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**Multiplication By Clever Form Of 1**: At a Glance

- Topics At a Glance
- Different Types of Numbers
- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
**Comparing Fractions**- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
**Multiplication by Clever Form of 1**- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
- Things to Do with Real Numbers
- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

This super handy trick lets you simplify an expression without changing its value. Which is good, because fractions should not be subject to inflation.

**Sample Problem**

Here's a horrible fraction. A *really* horrible fraction. This thing is getting coal for Christmas.

If we multiply it by 1, we won't change its value. If we multiply it by anything *equivalent* to 1 (such as ) we also won't change its value. Since each of our two mini-fractions has a 3 in its denominator, what happens if we multiply the whole thing by ?

Our new numerator is , and our new denominator is . Now the fraction's value hasn't changed, it looks much more manageable, and it might even get an Xbox under the tree this year.

We can also use this trick to rewrite decimal division problems...

3.4/7.8 x 10/10 = 34/78

...or when we have a division problem written as a fraction.

Example 1

1.52/3.1 x (10/10) = |

Exercise 1

Find the cleverly disguised form of 1 that will let you simplify the rotten fractions below, then simplify. And quickly, please - it hurts our eyes just to look at them.

Exercise 2

Find the cleverly disguised form of 1 that will let you simplify the rotten fractions below, then simplify. And quickly, please - it hurts our eyes just to look at them.