Simplification and Expansiono f Simple Fractions

To amplify fractions

We will perform the same multiplication operation on the numerator and the denominator: the value of the fraction will be preserved.

You can expand as many times as you want and by any number.

To simplify fractions:

We will perform the same division operation on the numerator and the denominator: the value of the fraction will be preserved.

This can only be done with a number that is completely divisible by both the numerator and the denominator.

It is possible to simplify only until reaching a fraction in which it is not possible to find a number that divides without remainder both in the numerator and the denominator.

Suggested Topics to Practice in Advance

  1. A fraction as a divisor
  2. Numerator
  3. Denominator
  4. Fractions
  5. Part of a quantity
  6. Remainder of a fraction
  7. Remainders
  8. Placing Fractions on the Number Line
  9. Common denominator

Practice Simplification and Expansion of Simple Fractions

Examples with solutions for Simplification and Expansion of Simple Fractions

Exercise #1

Simplify the following fraction:

124= \frac{12}{4}=

Video Solution

Step-by-Step Solution

Let's reduce as follows, divide the numerator by 4 and the denominator by 4:

12:44:4=31 \frac{12:4}{4:4}=\frac{3}{1}

Answer

31 \frac{3}{1}

Exercise #2

Simplify the following fraction:

11= \frac{1}{1}=

Video Solution

Step-by-Step Solution

Let's reduce as follows, we'll divide both the numerator and denominator by 1:

1:11:1=11 \frac{1:1}{1:1}=\frac{1}{1}

Answer

11 \frac{1}{1}

Exercise #3

Simplify the following fraction by a factor of 5:

1510= \frac{15}{10}=

Video Solution

Step-by-Step Solution

Let's reduce as follows, we'll divide both the numerator and denominator by 5:

15:510:5=32 \frac{15:5}{10:5}=\frac{3}{2}

Answer

32 \frac{3}{2}

Exercise #4

Simplify the following fraction:

128= \frac{12}{8}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

12:28:2=64 \frac{12:2}{8:2}=\frac{6}{4}

Answer

64 \frac{6}{4}

Exercise #5

Simplify the following fraction:

168= \frac{16}{8}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

16:28:2=84 \frac{16:2}{8:2}=\frac{8}{4}

Answer

84 \frac{8}{4}

Exercise #6

Simplify the following fraction:

210= \frac{2}{10}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

2:210:2=15 \frac{2:2}{10:2}=\frac{1}{5}

Answer

15 \frac{1}{5}

Exercise #7

Simplify the following fraction by a factor of 4:

48= \frac{4}{8}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 4 and the denominator by 4:

4:48:4=12 \frac{4:4}{8:4}=\frac{1}{2}

Answer

12 \frac{1}{2}

Exercise #8

Simplify the following fraction by a factor of 3:

36= \frac{3}{6}=

Video Solution

Step-by-Step Solution

We will reduce as follows, divide the numerator by 3 and the denominator by 3:

3:36:3=12 \frac{3:3}{6:3}=\frac{1}{2}

Answer

12 \frac{1}{2}

Exercise #9

Simplify the following fraction by a factor of 1:

310= \frac{3}{10}=

Video Solution

Step-by-Step Solution

We will reduce in the following way, divide the numerator by 1 and the denominator by 1:

3:110:1=310 \frac{3:1}{10:1}=\frac{3}{10}

Answer

310 \frac{3}{10}

Exercise #10

Simplify the following fraction:

416= \frac{4}{16}=

Video Solution

Step-by-Step Solution

We will reduce in the following way, divide the numerator by 4 and the denominator by 4:

4:416:4=14 \frac{4:4}{16:4}=\frac{1}{4}

Answer

14 \frac{1}{4}

Exercise #11

Enlarge the following fraction by the factor 4:

13= \frac{1}{3}=

Video Solution

Step-by-Step Solution

To solve the problem of enlarging the fraction 13\frac{1}{3} by a factor of 4, we will follow these steps:

  • Step 1: Identify the given fraction and enlargement factor. The fraction is 13\frac{1}{3} and the factor is 4.
  • Step 2: Multiply both the numerator and denominator of the fraction by the enlargement factor. This means we calculate:

1×43×4=412 \frac{1 \times 4}{3 \times 4} = \frac{4}{12}

Step 3: Check if the fraction can be simplified. Here, 412\frac{4}{12} can be simplified to 13\frac{1}{3}, but since we aim to express it in an "enlarged" form, 412\frac{4}{12} is a correct representation when enlarged by the given factor.

