Examples with solutions for All Operations in Fractions: In combination with other operations

Exercise #1

Solve the following exercise:

6712+314=? \frac{6}{7}-\frac{1}{2}+\frac{3}{14}=\text{?}

Video Solution

Step-by-Step Solution

To solve the expression 6712+314 \frac{6}{7} - \frac{1}{2} + \frac{3}{14} , we will follow these steps:

  • Step 1: Find a common denominator for the fractions.
  • Step 2: Convert each fraction to the common denominator.
  • Step 3: Perform the subtraction and addition as required.
  • Step 4: Simplify the result, if possible.

Let's work through the steps:

Step 1: The denominators are 7, 2, and 14. The least common multiple (LCM) of these numbers is 14.

Step 2: Convert each fraction:

  • 67 \frac{6}{7} becomes 6×27×2=1214 \frac{6 \times 2}{7 \times 2} = \frac{12}{14} .
  • 12 \frac{1}{2} becomes 1×72×7=714 \frac{1 \times 7}{2 \times 7} = \frac{7}{14} .
  • 314 \frac{3}{14} is already in the correct form as 314 \frac{3}{14} .

Step 3: Perform the operations:

  • Subtract: 1214714=514 \frac{12}{14} - \frac{7}{14} = \frac{5}{14} .
  • Add: 514+314=814 \frac{5}{14} + \frac{3}{14} = \frac{8}{14} .

Step 4: Simplify the fraction if possible. Here, 814 \frac{8}{14} simplifies to 47 \frac{4}{7} ; however, since the given choices list 814 \frac{8}{14} and it matches, there is no need for further simplification within the context of this question.

Therefore, the solution to the problem is 814 \frac{8}{14} .

Answer

814 \frac{8}{14}

Exercise #2

Solve the following exercise:

27+12714=? \frac{2}{7}+\frac{1}{2}-\frac{7}{14}=\text{?}

Video Solution

Step-by-Step Solution

To solve the expression 27+12714 \frac{2}{7}+\frac{1}{2}-\frac{7}{14} , follow these steps:

  • Step 1: Find the least common multiple (LCM) of the denominators 7, 2, and 14. The LCM is 14.
  • Step 2: Convert each fraction to have the denominator of 14:
        27 \frac{2}{7} becomes 2×27×2=414 \frac{2 \times 2}{7 \times 2} = \frac{4}{14}
        12 \frac{1}{2} becomes 1×72×7=714 \frac{1 \times 7}{2 \times 7} = \frac{7}{14}
        714 \frac{7}{14} remains 714 \frac{7}{14} since it's already over 14.
  • Step 3: Perform the operations in the expression 414+714714 \frac{4}{14} + \frac{7}{14} - \frac{7}{14} :
        First, add 414+714=1114 \frac{4}{14} + \frac{7}{14} = \frac{11}{14} .
        Then, subtract 1114714=414 \frac{11}{14} - \frac{7}{14} = \frac{4}{14} .
  • Step 4: The result is already simplified. Thus, the solution to the problem is 414 \frac{4}{14} .

Therefore, the solution to the problem is 414 \mathbf{\frac{4}{14}} , which corresponds to choice 3 \mathbf{3} .

Answer

414 \frac{4}{14}

Exercise #3

Solve the following exercise:

25+1213=? \frac{2}{5}+\frac{1}{2}-\frac{1}{3}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem 25+1213\frac{2}{5} + \frac{1}{2} - \frac{1}{3}, we will follow these steps:

  • Step 1: Find the least common denominator (LCD) for 25\frac{2}{5}, 12\frac{1}{2}, and 13\frac{1}{3}.
  • Step 2: Convert each fraction to have this common denominator.
  • Step 3: Perform the arithmetic operations.
  • Step 4: Simplify the result if necessary.

Now, let's proceed with the solution:
Step 1: The denominators are 5, 2, and 3. The least common multiple of these numbers is 30. Thus, the LCD is 30.

