Adding/Subtracting Signed Fractions

Adding/Subtracting Signed Fractions

Solve this problem on your paper:

 $12\frac{\text{6}}{\text{7}}-\left(-4\frac{3}{6}\right)$  

Multiple Choice

 $12\frac{\text{6}}{\text{7}}-\left(-4\frac{3}{6}\right)$  is a subtraction problem. According to the rules I should:

• Subtract

• Add

• Keep Change Change

Multiple Choice

 $12\frac{\text{6}}{\text{7}}+\ 4\frac{3}{6}$  

The answer to this problem will be:

• Positive, you add and keep the sign.

• Negative, you're subtracting

• Negative, 12 has the largers absolute value

• Positive, 12 has the larger absolute value

Multiple Choice

 $12\frac{\text{6}}{\text{7}}+\ 4\frac{3}{6}$  

Next, I need to:

• Add the whole numbers

• Add the numerators

• Find a common denominator

• Add straight across

Multiple Choice

 $12\frac{\text{6}}{\text{7}}+\ 4\frac{3}{6}$  

The least common denominator for 7 and 6 is:

• 21

• 42

• 81

• 7

Multiple Choice

 $12\frac{\text{6}}{\text{7}}+\ 4\frac{3}{6}$  

Re-written with common denominators is:

•  $12\frac{\text{6}}{\text{42}}+\ 4\frac{3}{42}$  
  

•  $12\frac{\text{36}}{\text{42}}+\ 4\frac{21}{42}$  
  

•  $12\frac{\text{36}}{\text{42}}+\ 4\frac{18}{42}$  
  

Multiple Choice

 $12\frac{\text{36}}{\text{42}}+\ 4\frac{21}{42}$  

Next we:

• Add the whole numbers

• Add the numerators

• Add the denominators

Multiple Choice

 $12\frac{\text{36}}{\text{42}}+\ 4\frac{21}{42}\ =\ 16$  

Next we:

• Add the whole numbers

• Add the numerators

• Add the denominators

Multiple Choice

 $12\frac{\text{36}}{\text{42}}+\ 4\frac{21}{42}\ =\ 16\ \frac{57}{ }$  

Next we:

• Add the whole numbers

• Add the numerators

• Add the denominators

• Keep the denominator the same

Multiple Choice

 $12\frac{\text{36}}{\text{42}}+\ 4\frac{21}{42}\ =\ 16\ \frac{57}{42}$  

Next we:

• All done!

• Write our answer as a negative

• Simplify by making 57/42 into a mixed number.

Multiple Choice

 $16\ \frac{57}{42}\ =\$  

•  $17\frac{15}{42}$  
  

•  $16\frac{15}{42}$  

Multiple Choice

 $17\frac{15}{42}$  

• We're done! Horray!

• Not so fast! $\frac{15}{42}$  Can be simplified!

Multiple Choice

What factor can be divided out of both 15 and 42?

• None! I already said we're done!

• 3

• 5

• 6

Multiple Choice

Write  $17\frac{15}{42}$  in simplest form:

•  $17\frac{15}{42}$  

•  $17\frac{5}{7}$  
  

•  $17\frac{5}{14}$  

•  $17\frac{1}{7}$