Solved on Nov 17, 2023

Simplify the expression $\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}$ and select the correct answer.

STEP 1

Assumptions1. The given expression is $\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}$ . . We need to simplify this expression to its simplest form.

STEP 2

We can simplify the expression by combining like terms. The like terms in this expression are the terms with the variable $y$ .
$\frac{9}{10} y - \frac{}{5} y$

STEP 3

Before we can combine these terms, we need to make sure they have the same denominator. The least common denominator (LCD) of10 and5 is10.
So, we rewrite $\frac{3}{5}$ as $\frac{6}{10}$ .

STEP 4

Now, we can subtract the fractions.
$\frac{9}{10} y - \frac{6}{10} y = \frac{3}{10} y$

STEP 5

Now, let's combine the constant terms $\frac{1}{4}$ and $\frac{7}{8}$ .
Again, we need to find the LCD of4 and8, which is8.
So, we rewrite $\frac{1}{4}$ as $\frac{2}{8}$ .

STEP 6

Now, we can add the fractions.
$\frac{2}{8} + \frac{}{8} = \frac{9}{8}$

STEP 7

The fraction $\frac{9}{}$ is an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator.
$\frac{9}{} =1 \frac{1}{}$

STEP 8

Now, we can write the simplified expression by combining the results from steps4 and7.
$\frac{3}{10} y +1 \frac{1}{8}$ So, the simplified form of the given expression is $\frac{3}{10} y +1 \frac{1}{8}$ .
Looking at the options, this matches with option C) $\frac{3}{10} y+1 \frac{1}{8}$ .

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Simplify the expression $\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}$ and select the correct answer.

STEP 1

Assumptions1. The given expression is $\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}$ . . We need to simplify this expression to its simplest form.

STEP 2

We can simplify the expression by combining like terms. The like terms in this expression are the terms with the variable $y$ .
$\frac{9}{10} y - \frac{}{5} y$

STEP 3

Before we can combine these terms, we need to make sure they have the same denominator. The least common denominator (LCD) of10 and5 is10.
So, we rewrite $\frac{3}{5}$ as $\frac{6}{10}$ .

STEP 4

Now, we can subtract the fractions.
$\frac{9}{10} y - \frac{6}{10} y = \frac{3}{10} y$

STEP 5

Now, let's combine the constant terms $\frac{1}{4}$ and $\frac{7}{8}$ .
Again, we need to find the LCD of4 and8, which is8.
So, we rewrite $\frac{1}{4}$ as $\frac{2}{8}$ .

STEP 6

Now, we can add the fractions.
$\frac{2}{8} + \frac{}{8} = \frac{9}{8}$

STEP 7

The fraction $\frac{9}{}$ is an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator.
$\frac{9}{} =1 \frac{1}{}$

STEP 8

Now, we can write the simplified expression by combining the results from steps4 and7.
$\frac{3}{10} y +1 \frac{1}{8}$ So, the simplified form of the given expression is $\frac{3}{10} y +1 \frac{1}{8}$ .
Looking at the options, this matches with option C) $\frac{3}{10} y+1 \frac{1}{8}$ .

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Simplify the expression 14+910y−35y+78\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}41​+109​y−53​y+87​ and select the correct answer.

STEP 1

Assumptions1. The given expression is 14+910y−35y+78\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}41​+109​y−53​y+87​. . We need to simplify this expression to its simplest form.

STEP 2

We can simplify the expression by combining like terms. The like terms in this expression are the terms with the variable yyy.910y−5y\frac{9}{10} y - \frac{}{5} y109​y−5​y

STEP 3

Before we can combine these terms, we need to make sure they have the same denominator. The least common denominator (LCD) of10 and5 is10.So, we rewrite 35\frac{3}{5}53​ as 610\frac{6}{10}106​.

STEP 4

Now, we can subtract the fractions.910y−610y=310y\frac{9}{10} y - \frac{6}{10} y = \frac{3}{10} y109​y−106​y=103​y

STEP 5

Now, let's combine the constant terms 14\frac{1}{4}41​ and 78\frac{7}{8}87​.Again, we need to find the LCD of4 and8, which is8.So, we rewrite 14\frac{1}{4}41​ as 28\frac{2}{8}82​.

STEP 6

Now, we can add the fractions.28+8=98\frac{2}{8} + \frac{}{8} = \frac{9}{8}82​+8​=89​

STEP 7

The fraction 9\frac{9}{}9​ is an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator.9=11\frac{9}{} =1 \frac{1}{}9​=11​

STEP 8

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Simplify the expression $\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}$ and select the correct answer.

Assumptions1. The given expression is $\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}$ . . We need to simplify this expression to its simplest form.

We can simplify the expression by combining like terms. The like terms in this expression are the terms with the variable $y$ .
$\frac{9}{10} y - \frac{}{5} y$

Before we can combine these terms, we need to make sure they have the same denominator. The least common denominator (LCD) of10 and5 is10.
So, we rewrite $\frac{3}{5}$ as $\frac{6}{10}$ .

Now, we can subtract the fractions.
$\frac{9}{10} y - \frac{6}{10} y = \frac{3}{10} y$

Now, let's combine the constant terms $\frac{1}{4}$ and $\frac{7}{8}$ .
Again, we need to find the LCD of4 and8, which is8.
So, we rewrite $\frac{1}{4}$ as $\frac{2}{8}$ .

Now, we can add the fractions.
$\frac{2}{8} + \frac{}{8} = \frac{9}{8}$

The fraction $\frac{9}{}$ is an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator.
$\frac{9}{} =1 \frac{1}{}$