14 cm piece of tape is cut into two pieces. The shorter piece is 2/5 as long as the longer one. which is the length of the shorter piece.

Question

14 cm piece of tape is cut into two pieces. The shorter piece is 2/5 as long as the longer one. which is the length of the shorter piece.

Answer 1

Well, let's do a little math here. Since the shorter piece is 2/5 as long as the longer piece, we can call the length of the longer piece "x". Therefore, the length of the shorter piece would be 2/5 * x.

Now, we know that the total length of tape is 14 cm, so we can set up an equation:

x + (2/5 * x) = 14

If we simplify this equation, we get:

5/5 * x + 2/5 * x = 14

Now, let's add those fractions together:

(5/5 + 2/5) * x = 14

(7/5) * x = 14

To isolate "x", we can divide both sides by 7/5:

x = 14 / (7/5)

Simplifying this further, we get:

x = 10

So, the length of the longer piece is 10 cm. And since the shorter piece is 2/5 as long, we can calculate its length:

(2/5) * 10 = 4

Therefore, the length of the shorter piece is 4 cm.

Answer 2

To find the length of the shorter piece, we'll follow these steps:

Step 1: Assign variables

Let's assign the variable "x" to represent the length of the longer piece.

Step 2: Express the relationship

According to the problem, the shorter piece is 2/5 as long as the longer piece. This can be written as:

Shorter piece = (2/5) * Longer piece

Step 3: Determine the length of the longer piece

We know that the total length of the tape is 14 cm. Since the longer piece is x cm, the shorter piece will be (14 - x) cm.

Step 4: Substitute the values

Substituting the expressions from Step 2 and Step 3 into each other, we can solve for x:

(14 - x) = (2/5) * x

Step 5: Solve for x

To solve for x, multiply both sides of the equation by 5:

5(14 - x) = 2x

Distribute 5 to both terms:

70 - 5x = 2x

Combine like terms:

70 = 7x

Divide both sides of the equation by 7:

x = 10

Step 6: Find the length of the shorter piece

To find the length of the shorter piece, substitute the value of x back into (14 - x):

Shorter piece = 14 - 10 = 4 cm

Therefore, the length of the shorter piece is 4 cm.

Answer 3

To find the length of the shorter piece, we need to set up an equation based on the given information.

Let's say the length of the longer piece is x cm. According to the problem, the shorter piece is 2/5 as long as the longer piece. So, the length of the shorter piece is (2/5) * x.

We know that the total length of the tape is 14 cm. Therefore, the sum of the lengths of the two pieces should be equal to 14 cm.

x + (2/5) * x = 14

To simplify the equation, we can multiply the entire equation by the denominator of the fraction, which is 5:

5x + 2x = 14 * 5

Now, we can solve for x:

7x = 70

Divide both sides of the equation by 7:

x = 70 / 7

x = 10

So, the longer piece is 10 cm.

Now, we can find the length of the shorter piece by substituting the value of x back into the expression we derived earlier:

Length of the shorter piece = (2/5) * 10
= 4 cm

Therefore, the length of the shorter piece is 4 cm.

Answer 4

let the longer piece be x cm

then the shorter piece is 14-x cm

14-x = (2/5)x
times 5
70 - 5x = 2x
70 = 7x
x = 10

the long piece is 10 cm, the shorter is 4 cm

check: is 4/10 = 2/5 ? , YES