Step 4: Verify against answer choices if applicable. In our list of choices, 412\frac{4}{12} is listed as choice 3, which matches our calculated answer.

Therefore, the solution to the problem is 412\frac{4}{12}.

Answer

412 \frac{4}{12}

Exercise #12

Increase the following fraction by a factor of 8:

25= \frac{2}{5}=

Video Solution

Step-by-Step Solution

To solve the problem of increasing the fraction 25\frac{2}{5} by a factor of 8, we follow these steps:

  • Multiply the numerator of the fraction by the factor of 8.
  • Multiply the denominator of the fraction by the same factor of 8 to preserve the value relation.
  • Check the result against the options provided, especially since this is a multiple-choice question.

Following these steps:

Step 1: Multiply the numerator:

The numerator is 2. Multiplying 2 by 8 gives 2×8=162 \times 8 = 16.

Step 2: Multiply the denominator:

The denominator is 5. Multiplying 5 by 8 gives 5×8=405 \times 8 = 40.

Thus, the fraction becomes 1640\frac{16}{40} after being increased by a factor of 8.

The correct answer among the provided choices is:

1640 \frac{16}{40}

Answer

1640 \frac{16}{40}

Exercise #13

Increase the following fraction by a factor of 5:

310= \frac{3}{10}=

Video Solution

Step-by-Step Solution

To solve the problem of increasing the fraction 310 \frac{3}{10} by a factor of 5, follow these steps:

  • Step 1: Multiply the numerator by 5.
    The original numerator is 3, so 3×5=15 3 \times 5 = 15 .
  • Step 2: Multiply the denominator by 5.
    The original denominator is 10, so 10×5=50 10 \times 5 = 50 .
  • Step 3: Write the new fraction.
    The resulting fraction after applying the factor is 1550 \frac{15}{50} .

Thus, when we increase the fraction 310 \frac{3}{10} by a factor of 5, we get 1550 \frac{15}{50} .

Therefore, the correct answer is 1550 \frac{15}{50} .

Answer

1550 \frac{15}{50}

Exercise #14

Increase the following fraction by a factor of 5:

67= \frac{6}{7}=

Video Solution

Step-by-Step Solution

To solve the problem, we need to increase the fraction 67 \frac{6}{7} by a factor of 5. This involves multiplying both the numerator and denominator by 5.

  • Step 1: Multiply the numerator of the fraction: 6×5=30 6 \times 5 = 30 .
  • Step 2: Multiply the denominator of the fraction: 7×5=35 7 \times 5 = 35 .
  • Step 3: Form the new fraction: 3035 \frac{30}{35} .

Thus, when you increase the fraction 67 \frac{6}{7} by a factor of 5, the result is 3035 \frac{30}{35} .

Answer

3035 \frac{30}{35}

Exercise #15

Increase the following fraction by a factor of 6:

811= \frac{8}{11}=

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Identify the given fraction as 811 \frac{8}{11} .
  • Step 2: Determine the factor to increase by, which is 6.
  • Step 3: Multiply the numerator by the factor: 8×6=48 8 \times 6 = 48 .
  • Step 4: Multiply the denominator by the factor: 11×6=66 11 \times 6 = 66 .

Now, let's perform the calculation to expand the fraction:

Starting with the original fraction:

811 \frac{8}{11}

We need to multiply both the numerator and the denominator by the factor of 6:

The new numerator is:

8×6=48 8 \times 6 = 48

The new denominator is:

11×6=66 11 \times 6 = 66

Thus, the fraction increased by a factor of 6 is:

4866 \frac{48}{66}

Therefore, the solution to the problem is 4866 \frac{48}{66} .

Answer

4866 \frac{48}{66}

Topics learned in later sections

  1. How do you simplify fractions?