Prealgebra
Questions Topics

# How do you evaluate 16\frac { 2} { 7} - 2\frac { 1} { 2} \cdot 1\frac { 1} { 7} + \frac { 9} { 14}?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Write a one sentence answer...

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

2

### This answer has been featured!

Featured answers represent the very best answers the Socratic community can create.

Feb 11, 2017

$16 \frac{2}{7} - 2 \frac{1}{2} \cdot 1 \frac{1}{7} + \frac{9}{14} = 14 \frac{1}{14}$

#### Explanation:

Given:

$16 \frac{2}{7} - 2 \frac{1}{2} \cdot 1 \frac{1}{7} + \frac{9}{14}$

First let us convert all of the mixed numbers to improper fractions:

$16 \frac{2}{7} = 16 + \frac{2}{7} = \frac{16 \cdot 7}{7} + \frac{2}{7} = \frac{112}{7} + \frac{2}{7} = \frac{114}{7}$

$2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{2 \cdot 2}{2} + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$

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

So our original expression can be rewritten as:

$\frac{114}{7} - \frac{5}{2} \cdot \frac{8}{7} + \frac{9}{14}$

Next note that multiplication has higher precedence than addition or multiplication, so we need to perform the multiplication $\frac{5}{2} \cdot \frac{8}{7}$ first:

$\frac{114}{7} - \textcolor{b l u e}{\frac{5}{2} \cdot \frac{8}{7}} + \frac{9}{14} = \frac{114}{7} - \frac{5 \cdot 8}{2 \cdot 7} + \frac{9}{14} = \frac{114}{7} - \frac{40}{14} + \frac{9}{14}$

In order to add or subtract these fractions, they need to have the same denominators, so we multiply $\frac{114}{7}$ by $\frac{2}{2}$ to give it a denominator $14$ like the other fractions:

$\frac{114}{7} = \frac{114 \cdot 2}{7 \cdot 2} = \frac{228}{14}$

So our express can be rewritten:

$\frac{228}{14} - \frac{40}{14} + \frac{9}{14} = \frac{228 - 40 + 9}{14}$

Then note that addition and subtraction have the same priority, so we need to evaluate them from left to right:

$\frac{\textcolor{b l u e}{228 - 40} + 9}{14} = \frac{188 + 9}{14} = \frac{197}{14}$

To express this as a mixed number, we divide $197$ by $14$ to give a quotient $14$ and remainder $1$, so:

$\frac{197}{14} = 14 + \frac{1}{14} = 14 \frac{1}{14}$

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Write a one sentence answer...

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

1
Feb 12, 2017

$= 14 \frac{1}{14}$

#### Explanation:

It is possible to work with the whole numbers separately when adding or subtracting.

Only for multiplication do we have to use improper fractions.

There are 3 terms, do the multiplication first.

$16 \frac{2}{7} \textcolor{b l u e}{- 2 \frac{1}{2} \times 1 \frac{1}{7}} + \frac{9}{14}$

$= 16 \frac{2}{7} \textcolor{b l u e}{- \frac{5}{2} \times \frac{8}{7}} + \frac{9}{14}$

We would usually cancel in the middle term. However we will need a common denominator in the next step so leave as it is. Simplify by multiplying straight across.

$16 \frac{4}{14} \textcolor{b l u e}{- \frac{40}{14}} + \frac{9}{14} \text{ }$ all have the same denominator

$= 16 \frac{4}{14} \textcolor{b l u e}{- 2 \frac{12}{14}} + \frac{9}{14} \text{ }$ change to a mixed number

$= 14 \frac{4 - 12 + 9}{14}$

$= 14 \frac{1}{14}$

Working with mixed numbers gives us smaller numbers to work with. The numbers in improper fractions are often uncomfortably big.

(Answer in the same form as the numbers were given.)

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Write a one sentence answer...

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

1
Feb 11, 2017

$14 \frac{1}{14}$

#### Explanation:

$16 \frac{2}{7} - 2 \frac{1}{2} \cdot 1 \frac{1}{7} + \frac{9}{14}$

$\therefore = \frac{114}{7} - \left(\frac{5}{2} \times \frac{8}{7}\right) + \frac{9}{14}$

$\therefore = \frac{114}{7} - \left(\frac{40}{14}\right) + \frac{9}{14}$

$\therefore = \frac{228 - 40 + 9}{14}$

$\therefore = \frac{197}{14}$

$\therefore = 14 \frac{1}{14}$

##### Just asked! See more
• 9 minutes ago
• 9 minutes ago
• 9 minutes ago
• 10 minutes ago
• A minute ago
• 3 minutes ago
• 5 minutes ago
• 5 minutes ago
• 7 minutes ago
• 7 minutes ago
• 9 minutes ago
• 9 minutes ago
• 9 minutes ago
• 10 minutes ago
##### Impact of this question
28 views around the world
You can reuse this answer
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 33, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9612346887588501, "perplexity": 2525.774277888717}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125944682.35/warc/CC-MAIN-20180420194306-20180420214306-00553.warc.gz"}