Again, the lowest common denominator is 24. This time the denominator of the 1st fraction is 8 while the denominator of the 2nd fraction is 6, so we have to multiply the numerator of the 1st fraction by 3 and the numerator of the 2nd fraction by 4.

We get:

7\cdot 3 = 21\\5\cdot 4 = 20

So the expression will be rewritten as:

\frac{7}{8}-\frac{5}{6}=\frac{21}{24}-\frac{20}{24}=\frac{21-20}{24}=\frac{1}{24}

6)

\frac{1}{6}+\frac{7}{8}=

Here the situation is similar to the first 4 exercises: using 24 as lowest common denominator, the numerators become

1\cdot 4 = 4\\7\cdot 3 = 21

So the expression becomes

\frac{1}{6}+\frac{7}{8}=\frac{4}{24}+\frac{21}{24}=\frac{4+21}{24}=\frac{25}{24}

Learn more about fractions:

brainly.com/question/605571

brainly.com/question/1312102

#LearnwithBrainly

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Answer:

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Step-by-step explanation:

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  1. Step one: you have to distribute the 10 to the numbers in the parentheses. That would leave us with a 10*x = 10x and 10*3 = 30
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Part three solve

  1. Step one: combine and put together what you have solved for. That would leave us with a -45x^{2}-36x+ 10x+30
  2. Step two: combine like terms. The like terms here are -36x and 10x. When you combine them you would get -26x.
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\huge{ \boxed{ \sf{ \frac{4}{3} }}}

Step-by-step explanation:

\star{ \sf{ \: Let \: the \: points \: be \: A \: and \: B}}

\star{ \sf{ \: Let \: a(2,-1)  \: be \: (x1 \:, y1) \: and \: b (5,3)  \: be \: (x2 \:, y2)}}

\underline{ \sf{Finding \: the \: slope \: of \: the \: line}}

\boxed{ \sf{Slope =  \frac{y2 - y1}{x2 - x1} }}

\mapsto{ \sf{Slope =  \frac{3 - ( - 1)}{5 - 2} }}

\mapsto{ \sf{Slope =  \frac{3 + 1}{5 - 2}}}

\mapsto{ \sf{Slope =  \frac{4}{3} }}

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Best regards! :D

~\text{TheAnimeGirl}

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