Find the area of the circle. *<br> 5 cm

harkovskaia [24]

$\boxed{\boxed{ \ \frac{9}{16} + \frac{1}{2} = \frac{17}{16} = 1\frac{1}{16} \ }}$

<h3>Further explanation</h3>

We will work on adding two fractions correctly with different denominators. The two denominators must be equated first.

In order to add these fractions, we need finding the common denominator by multiplying both denominators together.

$\boxed{\frac{9}{16} + \frac{1}{2} = \ ?}$

Both denominators, 16 and 2, are multiplied by one another. What about numerators? Pay attention to the treatment of each fraction.

$\boxed{= \big( \frac{9}{16} \times \frac{2}{2} \big) + \big( \frac{1}{2} \times \frac{16}{16} \big)}$

$\boxed{= \frac{18}{32} + \frac{16}{32}}$

$\boxed{= \frac{34}{32}}$

Let's take a break here to think.

Alternatively, develop a sharper method as below.

$\boxed{= \frac{(9 \times 2) + (16 \times 1)}{16 \times 2}}$

Note how this is performed. Absolutely indeed, cross-multiplication!

$\boxed{= \frac{18 + 16}{32}}$

$\boxed{= \frac{34}{32}}$

The numerator and denominator are divided by two to make it a simple fraction. After that, we simplify again into mixed fractions.

$\boxed{\boxed{ \ \frac{9}{16} + \frac{1}{2} = \frac{17}{16} = 1\frac{1}{16} \ }}$

Gently let's take a break once more to think strategically.

Observing the steps above, we still find a large number when there is a direct multiplication of the two denominators. Are there more highly recommended steps? Of course there is!

$\boxed{\frac{9}{16} + \frac{1}{2} = \ ?}$

The denominators 2 and 16 have LCM = 16. So, we convert the given fractions into equivalent fractions with denominator 16.

$\boxed{= \big( \frac{9}{16} \times \frac{1}{1} \big) + \big( \frac{1}{2} \times \frac{8}{8} \big)}$

$\boxed{= \frac{9}{16} + \frac{8}{16}}$

$\boxed{= \frac{17}{16}}$

Do not forget simplifying again into mixed fractions.

$\boxed{\boxed{ \ \frac{9}{16} + \frac{1}{2} = \frac{17}{16} = 1\frac{1}{16} \ }}$

In the form of fractions, the steps that must be considered are

equate the denominator,
simplify fractions, and
for the final answer, convert fractions to mixed fractions or decimal forms

<h3>Learn more</h3>

How do I solve brainly.com/question/1682776
90 is ¹/₁₀ of _________? brainly.com/question/96882
Investigating the stages of solving a word problem about one variable linear equations brainly.com/question/2038876

Keywords: add and simplify 9/16 + 1/2 =, solve, 2/7m - 1/7 = 3/14, operations, multiply, divide, fraction, equate, common denominator, numerator, both, LCM, alternative, different, method, way, steps, simple, mixed, convert, equivalent, cross-multiplication

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3 years ago

A has the coordinates (-4,3) and B has the coordinates (4,4). If Do1/2 (x,y) is a dialation of ABC, what is true about the image

coldgirl [10]

The answer is e c and a I took the test

4 0

3 years ago

The train has 240 seats.

skelet666 [1.2K]

1/3 because 80/240 is the fraction for the red seats and if you could put that in simplest form it would be 1/3

5 0

3 years ago

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In the first quadrant you start at (3,7) and move 3 units down what point will you end up with

blagie [28]

Answer:

(3, -3)

Step-by-step explanation:

6 0

3 years ago

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The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?

attashe74 [19]

Yes, this is a typical pythagorean triad.

Since the theorem is: $c^{2} = a^{2} + b^{2}$
And by inspection, $5^{2}$ would be the hypotenuse,
$5^{2} = 3^{2} + 4^{2}$
25 = 9 + 16
RHS = 9 + 16 = 25 = LHS
Therefore, we have proved that the values fit into pythagoras' theorem, which means that the triangle is a right triangle (that is the central idea of this theorem).

3 0

3 years ago

Find the area of the circle. * 5 cm