On the subject of Arithmetic

I need a clearer explanation of multiplying by fractions and other material covered in quizzes "Arithmetic Tricks" and "Arithmetic Tricks II" from the course "Algebra Fundamentals". I really find it difficult to understand and recall the tricks.

Here's what I can remember and explain: $47 + 53 = 50 + 50 = 100$

And I need a clearer explanation of how this one works: $\frac {1}{2} \times \frac {2}{3} \times \frac {3}{4} = \frac {1}{4}$ because the 2s on the numerator and denominator make a pair and cancel, the same phenomenon is displayed with the 3s.

Everything else is lost to me.

#Algebra

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

@Dylan Daniel, I noticed that you are a new member. I suggest you learn $\LaTeX$ .

Note: If you do not know where to start you can refer to my set: $\LaTeX$ Help

P.S. I am also a 4th grader

Mohammad Farhat - 2 years, 8 months ago

I already have a tab open for LATEX, so I know how to use it. Thanks, though.

Dylan Daniel - 2 years, 7 months ago

Take the case of $47 + 53$ . Take one 3 from 53 and give it to 47. We always try to convert numbers into multiples of 10 as it will easier to count in this case.

$53 - 3 + 47 + 3 = 50 + 50 = 100$

Simple !!! ☺️☺️☺️

Ram Mohith - 2 years, 8 months ago

Actually, expand $\displaystyle \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} = 1 \div 2 \times 2 \div 3 \times 3 \div 4$ Since $\displaystyle 2 \div 2 = 1; 3 \div 3 = 1$ , we are left with $1 \div 4$ which is the answer.

Mohammad Farhat - 2 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$