Step 2: Convert each fraction to have the common denominator of 30:
- Convert 25\frac{2}{5} to a fraction with denominator 30: 25=2×65×6=1230\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}.
- Convert 12\frac{1}{2} to a fraction with denominator 30: 12=1×152×15=1530\frac{1}{2} = \frac{1 \times 15}{2 \times 15} = \frac{15}{30}.
- Convert 13\frac{1}{3} to a fraction with denominator 30: 13=1×103×10=1030\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}.

Step 3: With all fractions having the same denominator, perform the operations:
1230+15301030=12+151030=1730\frac{12}{30} + \frac{15}{30} - \frac{10}{30} = \frac{12 + 15 - 10}{30} = \frac{17}{30}.

Step 4: Since 1730\frac{17}{30} is in its simplest form, no further simplification is needed.

Therefore, the correct answer is 1730\frac{17}{30}.

Answer

1730 \frac{17}{30}

Exercise #4

Solve the following exercise:

91045+12=? \frac{9}{10}-\frac{4}{5}+\frac{1}{2}=\text{?}

Video Solution

Step-by-Step Solution

To solve the expression 91045+12 \frac{9}{10} - \frac{4}{5} + \frac{1}{2} , we first seek a common denominator for the fractions. The denominators are 10, 5, and 2.

The least common multiple of these numbers is 10, as it is the smallest number that all denominators divide perfectly.

  • Convert 45 \frac{4}{5} to a fraction with a denominator of 10: 45=4×25×2=810 \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} .
  • Convert 12 \frac{1}{2} to a fraction with a denominator of 10: 12=1×52×5=510 \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} .

Now, the expression becomes 910810+510 \frac{9}{10} - \frac{8}{10} + \frac{5}{10} .

Perform the operations:

  • Subtract: 910810=110 \frac{9}{10} - \frac{8}{10} = \frac{1}{10} .
  • Add: 110+510=610 \frac{1}{10} + \frac{5}{10} = \frac{6}{10} .

Thus, the value of the expression is 610 \frac{6}{10} .

The correct answer is 610\frac{6}{10}.

Answer

610 \frac{6}{10}

Exercise #5

Solve the following exercise:

410+1512=? \frac{4}{10}+\frac{1}{5}-\frac{1}{2}=\text{?}

Video Solution

Step-by-Step Solution

To solve the expression 410+1512 \frac{4}{10} + \frac{1}{5} - \frac{1}{2} , we will follow these steps:

  • Step 1: Find a Common Denominator
    The denominators we have are 10, 5, and 2. The least common denominator (LCD) among these numbers is 10.

  • Step 2: Convert Fractions to Equivalent Fractions with the LCD
    - 410 \frac{4}{10} is already using 10 as the denominator.
    - 15=1×25×2=210 \frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10} .
    - 12=1×52×5=510 \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} .

  • Step 3: Perform the Arithmetic Operations
    Substitute the converted fractions into the original expression:
    410+210510 \frac{4}{10} + \frac{2}{10} - \frac{5}{10}
    Combine the numerators over the common denominator:
    4+2510=110 \frac{4 + 2 - 5}{10} = \frac{1}{10}

  • Step 4: Simplify the Result
    The fraction 110 \frac{1}{10} is already in its simplest form.

Therefore, the solution to the problem is 110 \frac{1}{10} .

Answer

110 \frac{1}{10}

Exercise #6

Solve the following exercise:

38+1214=? \frac{3}{8}+\frac{1}{2}-\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem, let's work through the following steps:

  • Step 1: Identify the least common denominator (LCD) for all fractions.
    - The denominators are 8, 2, and 4. The LCM of these numbers is 8.

  • Step 2: Convert each fraction to have this common denominator of 8.
    - 38\frac{3}{8} is already with a denominator of 8.
    - 12\frac{1}{2} can be rewritten as 48\frac{4}{8} because 1×42×4=48\frac{1 \times 4}{2 \times 4} = \frac{4}{8}.
    - 14\frac{1}{4} can be rewritten as 28\frac{2}{8} because 1×24×2=28\frac{1 \times 2}{4 \times 2} = \frac{2}{8}.

  • Step 3: Perform the arithmetic operations.
    - Add 38\frac{3}{8} and 48\frac{4}{8}, which gives 3+48=78\frac{3 + 4}{8} = \frac{7}{8}.
    - Subtract 28\frac{2}{8} from 78\frac{7}{8}, giving 728=58\frac{7 - 2}{8} = \frac{5}{8}.

