Question

Simplify these improper fractions. Remember to divide the denominator into the numerator to simplify.
_____
1. 190/7 = 7) 190

2. 88/8 =

3. 762/7 =


Decomposed these mixed numbers into improper fractions. To do this, multiply the denominator by the whole number, then add the numerator and put this number over the denominator.

4. 4 3/5 =

5. 5 1/9 =

6. 9 8/12 =

Add these fractions together. Find a common denominator first. Two strategies to do this are:
1. Look to see if the smaller denominator number will go into the
larger denominator number

2. Multiply the two denominators together

Use 9 as the common denominator for this problem
7. 9 4/9
+2 2/3


Use 12 as the common denominator for this problem
8. 3 2/12
+ 1 5/6


Use 32 for the common denominator for this problem
9. 6 3/8
+ 1 1/4


Use 30 for the common denominator for this problem
10. 6 1/5
+ 1 3/6

You find the common denominator for this problem
11. 4 7/8
+1 ¼

You find the common denominator for this problem
12. 6 3/8
+4 1/5

Answer 1

First Portion:
1:
How many times can 190 go into 7? 27 times, leaving 1 left so, \(27\dfrac{1}{7}\)
2:
How many times can 88 go into 8? 11 times, so, \(11\)
3:
How many times can 762 go into 7? 108 times, leaving 6 left, so \(108\dfrac{6}{7}\)

Answer 2

Second Portion:
\(\dfrac{whole~number \times denominator + numerator}{denominator}\)
4:
\(4\times 5+3\) = \(\dfrac{23}{5}\)
5:
\(5\times 9+1\) = \(\dfrac{46}{9}\)
6:
\(9\times 12+8\) = \(\dfrac{116}{12}\)

Answer 3

Third Portion:
7:
Let's look for a similar denominator, well, how many times can 3 go into 9? 3 times, so multiply \(2\dfrac{2}{3}\) by 3,
\(\dfrac{8}{3} \times 3\) = \(\dfrac{24}{9}\) = \(2\dfrac{6}{9}\)
Now add these together,
\(2\dfrac{6}{9}\) + \(9\dfrac{4}{9}\) = \(11\dfrac{10}{9}\) = \(12\dfrac{1}{9}\)
8:
Look for a similar denominator, how many times can 6 go into 12? 2 times, so multiply \(1\dfrac{5}{6}\) by 2,
\(\dfrac{11}{6} \times 2\) = \(\dfrac{22}{12}\) = \(1\dfrac{10}{12}\)
Now add them together,
\(1\dfrac{10}{12}\) + \(3\dfrac{2}{12}\) = \(4\dfrac{12}{12}\) = \(5\)
9:
For this one, common denominator is 32, so multiply each fraction by the other fraction's opposite,
\(\dfrac{51}{8} \times 4\) = \(\dfrac{204}{32}\)
\(\dfrac{5}{4} \times 8\) = \(\dfrac{40}{32}\)
Add together,
\(\dfrac{204+40}{32}\) = \(\dfrac{244}{32}\) = \(7\dfrac{20}{32}\)
10:
Multiply denominators,
\(6\dfrac{1}{5} \times 6\) = \(\dfrac{186}{30}\)
\(1\dfrac{3}{6} \times 5\) = \(\dfrac{45}{30}\)
Add together,
\(\dfrac{186+45}{30}\) = \(\dfrac{231}{30}\) = \(7\dfrac{21}{30}\)
11:
How many times can 4 go into 8? 2 times, so multiply by 2,
\(\dfrac{5}{4}\times 2\) = \(\dfrac{10}{8}\) = \(1\dfrac{2}{8}\)
Add together,
\(1\dfrac{2}{8}\) + \(4\dfrac{7}{8}\) = \(5\dfrac{9}{8}\) = \(6\dfrac{1}{8}\)
12:
Multiply each fraction by other fractions denominator,
\(6\dfrac{3}{8} \times 5\) = \(\dfrac{255}{40}\)
\(4\dfrac{1}{5} \times 8\) = \(\dfrac{168}{40}\)
Add together,
\(\dfrac{255+168}{40}\) = \(\dfrac{423}{40}\) = \(10\dfrac{23}{40}\)

Answer 4

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Answer 5

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