How do you evaluate #5\frac { 3} { 4} + 4\frac { 1} { 2} #?

Question

Aurora Arias · Accepted Answer

Explained in a lot of detail

#10 1/4# Once well practised you will be able to solve this problem type in just a few lines. Consider this as #5+3/4+4+1/2# #color(brown)("The whole number part is "5+4=9)# Consider the fraction part. We have #3/4+1/2# ................................................................................................ A fractions structure is such that you have: #("count")/("indicator the size of what is being counted")->("numerator")/("denominator")# You can not #ul("directly add")# the counts unless the 'size indicators' are the same. Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its actual value. .............................................................................................................. #color(green)(3/4" "+" "[1/2color(red)(xx1)])# #color(green)(3/4" "+" "[1/2color(red)(xx2/2)])# #3/4" "+" "2/4" "=" "(3+2)/4=5/4# but #5/4# is the same as #4/4+1/4=1 +1/4# #color(brown)("So the fraction part is "3/4+1/2=1 1/4# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Putting it all together")# #color(blue)(9+1 1/4=10 1/4)#

Aurora Arias · Answer

undefined To evaluate $5\frac{3}{4} + 4\frac{1}{2}$, first convert the mixed numbers to improper fractions. Then, add the fractions together.

$$
5\frac{3}{4} + 4\frac{1}{2} = \frac{(5 \times 4) + 3}{4} + \frac{(4 \times 2) + 1}{2}
$$

$$
= \frac{20 + 3}{4} + \frac{8 + 1}{2}
$$

$$
= \frac{23}{4} + \frac{9}{2}
$$

To add these fractions, you need to find a common denominator, which is 4 for the first fraction and 2 for the second fraction.

$$
= \frac{23 \times 2}{4 \times 2} + \frac{9 \times 2}{2 \times 2}
$$

$$
= \frac{46}{8} + \frac{18}{4}
$$

$$
= \frac{46}{8} + \frac{36}{8}
$$

Now, add the fractions:

$$
= \frac{46 + 36}{8}
$$

$$
= \frac{82}{8}
$$

Reduce the fraction:

$$
= \frac{41}{4}
$$

Therefore, $5\frac{3}{4} + 4\frac{1}{2} = \frac{41}{4}$.