  • Step 4: Simplify the answer if necessary.
    58\frac{5}{8} is already in its simplest form.

Therefore, the solution to the problem is 58 \frac{5}{8} .

Answer

58 \frac{5}{8}

Exercise #7

Complete the following exercise:

14:12+14=? \frac{1}{4}:\frac{1}{2}+\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem 14:12+14 \frac{1}{4} : \frac{1}{2} + \frac{1}{4} , follow these steps:

Step 1: Perform the division 14:12 \frac{1}{4} : \frac{1}{2} .

  • When dividing by a fraction, multiply by the reciprocal. Hence, 14:12 \frac{1}{4} : \frac{1}{2} becomes 14×21 \frac{1}{4} \times \frac{2}{1} .
  • Multiply the numerators: 1×2=2 1 \times 2 = 2 .
  • Multiply the denominators: 4×1=4 4 \times 1 = 4 .
  • So, 14×21=24=12 \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2} after simplification.

Step 2: Now add the result from Step 1 to 14\frac{1}{4}.

  • We need to add 12+14 \frac{1}{2} + \frac{1}{4} .
  • Convert 12\frac{1}{2} to have a common denominator with 14\frac{1}{4}. 12=24\frac{1}{2} = \frac{2}{4}.
  • Add the fractions: 24+14=34\frac{2}{4} + \frac{1}{4} = \frac{3}{4}.

Therefore, the solution to the problem is 34 \frac{3}{4} .

Answer

34 \frac{3}{4}

Exercise #8

Complete the following exercise:

12:1214=? \frac{1}{2}:\frac{1}{2}-\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem, 12:1214\frac{1}{2}:\frac{1}{2}-\frac{1}{4}, follow these steps:

  • Step 1: First, interpret the division 12:12\frac{1}{2} : \frac{1}{2} as multiplication by the reciprocal. This becomes 12×21\frac{1}{2} \times \frac{2}{1}.
  • Step 2: Perform the multiplication: 12×21=1×22×1=22=1. \frac{1}{2} \times \frac{2}{1} = \frac{1 \times 2}{2 \times 1} = \frac{2}{2} = 1.
  • Step 3: Next, subtract 14\frac{1}{4} from 1: 114=4414=34. 1 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4}.

Therefore, the solution to the problem is 34\frac{3}{4}.

Answer

34 \frac{3}{4}

Exercise #9

Solve the following exercise:

34:54+12=? \frac{3}{4}:\frac{5}{4}+\frac{1}{2}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the division 34:54 \frac{3}{4} : \frac{5}{4} .
  • Step 2: Use the formula ab:cd=ab×dc\frac{a}{b} : \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}.
  • Step 3: Simplify the division result.
  • Step 4: Add 12 \frac{1}{2} to the result of the division.
  • Step 5: Simplify the addition result to get the final answer.

Now, let's work through each step:

Step 1: We need to calculate 34:54 \frac{3}{4} : \frac{5}{4} . Using the division of fractions formula, this becomes:

34×45=3×44×5=1220 \frac{3}{4} \times \frac{4}{5} = \frac{3 \times 4}{4 \times 5} = \frac{12}{20} .

Step 2: Simplify 1220 \frac{12}{20} . Divide the numerator and the denominator by their greatest common divisor, which is 4:

12÷420÷4=35 \frac{12 \div 4}{20 \div 4} = \frac{3}{5} .

Step 3: Add 12 \frac{1}{2} to the result 35\frac{3}{5}:

The common denominator for addition is 10. Therefore:

35=3×25×2=610 \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} and 12=1×52×5=510 \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} .

Add these two fractions:

610+510=6+510=1110 \frac{6}{10} + \frac{5}{10} = \frac{6 + 5}{10} = \frac{11}{10} .

Therefore, the solution to the problem is 1110 \frac{11}{10} .

