Solved on Dec 07, 2023

Select the two true equations: $5=\frac{5}{1}$ and $\frac{4}{1}=4$

STEP 1

Assumptions
1. We are given six different equations.
2. We need to determine which of these equations are true.
3. A true equation will have equal values on both sides.

STEP 2

Evaluate equation (1) $5=\frac{5}{1}$ .

STEP 3

Recognize that any number divided by 1 is equal to itself.
$\frac{5}{1} = 5$

STEP 4

Conclude that equation (1) is true because both sides are equal.

STEP 5

Evaluate equation (C) $3=\frac{3}{3}$ .

STEP 6

Recognize that any number divided by itself is equal to 1.
$\frac{3}{3} = 1$

STEP 7

Conclude that equation (C) is not true because the left side is 3 and the right side is 1, which are not equal.

STEP 8

Evaluate equation (c) $2=\frac{1}{2}$ .

STEP 9

Recognize that $\frac{1}{2}$ is one half, which is not equal to 2.

STEP 10

Conclude that equation (c) is not true because the left side is 2 and the right side is $\frac{1}{2}$ , which are not equal.

STEP 11

Evaluate equation (C) $\frac{4}{1}=4$ .

STEP 12

Recognize that any number divided by 1 is equal to itself.
$\frac{4}{1} = 4$

STEP 13

Conclude that equation (C) is true because both sides are equal.

STEP 14

Evaluate equation () $\frac{1}{3}=3$ .

STEP 15

Recognize that $\frac{1}{3}$ is one third, which is not equal to 3.

STEP 16

Conclude that equation () is not true because the left side is $\frac{1}{3}$ and the right side is 3, which are not equal.

STEP 17

Evaluate equation (1) $\frac{4}{4}=4$ .

STEP 18

Recognize that any number divided by itself is equal to 1.
$\frac{4}{4} = 1$

STEP 19

Conclude that equation (1) is not true because the left side is $\frac{4}{4}$ , which equals 1, and the right side is 4, which are not equal.

STEP 20

Identify the two correct equations from the given options.
The two correct equations are:
(1) $5=\frac{5}{1}$
(C) $\frac{4}{1}=4$

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Select the two true equations: 5=515=\frac{5}{1}5=15​ and 41=4\frac{4}{1}=414​=4

STEP 1

Assumptions1. We are given six different equations.2. We need to determine which of these equations are true.3. A true equation will have equal values on both sides.

STEP 2

Evaluate equation (1) 5=515=\frac{5}{1}5=15​.

STEP 3

Recognize that any number divided by 1 is equal to itself.51=5\frac{5}{1} = 515​=5

STEP 4

Conclude that equation (1) is true because both sides are equal.

STEP 5

Evaluate equation (C) 3=333=\frac{3}{3}3=33​.

STEP 6

Recognize that any number divided by itself is equal to 1.33=1\frac{3}{3} = 133​=1

STEP 7

Conclude that equation (C) is not true because the left side is 3 and the right side is 1, which are not equal.

STEP 8

Evaluate equation (c) 2=122=\frac{1}{2}2=21​.

STEP 9

Recognize that 12\frac{1}{2}21​ is one half, which is not equal to 2.

STEP 10

Conclude that equation (c) is not true because the left side is 2 and the right side is 12\frac{1}{2}21​, which are not equal.

STEP 11

Evaluate equation (C) 41=4\frac{4}{1}=414​=4.

STEP 12

Recognize that any number divided by 1 is equal to itself.41=4\frac{4}{1} = 414​=4

STEP 13

Conclude that equation (C) is true because both sides are equal.

STEP 14

Evaluate equation () 13=3\frac{1}{3}=331​=3.

STEP 15

Recognize that 13\frac{1}{3}31​ is one third, which is not equal to 3.

STEP 16

Conclude that equation () is not true because the left side is 13\frac{1}{3}31​ and the right side is 3, which are not equal.

STEP 17

Evaluate equation (1) 44=4\frac{4}{4}=444​=4.

STEP 18

Recognize that any number divided by itself is equal to 1.44=1\frac{4}{4} = 144​=1

STEP 19

Conclude that equation (1) is not true because the left side is 44\frac{4}{4}44​, which equals 1, and the right side is 4, which are not equal.

STEP 20

Identify the two correct equations from the given options.The two correct equations are:(1) 5=515=\frac{5}{1}5=15​(C) 41=4\frac{4}{1}=414​=4

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Select the two true equations: $5=\frac{5}{1}$ and $\frac{4}{1}=4$

Assumptions
1. We are given six different equations.
2. We need to determine which of these equations are true.
3. A true equation will have equal values on both sides.

Evaluate equation (1) $5=\frac{5}{1}$ .

Recognize that any number divided by 1 is equal to itself.
$\frac{5}{1} = 5$

Evaluate equation (C) $3=\frac{3}{3}$ .

Recognize that any number divided by itself is equal to 1.
$\frac{3}{3} = 1$

Evaluate equation (c) $2=\frac{1}{2}$ .

Recognize that $\frac{1}{2}$ is one half, which is not equal to 2.

Conclude that equation (c) is not true because the left side is 2 and the right side is $\frac{1}{2}$ , which are not equal.

Evaluate equation (C) $\frac{4}{1}=4$ .

Recognize that any number divided by 1 is equal to itself.
$\frac{4}{1} = 4$

Evaluate equation () $\frac{1}{3}=3$ .

Recognize that $\frac{1}{3}$ is one third, which is not equal to 3.

Conclude that equation () is not true because the left side is $\frac{1}{3}$ and the right side is 3, which are not equal.

Evaluate equation (1) $\frac{4}{4}=4$ .

Recognize that any number divided by itself is equal to 1.
$\frac{4}{4} = 1$

Conclude that equation (1) is not true because the left side is $\frac{4}{4}$ , which equals 1, and the right side is 4, which are not equal.

Identify the two correct equations from the given options.
The two correct equations are:
(1) $5=\frac{5}{1}$
(C) $\frac{4}{1}=4$