Explanation

Explanation

Explanation

To find the fraction midway between 1/5 and 1/7, let's find their average:

Midpoint = ((1/5) + (1/7)) / 2

First, find the common denominator for 5 and 7, which is 35:

(1/5) = 7/35

(1/7) = 5/35

Now, find the average:

Midpoint = ((7/35) + (5/35)) / 2

= (12/35) / 2

= 12/70

= 6/35

Explanation

Explanation

Let's denote the unknown number as x.

Given that 3/4 of 28 is equal to 21/5 of x:

(3/4) * 28 = (21/5) * x

First, calculate 3/4 of 28:

(3/4) * 28 = 21

Now, equate this to 21/5 of x:

21 = (21/5) * x

Multiply both sides by 5:

105 = 21x

Divide both sides by 21:

x = 105 / 21

x = 5

Explanation

The numbers whose squares end with 6 are those ending in 4 or 6.

Let's find the first two perfect squares that end with 6:

1. 4^2 = 16

2. 6^2 = 36

The difference between these two perfect squares is:

36 - 16 = 20

Explanation

A number is a perfect square (or a square number) if its square root is an integer;

that is to say, it is the product of an integer with itself.

Here, the square root of 513 is about 22.650.

Explanation

The product of two numbers is equal to the product of their LCM and HCF.

Given:

Product = 330

HCF = 11

Let's denote the LCM as x:

330 = 11 * x

Divide both sides by 11:

x = 330 / 11

x = 30

Explanation

To find the L.C.M. of 12, 20, 24, and 32, we follow prime factorization:

12 = 2² × 3

20 = 2² × 5

24 = 2³ × 3

32 = 2⁵

Take the highest powers of all prime factors:

2⁵ (from 32)

3 (from 12 or 24)

5 (from 20)

Now multiply:

2⁵ × 3 × 5 = 32 × 3 × 5 = 96 × 5 = 480

Explanation

Prime Factorization

1050 = 2 × 3 × 5 × 5 × 7

750 = 2 x 3 x 5 x 5 x 5

Common Factor = 2 x 3 x 5 x 5 = 150

Greatest Common Factor (GCF) = 150