Answer

1110 \frac{11}{10}

Exercise #10

34×3414= \frac{3}{4}\times\frac{3}{4}-\frac{1}{4}=

Video Solution

Step-by-Step Solution

To solve this mathematical problem, follow these steps:

  • Step 1: Multiply the fractions 34\frac{3}{4} and 34\frac{3}{4}.
  • Step 2: Subtract 14\frac{1}{4} from the product obtained in Step 1.

Let's execute each step in detail:

Step 1: Calculate the product of 34\frac{3}{4} and 34\frac{3}{4}.

To multiply two fractions, multiply their numerators and their denominators separately:

34×34=3×34×4=916 \frac{3}{4} \times \frac{3}{4} = \frac{3 \times 3}{4 \times 4} = \frac{9}{16}

Step 2: Subtract 14\frac{1}{4} from 916\frac{9}{16}.

Before we subtract 14\frac{1}{4} from 916\frac{9}{16}, we need a common denominator. The common denominator for these fractions is 16:

14=1×44×4=416 \frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}

Now subtract 416\frac{4}{16} from 916\frac{9}{16}:

916416=9416=516 \frac{9}{16} - \frac{4}{16} = \frac{9 - 4}{16} = \frac{5}{16}

Therefore, the solution to the given problem is 516 \frac{5}{16} .

Answer

516 \frac{5}{16}

Exercise #11

12×12+34= \frac{1}{2}\times\frac{1}{2}+\frac{3}{4}=

Video Solution

Step-by-Step Solution

To solve 12×12+34\frac{1}{2} \times \frac{1}{2} + \frac{3}{4}, follow these steps:

  • Step 1: Multiply 12×12\frac{1}{2} \times \frac{1}{2} by using the multiplication of fractions formula:
    12×12=1×12×2=14\frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4}.
  • Step 2: Add 14\frac{1}{4} to 34\frac{3}{4}.
    Since 14\frac{1}{4} and 34\frac{3}{4} already have the same denominator, the addition can be done directly:
    14+34=1+34=44=1\frac{1}{4} + \frac{3}{4} = \frac{1 + 3}{4} = \frac{4}{4} = 1.

Therefore, the correct solution to the expression is 1 1 .

Answer

1 1

Exercise #12

35×23+25= \frac{3}{5}\times\frac{2}{3}+\frac{2}{5}=

Video Solution

Step-by-Step Solution

To solve the problem 35×23+25 \frac{3}{5} \times \frac{2}{3} + \frac{2}{5} , we proceed with the following steps:

  • Step 1: Multiply the fractions 35\frac{3}{5} and 23\frac{2}{3}.

The multiplication yields:

35×23=3×25×3=615\frac{3}{5} \times \frac{2}{3} = \frac{3 \times 2}{5 \times 3} = \frac{6}{15}

  • Step 2: Simplify the product 615\frac{6}{15}.

Both 6 and 15 share a common factor of 3:

615=6÷315÷3=25\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}

  • Step 3: Add 25\frac{2}{5} to the simplified result 25\frac{2}{5}.

Since the fractions 25\frac{2}{5} and 25\frac{2}{5} have the same denominator, add the numerators while keeping the denominator:

25+25=2+25=45\frac{2}{5} + \frac{2}{5} = \frac{2+2}{5} = \frac{4}{5}

Therefore, the solution to the problem is 45 \frac{4}{5} .

Answer

45 \frac{4}{5}

Exercise #13

23×13+29= \frac{2}{3}\times\frac{1}{3}+\frac{2}{9}=

Video Solution

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Step 1: Multiply the fractions. Calculate 23×13 \frac{2}{3} \times \frac{1}{3} .
  • Step 2: Add the product to another fraction. Add the result to 29 \frac{2}{9} .

Now, let's work through the calculations:

Step 1: Multiply 23\frac{2}{3} by 13\frac{1}{3}.

The formula for multiplying fractions is:

ab×cd=a×cb×d \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} .

Substitute the values:

23×13=2×13×3=29 \frac{2}{3} \times \frac{1}{3} = \frac{2 \times 1}{3 \times 3} = \frac{2}{9} .

Step 2: Add 29\frac{2}{9} to the product.

We found in Step 1 that 23×13=29 \frac{2}{3} \times \frac{1}{3} = \frac{2}{9} .

