Mathematical Expression Comparison: Identifying the Maximum Value Exercise

Question

Choose the exercise for the highest result

Video Solution

Solution Steps

00:00 Choose the largest one
00:07 Multiply this fraction by 2 to find a common denominator
00:17 Add under the same denominator
00:23 This is the calculation for the first addition
00:29 Let's continue to the second addition, add under the same denominator
00:34 This is the calculation for the second addition
00:37 Let's continue to the third addition
00:43 Multiply this fraction by 5 to find a common denominator
00:50 Add under the same denominator
00:57 This is the calculation for the third addition
01:04 Reduce the calculation by 2
01:21 Let's continue to the fourth addition
01:26 Multiply this fraction by 5 to find a common denominator
01:34 Add under the same denominator
01:38 This is the calculation for the fourth addition
01:41 Now let's compare the calculations and find the largest one
01:44 Let's convert all calculations to decimal points and determine
02:00 And this is the solution to the question

Step-by-Step Solution

To solve this problem, let's evaluate each of the fraction addition expressions:

  • Expression 1: 12+14 \frac{1}{2} + \frac{1}{4}
    To add these fractions, we need a common denominator. The least common denominator of 2 and 4 is 4.
    Thus, 12=24\frac{1}{2} = \frac{2}{4} and keep 14\frac{1}{4} as it is.
    Adding the two fractions, 24+14=34\frac{2}{4} + \frac{1}{4} = \frac{3}{4}.
  • Expression 2: 13+13 \frac{1}{3} + \frac{1}{3}
    Since these have the same denominator, we can directly add them:
    13+13=23\frac{1}{3} + \frac{1}{3} = \frac{2}{3}.
  • Expression 3: 12+310 \frac{1}{2} + \frac{3}{10}
    The least common denominator of 2 and 10 is 10.
    Convert 12\frac{1}{2} to 510\frac{5}{10} and add it to 310\frac{3}{10}:
    510+310=810=45\frac{5}{10} + \frac{3}{10} = \frac{8}{10} = \frac{4}{5}.
  • Expression 4: 510+15 \frac{5}{10} + \frac{1}{5}
    Convert the fractions to have the same denominator. Here, the least common denominator is 10.
    Keep 510\frac{5}{10} as it is, and convert 15\frac{1}{5} to 210\frac{2}{10}:
    510+210=710\frac{5}{10} + \frac{2}{10} = \frac{7}{10}.

Now, let's compare these results:
- 34=0.75\frac{3}{4} = 0.75
- 23=0.666\frac{2}{3} = 0.666\ldots
- 45=0.8\frac{4}{5} = 0.8
- 710=0.7\frac{7}{10} = 0.7

Comparing these decimals, we see that 0.80.8 (from Expression 3) is the largest result.

Therefore, the expression with the highest result is 12+310 \frac{1}{2} + \frac{3}{10} .

Answer

12+310 \frac{1}{2}+\frac{3}{10}