Now add 29+29=2+29=49 \frac{2}{9} + \frac{2}{9} = \frac{2 + 2}{9} = \frac{4}{9} .

Therefore, the solution to the expression is 49 \frac{4}{9} .

Answer

49 \frac{4}{9}

Exercise #14

34×12+58= \frac{3}{4}\times\frac{1}{2}+\frac{5}{8}=

Video Solution

Step-by-Step Solution

To solve the problem 34×12+58 \frac{3}{4} \times \frac{1}{2} + \frac{5}{8} , we'll follow these steps:

  • Step 1: Multiply the fractions 34×12 \frac{3}{4} \times \frac{1}{2} .
  • Step 2: Add the result to 58 \frac{5}{8} .

Now, let's work through the steps:

Step 1: Compute the product of the first two fractions:
34×12=3×14×2=38 \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}

Step 2: Add the resulting fraction to 58 \frac{5}{8} by finding a common denominator:

The fractions 38\frac{3}{8} and 58\frac{5}{8} already have the same denominator, so we can simply add them:
38+58=3+58=88=1 \frac{3}{8} + \frac{5}{8} = \frac{3 + 5}{8} = \frac{8}{8} = 1

Therefore, the solution to the problem is 1 1 .

Answer

1 1

Exercise #15

44×12+38= \frac{4}{4}\times\frac{1}{2}+\frac{3}{8}=

Video Solution

Step-by-Step Solution

To solve the expression 44×12+38 \frac{4}{4} \times \frac{1}{2} + \frac{3}{8} , follow these steps:

  • Step 1: Simplify 44 \frac{4}{4} . Since 44=1 \frac{4}{4} = 1 , the expression becomes 1×12+38 1 \times \frac{1}{2} + \frac{3}{8} .
  • Step 2: Perform the multiplication.
    Calculate 1×12=12 1 \times \frac{1}{2} = \frac{1}{2} .
  • Step 3: Add 12 \frac{1}{2} to 38 \frac{3}{8} .
    First, convert 12 \frac{1}{2} to an equivalent fraction with a denominator of 8: 12=48 \frac{1}{2} = \frac{4}{8} .
  • Step 4: Now, add the fractions: 48+38=78 \frac{4}{8} + \frac{3}{8} = \frac{7}{8} .

Thus, the final result is 78 \frac{7}{8} .

Answer

78 \frac{7}{8}

Exercise #16

23×23+49= \frac{2}{3}\times\frac{2}{3}+\frac{4}{9}=

Video Solution

Step-by-Step Solution

To solve the given problem, we will follow these steps:

  • Step 1: Perform the multiplication of the fractions.
  • Step 2: Simplify the result, if applicable.
  • Step 3: Add the simplified fractional result to the given fraction, ensuring the denominators align properly.
  • Step 4: Simplify the final result, if necessary.

Let's go through each step:

Step 1: Multiply the fractions 23×23=2×23×3=49 \frac{2}{3} \times \frac{2}{3} = \frac{2 \times 2}{3 \times 3} = \frac{4}{9} .

Step 2: The result from step 1 is 49\frac{4}{9}, which cannot be further simplified.

Step 3: Add the result from Step 2 to 49\frac{4}{9} given in the problem:
We have two fractions 49\frac{4}{9} and 49\frac{4}{9}, and since they already have a common denominator, we add them directly:
49+49=4+49=89\frac{4}{9} + \frac{4}{9} = \frac{4 + 4}{9} = \frac{8}{9}.

Step 4: The fraction 89\frac{8}{9} is already in its simplest form.

Therefore, the solution to the problem is 89 \frac{8}{9} .

Answer

89 \frac{8}{9}

Exercise #17

14×12+38= \frac{1}{4}\times\frac{1}{2}+\frac{3}{8}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Multiply the given fractions.
  • Step 2: Simplify if necessary.
  • Step 3: Perform the addition of resulting fractions.

Now, let's work through each step:

Step 1: Multiply the fractions:
14×12=1×14×2=18\frac{1}{4} \times \frac{1}{2} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8}

Step 2: We find that the result is already simplified.

Step 3: Add 18 \frac{1}{8} to 38 \frac{3}{8} :
18+38=1+38=48=12\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8} = \frac{1}{2}

The fractions have the same denominator, allowing for direct addition.

Therefore, the solution to the problem is 12 \frac{1}{2} .

Answer

12 \frac{1}{2}

Exercise #18

14×45+1120= \frac{1}{4}\times\frac{4}{5}+\frac{11}{20}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll approach it in the following steps:

Step 1: Perform the Multiplication
The expression begins with multiplying two fractions: 14×45 \frac{1}{4} \times \frac{4}{5} . Using the formula for multiplying fractions, we get:
1×44×5=420 \frac{1 \times 4}{4 \times 5} = \frac{4}{20}
Simplifying 420 \frac{4}{20} by dividing both numerator and denominator by 4 gives:
15 \frac{1}{5}

Step 2: Add the Result to the Second Fraction
Now, we need to add 15 \frac{1}{5} to 1120 \frac{11}{20} . To do this, we first find a common denominator.
The least common denominator between 5 and 20 is 20. Convert 15 \frac{1}{5} to twentieths:
15=420 \frac{1}{5} = \frac{4}{20}
Now add 420 \frac{4}{20} to 1120 \frac{11}{20} :
420+1120=1520 \frac{4}{20} + \frac{11}{20} = \frac{15}{20}

Step 3: Simplify the Final Result
Simplify 1520\frac{15}{20} by dividing the numerator and the denominator by 5:
15÷520÷5=34 \frac{15 \div 5}{20 \div 5} = \frac{3}{4}

Therefore, the solution to the problem is 34\frac{3}{4}. This matches choice 1, which is 34\frac{3}{4}.

Answer

34 \frac{3}{4}

Exercise #19

45×12+310= \frac{4}{5}\times\frac{1}{2}+\frac{3}{10}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Multiply the first two fractions.
  • Step 2: Add the result to the third fraction.
  • Step 3: Simplify the final result.

Now, let's work through each step:
Step 1: Multiply 45 \frac{4}{5} by 12 \frac{1}{2} . According to the multiplication rule for fractions, we have:
45×12=4×15×2=410 \frac{4}{5} \times \frac{1}{2} = \frac{4 \times 1}{5 \times 2} = \frac{4}{10} Step 2: We need to add 410 \frac{4}{10} to 310 \frac{3}{10} . Since these fractions have the same denominator, we can add them directly:
410+310=4+310=710 \frac{4}{10} + \frac{3}{10} = \frac{4 + 3}{10} = \frac{7}{10} Step 3: The sum 710 \frac{7}{10} is already in simplest form.

Therefore, the solution to the problem is 710 \frac{7}{10} , which matches choice (3) \text{(3)} .

Answer

710 \frac{7}{10}

Exercise #20

Solve the following exercise:

110+3512=? \frac{1}{10}+\frac{3}{5}-\frac{1}{2}=\text{?}

Video Solution

Step-by-Step Solution

To solve the exercise 110+3512 \frac{1}{10} + \frac{3}{5} - \frac{1}{2} , we must follow these steps:

Step 1: Find the Least Common Denominator (LCD).
The denominators we have are 10, 5, and 2. The LCD for these numbers is 10.

Step 2: Convert each fraction to have the common denominator of 10.
- 110 \frac{1}{10} is already with the denominator 10.
- Convert 35 \frac{3}{5} :35×22=610 \frac{3}{5} \times \frac{2}{2} = \frac{6}{10}
- Convert 12 \frac{1}{2} :
12×55=510 \frac{1}{2} \times \frac{5}{5} = \frac{5}{10}

Step 3: Perform the addition and subtraction.
Now operate: 110+610510=1+6510=210 \frac{1}{10} + \frac{6}{10} - \frac{5}{10} = \frac{1 + 6 - 5}{10} = \frac{2}{10}

Step 4: Simplify the result.
The fraction 210\frac{2}{10} simplifies to 15\frac{1}{5} because both the numerator and denominator are divisible by 2.

Therefore, the solution to the problem is 15\frac{1}{5}.

Answer

15 \frac{1}{5}